DE102011078849B4 - Determining excitation parameters for parallel MR imaging using elements of a k-space covariance matrix for signal noise in k-space data - Google Patents

Abstract

In a method and a device for determining excitation parameters, in particular for determining an excitation profile, for MR imaging, elements of a k-space covariance matrix for signal noise in k-space data, which in a data acquisition on an examination subject with the plurality of receive channels be detected. For several voxels of the examination subject, computationally elements of at least one image space covariance matrix are determined as a function of the k-space covariance matrix. The excitation parameters (41) are determined as a function of the determined elements of the at least one image space covariance matrix.

Description

The invention relates to a method and a device for determining excitation parameters for MR imaging. More particularly, the invention relates to a method and apparatus for MR data acquisition that allows the generation of spatially varying excitation profiles using multiple transmit channels.

MR imaging is now widely used because it allows the acquisition of two-dimensional or three-dimensional image data that can image structures inside a high-resolution object. In MR imaging, the nuclear spins of hydrogen nuclei in the examination subject are aligned in a main magnetic field (B ₀ ) and then excited by the irradiation of RF (radio-frequency) pulses. The excited magnetization is detected, whereby a spatial coding is achieved by various known methods.

Parallel data acquisition with multiple receive coils can reduce the time required for data collection. However, such data acquisition may result in degradation of the signal-to-noise ratio. For example, it is not possible to separate signal contributions from different voxels in the k-space data acquired with the plurality of receive channels. The resulting degradation of the signal-to-noise ratio is often quantified by a location-dependent geometry factor (g-factor).

In addition to a parallel data acquisition with multiple receiving coils, a parallel excitation ("parallel transmit") with multiple transmit channels can be carried out in MR imaging. The plurality of transmission channels may be a plurality of transmitting coils, which are controlled in each controlled so that a desired spatially varying excitation profile is formed. For parallel excitation and parallel data recording the same coils or coil segments can be used, which are coupled via a transmitting / receiving pair each with both a transmission path for an excitation and with a reception path for data acquisition.

Examples of MR imaging using multiple transmit channels for excitation and multiple receive channels for data acquisition are described in Lawrence L. Wald, Elfar Adalsteinsson: "Parallel Transmit Technology for High Field MRI", MAGNETOM Flash 1/2009, pp. 124-135 (2009), Siemens AG, Erlangen, Germany, and Andrew G. Webb, Christopher M. Collins, "Parallel Transmit and Receive Technology in High Field Magnetic Resonance Neuroimaging," International Journal of Imaging Systems and Technology - Special Issue to Neuroimaging, Vol 20, 2-13 (2010), Wiley, New York, USA.

The US Pat. No. 7,336,145 B1 and the DE 10 2009 016 341 A1 describe in each case methods in which an excitation for a magnetic resonance imaging is determined in order to achieve a specific target magnetization. The US Pat. No. 7,336,145 B1 uses the least squares method to determine appropriate excitation pulses to achieve a desired transverse magnetization. The DE 10 2008 061 455 A1 and the DE 10 2008 015 054 B3 describe further examples of methods in which a target magnetization is set in a targeted manner.

D. Mitsouras et al., "Strategies for Inner Volume 3D almost echoing magnetic resonance imaging using non-selective refocusing radio frequency pulses", Med. Phys. 33 (2006), p. 173-186 describes "Fast Spin Echo" (FSE) methods in which an improved signal-to-noise ratio is achieved by selective excitation.

Lin H. Lin et al., "Parallel MRI reconstruction using variance partitioning regularization", Magn. Reson. Med. 58 (2007), pp. 735-744 describes a regularization method for processing data obtained in MR imaging.

Y. Ding et al., "Accurate Noise Level and Noise Covariance Matrix Assessment in Phased Array Coil Without a Noise Scan", Proc. Int. Soc. Magn. Reson. Med. 2010, no. 648 describes a method with which a covariance matrix of the k-space noise can be obtained from the k-space data during image acquisition and without separate data acquisition.

The parallel excitation to generate a spatially varying excitation profile in more than one dimension can be used to at least partially reduce the degradation in signal-to-noise ratio that occurs in multi-channel data acquisition. For example, by limiting the excitation to the region of interest of the subject of interest (RoI), it would be possible to reduce signal degradation due to correlated noise from voxels outside the RoI. However, to achieve such excitation localization, it may be necessary to use long excitation pulses and / or high excitation power. This is undesirable.

It is the object of the invention to provide a method and a device with which the excitation parameter, in particular an excitation profile, for MR imaging can be determined so that the signal-to-noise ratio for voxels of the RoI can be improved ,

In particular, it is an object of the invention to provide such a method and apparatus which does not require complete suppression of the excitation signal outside the RoI.

A method, a device, an MR system and a computer program having the features defined in the independent claims are specified. The dependent claims define embodiments.

According to one aspect of the invention, there is provided a method of determining excitation parameters for MR imaging in which a parallel excitation with multiple transmit channels and a parallel data acquisition with multiple receive channels occurs. In the method, elements of a k-space covariance matrix for signal noise in k-space data acquired during a data acquisition on an examination object with the plurality of reception channels are determined. For several voxels of the examination subject, computationally elements of at least one image space covariance matrix are determined as a function of the k-space covariance matrix. The excitation parameters are determined as a function of the determined elements of the at least one image space covariance matrix.

The excitation parameters that are determined may correspond to or influence an excitation profile. The elements of the image space covariance matrix that are detected may be diagonal or extra-diagonal elements of the image space covariance matrix for voxels in the RoI. All elements of the image space covariance matrix can also be determined.

In the method, excitation parameters that represent or influence an excitation profile for MR imaging are determined systematically as a function of a covariance between voxels of the examination subject. As a result, excitation parameters can be selected in such a way that the local geometry factor for voxels in a RoI is reduced.

The method takes into account that a differentiation between voxels is possible with parallel data acquisition by the different receiving coils and their respective location-dependent sensitivity. This possibility is taken into account by the covariance matrix in k-space or in space, which is characteristic for the respective coil arrangement and the respectively examined section of the examination subject. The selection of an excitation profile as a function of the image space covariance matrix takes into account that the signal of all points outside the RoI need not be suppressed for the respective coil arrangement, and permits the systematic identification of a suitable excitation profile.

In the method, the k-space covariance matrix may be determined based on the data obtained in a data acquisition using an excitation profile that is homogeneous in the sense that it does not vary significantly within an excited layer. A homogeneous excitation profile can be used to determine the k-space covariance matrix, in which relative fluctuations of the amplitude in a layer are smaller than a threshold value.

The excitation parameters may represent or influence known information prior to MR data acquisition, on which the image space covariance matrix depends. The excitation parameters can be determined such that the elements of the image space covariance matrix satisfy a predetermined condition.

The information known before MR data acquisition is also referred to as prior information since it is known in advance ("prior"). In any case, if the excitation parameters represent or specify a spatially varying excitation profile, zeros of the spatially varying signal amplitude are prior information. For example, it is known in advance that voxels in which no excitation occurs do not provide a signal contribution. In this way, the influence of the excitation parameters on the image space covariance matrix can be systematically taken into account.

The elements of the image space covariance matrix that are detected may include at least diagonal elements of the image space covariance matrix corresponding to voxels from the RoI. The elements of the image space covariance matrix that are detected may alternatively or additionally include extradiagonal elements of the image space covariance matrix indicating covariances between a voxel in the RoI and voxels outside the RoI.

To define the excitation parameters, covariances of the prior information can be determined such that geometry factors for voxels in a RoI of the examination object fulfill a predetermined condition. In this way, covariances of the prior information can first be systematically determined such that the image space covariance matrix fulfills a desired condition. The covariances of the prior information can then be used to draw conclusions about an excitation profile to be used.

umfassen, wobei C₀ die Kovarianzmatrix der Prior-Informationen, E die Codiermatrix, C die k-Raum-Kovarianzmatrix, D_ρ eine Bildraum-Kovarianzmatrix, deren Elemente die vorgegebene Bedingung erfüllen, und I eine Einheitsmatrix bezeichnet. Dies erlaubt eine systematische Ermittlung der Matrix C₀. Aus der Matrix C₀ kann auf ein geeignetes Anregungsprofil geschlossen werden. Insbesondere kann durch rechnerische Ermittlung von C₀ systematisch ermittelt werden, an welchen Voxeln eine Anregung unterdrückt werden muss, um unter Berücksichtigung der räumlichen Selektivität der Empfangsspulen Rauschen in den resultierenden Bilddaten für die RoI zu unterdrücken. Es kann auch ermittelt werden, in welchen Voxeln keine Unterdrückung der Signalamplitude erforderlich ist. Dadurch werden die Anforderungen an das Anregungsprofil reduziert.For setting the excitation parameters, a covariance matrix of the prior information can be determined for which the elements of the image space covariance matrix satisfy the predetermined condition. Determining the covariance matrix of the prior information may involve solving the equation

where C ₀ denotes the covariance matrix of the prior information, E the coding matrix, C the k-space covariance matrix, D _ρ a picture space covariance matrix whose elements satisfy the given condition, and I denotes a unit matrix. This allows a systematic determination of the matrix C ₀ . From the matrix C ₀ can be concluded that a suitable excitation profile. In particular, it can be systematically determined by computational determination of C ₀ on which voxels an excitation must be suppressed in order to suppress noise in the resulting image data for the RoI, taking into account the spatial selectivity of the receiver coils. It can also be determined in which voxels no suppression of the signal amplitude is required. This reduces the requirements for the excitation profile.

The covariances of the prior information can be determined in an iterative procedure. As a result, the excitation parameters can be determined in a systematic method.

The covariances of the prior information can be determined automatically under compulsory conditions. It can thereby be taken into account that even with a plurality of excitation coils not every arbitrary covariance matrix of signal amplitudes can be realized. Typically, it is z. For example, it is possible to suppress diagonal elements of such a covariance matrix of the prior information, while an immediate control of the extradiagonal elements is impossible or only possible with difficulty.

In the method, the elements of the image space covariance matrix, which are assigned to the corresponding set of excitation parameters, can be computationally determined for a plurality of sets of the excitation parameters. The excitation parameters for the MR imaging can be determined as a function of the elements of the image space covariance matrix respectively determined for the several sets of the excitation parameters. For example, a weighting function can be defined, which is determined depending on the determined elements of the image space covariance matrix. The set of excitation parameters for the subsequent MR imaging for which the evaluation function is extremal can be defined. The evaluation can be made under the constraint that the amplitude of the excitation profile in the RoI is not suppressed.

The multiple sets of excitation parameters may correspond to multiple excitation profiles. For example, the excitation profile may be sinusoidally or cosinusoidally modulated as a function of location. The tested excitation profiles can be chosen under additional conditions. For example, only excitation profiles can be selected for evaluation that have no zero in the RoI. Alternatively or additionally, excitation profiles can be evaluated which have a maximum in RoI.

In the method, extra-diagonal elements of the at least one image space covariance matrix can be determined and voxels of the examination object can be determined therefrom whose correlation with voxels in a RoI of the examination object exceeds a threshold value. In this way it can be determined directly from the image space covariance matrix in a heuristic manner which voxels are to be suppressed.

The excitation parameters can be determined such that one of diagonal elements of the image space covariance matrix, which correspond to voxels in a RoI of the examination subject, is minimized. For example, for several excitation profile the size Tr (RC _ρ R ^† ) (2) evaluated and minimized, where Tr denotes the track operator, C _ρ the image space covariance matrix for the respective excitation profile and R a projection operator for the RoI. The magnitude represents the sum of the standard deviations of the signals for voxels in the RoI. By minimizing this size, an excitation profile is determined for which signal noise in the RoI is reduced compared to a homogeneous excitation profile.

The determined elements of the k-space covariance matrix may include covariances of k-space data acquired with different take-up coils. In this way, correlations between the k-space data acquired with different pickup coils are taken into account in determining an excitation profile.

With the method, an excitation profile for MR imaging for measuring echo-time-dependent quantities, in particular for a multi-echo imaging sequence, can be determined. In such applications, spatial variations of the flip angle are less critical to the spins within the RoI than in other applications that require a substantially constant flip angle in the RoI to avoid excessive contrast variations. Thus, in applications for determining echo-time dependent quantities, for example T ₂ * measurements, there is greater freedom in choosing an excitation profile. This facilitates the selection of an excitation profile with the aim of reducing noise in image space data for the RoI.

The excitation parameters can be determined such that different portions of the acquired MR image are suppressed for different echo times.

According to a further aspect, an apparatus for determining excitation parameters for MR imaging, in which a parallel excitation with a plurality of transmit channels and a parallel data acquisition with a plurality of receive channels, is specified. The device comprises an interface for receiving k-space data acquired in a data acquisition on an examination object with the plurality of reception channels and an electronic computing device. The electronic computing device is set up to determine elements of a k-space covariance matrix for signal noise in the k-space data acquired with the plurality of reception channels. The computing device is furthermore designed to computationally determine elements of at least one image space covariance matrix as a function of the k-space covariance matrix for a plurality of voxels of the examination subject. The computing device is further configured to automatically set the excitation parameters as a function of the determined elements of the at least one image space covariance matrix.

With such a device, taking into account correlations in the reconstructed image data, an excitation profile can be systematically determined with which signal noise in image data for the RoI is reduced. The excitation profile can be optimized under the constraint that there should be no significant suppression of the excitation in the RoI.

The apparatus may be adapted to carry out the method according to one aspect or embodiment.

According to a further aspect, a magnetic resonance system for MR imaging is specified. The magnetic resonance system comprises an excitation device with a plurality of transmission channels, which is set up for the controllable generation of a spatially variable excitation profile. The magnetic resonance system further comprises a receiving device with a plurality of receiving channels for MR data acquisition after an excitation. The magnetic resonance system also includes a device coupled to the excitation device according to an exemplary embodiment, in order to define an excitation profile and to control the excitation device accordingly.

The exciter may include a plurality of separate coils or segments of a coil array. The receiving device may include a plurality of separate coils or segments of a coil array. The coils or the coil array can be used both by the excitation device and by the detection device, with corresponding transceiver switches being provided.

According to a further aspect, a computer program is specified which can be loaded directly into a memory of a programmable device of a magnetic resonance system, the computer program comprising a sequence of control commands which, when executed by the device of the magnetic resonance system, the device for carrying out the method according to one aspect or exemplary embodiment cause. The computer program may be stored on a non-transient medium.

Methods and devices according to embodiments can be used in particular for MR imaging, in which a uniform flip angle of the spins in the RoI is not absolutely necessary, for example, to create a T ₂ * card. The embodiments are not limited to this application.

Embodiments of the invention are explained below with reference to the drawings.

1 is a schematic representation of an MR system with a device for determining an excitation profile.

2 is a schematic representation of image data.

3 is a schematic representation of a determined excitation profile.

4 is a flowchart of a method according to an embodiment.

5 is a flowchart of a method according to another embodiment.

6 is a flowchart of a method according to another embodiment.

While reference is made in the following description for explanation in part to certain MR imaging sequences, for example for determining T ₂ * times, it is also possible to use sequences other than those mentioned.

1 schematically shows a magnetic resonance (MR) system 1 , The MR system 1 has a magnet 10 for generating a polarization field B0. An examination object 11 can on a lounger 13 relative to the magnet 10 be moved. The MR system 1 has a gradient system 14 for generating magnetic field gradients used for imaging and spatial encoding. A gradient unit 17 is for controlling the gradient system 14 intended.

To excite the magnetic polarization generated in the B0 field is a radio frequency (RF) coil arrangement 15 provided, the multiple excitation coils 15a and 15b which can generate a high frequency field. At the excitation coils 15a and 15b it does not have to be separate coils. Rather, these may for example be formed as segments of a coil array. For driving the RF coil assembly is an RF unit 16 intended. The RF unit 16 is configured such that the RF coil assembly 15 is controllable so that selectively different excitation profiles can be generated. For this purpose, the RF unit several control paths 16a . 16b each of which has one of the excitation coils 15a . 15b assigned. While for clarity in 1 along the axial direction offset excitation coils 15a and 15b are shown, the plurality of excitation coils of the RF coil assembly may also have a different arrangement. In particular, the different excitation coils or segments of a coil array of the RF coil arrangement can be arranged circumferentially along a cylindrical surface in order to realize different excitation profiles within a slice of the examination subject. Arrangements which can be used in embodiments are described in Lawrence L. Wald, Elfar Adalsteinsson: "Parallel Transmission Technology for High Field MRI", MAGNETOM Flash 1/2009, p. 124-135 (2009), Siemens AG, Erlangen, Germany and the proofs mentioned there.

The recording of MR signals from an examination area 12 can be done by means of a coil arrangement. The MR system 1 includes several receiver coils 22 . 23 for detecting MR signals and corresponding receiver circuits 24 . 25 , The receiver coils may each be local receiver coils or component coils. These may be part of a larger coil array (eg, phased array coils) that may include additional receiver coils.

While in 1 for explanation, separate excitation coils 15a . 15b and receiver coils 22 . 23 are shown, the same coils or segments of a component coil can be used for both excitation and for data acquisition. In this case, for example, both the receiver circuit 24 as well as the control path 16b via a transmitting / receiving switch with the coil 22 be coupled. Upon excitation, the corresponding coil of the associated control path of the RF unit 16 controlled so that a desired excitation occurs. During data acquisition, the signal detected by the coil is conducted via the transmitting / receiving switch to the corresponding receiver circuit in order to be further processed there.

The MR system 1 becomes central to a control unit 18 controlled. The control unit 18 controls the injection of RF pulses and the acquisition of resulting MR signals. A reconstruction of image data from the MR raw data and a further processing of the image data takes place in a computing device 19 , The raw data can be sent via a suitable interface 26 For example, a bus to the computing device 19 to be provided. While the control unit 18 and the computing device 19 in 1 are shown schematically as separate elements, a single computer can perform both functions. Via an input unit 20 For example, an operator may select different protocols and enter and modify data collection parameters displayed on a display 21 are displayed. For example, the operator may select a region of interest ("RoI") of the examination subject for which signal noise is to be reduced.

The control unit 18 and the computing device 19 are set up to determine an excitation profile in an MR data acquisition, that of the excitation coils 15a . 15b is produced. The excitation profile can be selected such that, within a slice of the examination object, excitation of the nuclear spins takes place spatially selectively. As will be described in more detail, the excitation profile is systematically determined so that a signal-to-noise ratio for voxels in the RoI is reduced compared to a homogeneous excitation. The selection of the excitation profile may be such that no reduction in the signal for these voxels accompanies the reduction of the noise for voxels of the RoI. The determination of the excitation profile is done systematically in dependence on a noise covariance matrix, the covariances of signal noise in k-space in the of the multiple receiver coils 22 . 23 represented at a first MR data acquisition detected signals. In this way, when determining the excitation profile, it can be systematically taken into account that the different spatial selectivity of the receiver coils makes it possible to distinguish signals from different voxels to a certain extent. Thus, with parallel data acquisition, it is not necessary to completely suppress the excitation signal anywhere outside the RoI in order to achieve image data with reduced noise in the RoI.

As will also be described in more detail below, to determine the excitation profile as a function of the k-space covariance matrix, it is possible to take into account constraints imposed by the plurality of excitation coils 15a . 15b be imposed.

The first MR data acquisition, which can be performed with a homogeneous excitation and serves to determine the k-space covariance matrix, can be carried out such that the resulting data have a lower resolution than the subsequent MR data acquisition using the excitation profile. In this way, the arithmetic effort in determining the excitation profile can be kept moderate.

The MR data acquisition using homogeneous excitation can also be carried out in a shorter time than the subsequent higher-resolution MR data acquisition.

The control unit 18 is designed to be dependent on one of the computing device 19 determined excitation profile controls the MR system for performing the MR data acquisition. This is the RF unit 16 so controlled that the excitation coils 15a . 15b generate the desired excitation profile. The MR data acquisition can be done using a variety of different sequences. For example, the control unit 18 control the plant according to a turbo spin echo or MGRE sequence. The echo sequence can be part of an EPI sequence in which all k-space lines are scanned within a repetition time, ie in which a complete image data record is recorded after excitation. It is also possible to use segmented EPI sequences with which a part of the k-space is scanned with an echo train. An EPI sequence may be gradient echo or spin echo-based. The resulting image data can be assigned an equivalent echo time. In particular, the control can be such that a multi-echo sequence, such. MGRE, which generates a sequence of gradient echoes by repeatedly switching gradients. With an echo train can each a k-space line are sampled, each echo corresponding to a different echo time. From the echo trains for the scanned k-space lines can then for each echo time and each receiver coil 22 . 23 an image data set to be reconstructed.

The MR system 1 may be arranged to perform accelerated imaging, for example, a partial parallel acquisition (ppa) such as SENSE, GRAPPA or SMASH. It can control unit 18 be set up so that by omitting k-space lines make only an incomplete scan of k-space, but the recording of MR signals simultaneously with the receiver coils 22 and 23 and possibly further coils. Depending on the method, a reconstruction of the missing data can then take place in k-space or in image space. The control unit 18 may be arranged to perform the "k-TE Generalized Autocalibrating Partially Parallel Acquisition (GRAPPA) for Accelerated Multiple Gradient-Recalled Echo (MGRE) R ₂ * Mapping in the Abdomen", by Xiaoming Yin et al., Magnetic Resonance in Medicine 61 : 507-516 (2009) to perform the k-TE-GRAPPA method. k-TE-GRAPPA uses an MGRE acquisition sequence in which peripheral areas of k-space are scanned incompletely. Skipped k-space lines are reconstructed not only using adjacent k-space lines acquired with adjacent receive coils of a coil array, but also using k-space lines for adjacent echo times. The result is complete image data sets for the different echo times and for each of the receiver coils used.

The image reconstruction of the image data may be from computing device 19 be carried out by conventional reconstruction method for the respective acquisition sequence. By determining the excitation profile as a function of the k-space covariance matrix in k-space signals in the first MR data acquisition, the resulting image data in the RoI have an improved signal-to-noise ratio.

The operation of the computing device 19 in determining the excitation profile will be described below with reference to 2 - 6 described in more detail.

2 is a schematic representation of image data 31 representing a slice of the examination subject. In many applications, only a specific image area is the RoI 32 , of interest to imaging. In particular, a worse signal-to-noise ratio is outside the RoI 32 tolerable while for the RoI 32 the best possible signal-to-noise ratio should be achieved.

The noise for voxels in the ROI 32 could be reduced by only within the ROI 32 an excitation of spins occurs in MR data acquisition. However, this is often not possible for a given arrangement with multiple excitation coils, or only with long pulse durations and / or high pulse intensity, which are undesirable for various reasons.

With devices and methods according to exemplary embodiments, those voxels are systematically dependent on covariances of the signal noise detected in a first MR data acquisition 33 which should be suppressed to obtain a better signal-to-noise ratio in the RoI. The signal suppression for the voxels 33 This can be done by the excitation profile at the voxels 33 is suppressed. The excitation profile can be selective for voxels outside the RoI 32 be suppressed to attenuate the signal for voxels of RoI 32 to avoid.

3 is a schematic representation of an exemplary excitation profile 41 , which is determined with devices and methods according to embodiments. The amplitude of the RF excitation pulse is a function of the location along a line 34 the image data in 2 shown.

In an area that is the RoI 32 corresponds, the excitation profile has a relatively large amplitude 42 on. The excitation of the voxels, the RoI 32 can be chosen as large as possible. Depending on the application, the excitation profile may be chosen such that the relative or absolute variation of the amplitude in the RoI is less than a threshold value. However, this may not be necessary depending on the application. For example, in the measurement of echo-time-dependent quantities, larger fluctuations in the amplitude of the excitation profile within the RoI can be tolerated.

The excitation profile is chosen so that the amplitude in areas 43 . 44 is suppressed, which correspond to voxels that are outside the RoI and significantly increase the signal noise for image data in the RoI. The amplitude of the excitation profile in the areas 43 . 44 is chosen so that it can be significantly smaller than the amplitude of the excitation profile in the RoI.

With methods and devices, the influence of different excitation profiles on a signal noise of the image data in the RoI can be determined in advance by calculation. A quantitative assessment of different excitation profiles can be made. In this way, an excitation profile can be determined for which the signal-to-noise ratio of the voxels in the RoI is greater than a predetermined threshold value. Alternatively, an excitation profile can be determined under a given class of possible excitation profiles for which the noise of the image data in the RoI is minimized under the constraint that the signal for voxels of the RoI is not reduced.

By computationally determining the influence of different excitation profiles on the noise in the RoI in the image data, it is also possible to determine those voxels which have only a small influence on the noise in voxels of the RoI in the image data. Thus, voxels can be detected that only slightly influence the signal noise in the RoI in the image data. The knowledge of these voxels gives greater freedom in choosing a suitable excitation profile. In particular, excitation profiles can be selected which have an amplitude at the voxels which are only weakly correlated with voxels in the RoI, which does not necessarily have to be suppressed and can even be comparable to the amplitude for voxels in the RoI. This loosens the requirements for possible excitation profiles compared to a step function.

Various methods by which an excitation profile can be determined so that the signal-to-noise ratio for voxels of the RoI can be improved are described in more detail below. With such methods, the local geometry factor in the RoI can thus be reduced. The methods can be used by the computing device 19 the MR system 1 be performed.

The covariance matrix of image data can be generally represented as

Here, C _ρ denotes the image space covariance matrix, E the coding matrix, C the k-space covariance matrix, C ₀ a covariance matrix for previously known information, and I a unit matrix. In conventional notation, the superscript dagger designates the adjoint of the corresponding matrix, ie the transpose of the complex conjugate matrix.

In methods and devices according to embodiments, based on equation (3), which establishes a relationship between covariances C of k-space data and covariances C _ρ acquired in a first MR data acquisition C _ρ image data, it can be determined for which excitation profile noise for voxels, which are in the RoI, can be reduced. The determination of the corresponding excitation profile can be done in various ways, as with reference to 4 - 6 will be described in more detail.

If M denotes the number of pixels, K the number of k-space points detected with each of the receiver coils, and L the number of receiver coils, then the image space covariance matrix C _{ρ is} an M × M matrix. The k-space covariance matrix C is an NxN matrix, where N = K * L is the total number of k-space points sampled with the L receiver coils. The matrix C ₀ and the matrix I in equation (3) are M × M matrices.

sein, wobei S die so genannte Auswahlmatrix ist, die nur die tatsächlich abgetasteten k-Raum-Punkte auswählt, FFT eine Fourier-Transformations-Matrix ist, die die Abbildung vom Ortsraum in den k-Raum definiert, und [B – / 1 ] eine der jeweiligen Spule zugeordnete Matrix ist, deren Hauptdiagonalelemente gleich der Sensitivität der entsprechenden Spule am jeweiligen Voxel sind und deren Außerdiagonalelemente alle gleich 0 sind.The coding matrix E is the matrix which maps the amplitude of a signal present in the MR data acquisition in the spatial domain into a vector of k-space data with N elements which would be detected in the noise-free case. General is d → = Eρ → + n →, (4) where d → is a column vector with N elements, in which the detected k-space signals are combined, where ρ → is a column vector with M elements, which represents the amplitude of the spin signal in the space space, and where n → a column vector with N elements is that represents signal noise. The coding matrix E is thus an N × M matrix which defines a mapping of the amplitude from the spatial domain into the k-space signals detected by the multiple receiver coils. The coding matrix E may have different shapes depending on the pulse sequence and the sampling used. For example, can

where S is the so-called selection matrix which selects only the actually scanned k-space points, FFT is a Fourier transform matrix defining the mapping from the space of space into k-space, and [B - / 1 ] is a matrix associated with the respective coil whose main diagonal elements are equal to the sensitivity of the corresponding coil at the respective voxel and whose extradiagonal elements are all equal to 0.

wobei in dem Vektor d →_{Spule l} mit K Elementen jeweils die k-Raum-Daten zusammengefasst sind, die mit der l-ten Spule abgetastet werden.For a coding matrix of the form given in equation (5), the column vector of detected k-space data may be represented as

wherein in the vector d → _{coil l} with K elements in each case the k-space data are combined, which are scanned with the l-th coil.

The matrix C in equation (3) represents the covariance matrix for signal noise in k-space. The matrix can be estimated from the k-space data obtained in a first MR data acquisition, in particular in homogeneous excitation data acquisition.

Assuming that the noise n → in equation (4) is Gaussian white noise, the probability distribution for measured k-space data can be represented as P (d → | ρ →, {w}, C) = (2π) ^-N | C | ^-1 exp (- 1/2 (d → - Eρ →) ^† C ^-1 (d → - Eρ →)). (7)

Here {w} designate further parameters on which the probability distribution can conditionally depend. The correlation matrix C of the noise in k-space can be determined in methods and devices according to exemplary embodiments, for example from the k-space signals, which are obtained for a data acquisition with homogeneous excitation.

For simplification, a coordinate transformation is introduced such that A → = Tρ → (8) and E = HT, (9) in which

A corresponding transformation can be defined for each of several echo times in imaging sequences in which a plurality of echo signals are detected.

The transformation defined in equations (8) - (11) defines an image such that H ^† C ^-1 H = I. (12)

Using Equations (8) and (12), the probability distribution can be expressed as Equation (7) P (d → | A →, {w}, C) = (2π) ^-N | C | ^-1 exp (- 1/2 (d → - EA →) ^† C ^-1 (d → - EA →)) (13) where the probability distribution depends conditionally on the vector A →. From the transformations of equations (8) - (12), the exponent in equation (13) can be represented as - 1/2 (d → - HA →) ^† C ^-1 (d → - HA →) = - 1/2 (d → ^† C ^-1 d → - d → ^† C ^-1 HA → - A → ^† H ^† C ^-1 d → + A → ^† A →), (14) where at the last term of the right side of equation (14) equation (12) has already been considered.

The vector A → represents the spatially resolved signal amplitude transformed by the matrix T according to equation (8). The vector A → can generally have complex-valued vector elements.

In an MR imaging method and a corresponding MR system, which allow a spatially resolved excitation, it is possible to force elements of the vector ρ → to the value 0 so that no excitation takes place at the corresponding voxel. Accordingly, certain information about the vector A → is already known by the choice of the excitation profile. This can be represented mathematically such that a conditional probability distribution for A → is defined such that P (A → A → ₀ , C ₀ ) = (2π) ^-M | C ₀ | ^-1 exp (- 1/2 (A → - A → ₀ ) ^† C -1 / 0 (d → - A → ₀ )). (15)

Here, A → ₀ denotes the most probable value for the vector A → and C ₀ denotes the covariance matrix for the vector A → defined according to equation (8). A → ₀ and C ₀ represent hyperparameters. A → ₀ and C ₀ are related to physical quantities by the transformation defined in equation (8): A → ₀ = Tρ → ₀ (16) and C ₀ = TC _ρ0 T ^† . (17)

The covariance matrix C ₀ for the vector A → defined according to equation (8) depends on the excitation profile in the case of MR imaging in which the excitation profile can be controlled. The excitation profile can be used to specify which voxels do not supply signal contributions. This prior information ("prior information") can be used in the reconstruction. The covariance matrix C ₀ represents covariances of the prior information.

wobei das Integral auf der rechten Seite über die M komplexwertigen Vektorelemente des Vektors A → ausgeführt wird. Auf diese Weise wird A → ausintegriert. Die Wahrscheinlichkeitsverteilungen in Gleichung (18) sind durch Gleichungen (13) und (15) gegeben. Durch Multiplikation der Wahrscheinlichkeitsverteilungen in Gleichung (18) resultiert eine Gaußfunktion mit einem Exponenten, der bilinear in A → ist, so dass das entsprechende Integral ausgeführt werden kann.Using Bayesian statistics, an effective probability distribution conditionally dependent on the hyperparameters A → ₀ and C ₀ for detected k-space data can be determined:

wherein the integral on the right side is carried out over the M complex-valued vector elements of the vector A →. In this way A → is integrated. The probability distributions in equation (18) are given by equations (13) and (15). By multiplying the probability distributions in equation (18), a Gaussian function with an exponent bilinear in A → results, so that the corresponding integral can be performed.

From the effective probability distribution of Eq. (18), the most probable signal amplitude can be represented as a function of acquired k-space data as

The covariance matrix of the spatially resolved signal amplitude can also be determined and yields equation (4).

As described with reference to equation (15), the covariance matrix C _{0 represents} fluctuations of the vector A →, which in turn depends on the location-dependent signal amplitude according to equation (8). By selecting the excitation profile, the covariance matrix C ₀ can be influenced. For example, main diagonal elements of C ₀ can be suppressed by selecting a suitable excitation profile according to equation (17) in order to reduce signal contributions from voxels outside the RoI.

Various systematic approaches are possible in order, depending on the k-space covariance matrix C and the coding matrix E, to select an excitation profile for MR imaging in such a way that the noise in the image data is reduced for a desired RoI.

For example, equation (3) can be computationally resolved so that a desired covariance matrix D _{ρ would result} for covariances in the image space with desired properties:

The target covariance matrix D _ρ for data in the image space may be chosen such that the major diagonal elements for voxels in the RoI are smaller than a threshold, or that the sum of the major diagonal elements for the voxels in the RoI is smaller than a threshold.

There are several target covariance matrices D _ρ that result in reduced noise in image data for voxels of RoI. Among these, those can be selected which lead to a realizable covariance matrix C ₀ . For example, by parallel excitation with a plurality of excitation _coils , a suppression of main diagonal _{elements of} the matrix C ₀ or C _ρ0 can be achieved. Unless a priori spatial correlations between voxels are assumed, off-diagonal elements should be zero. In order not to suppress signals from the _RoI , solutions for C ₀ or C _{ρ 0} , which lead to a suppression of signals from the RoI, should not be accepted.

Starting from equation (4) different target covariance matrices D _{ρ can be} tested until a technically feasible covariance matrix C _{0 is} found. Systematic techniques for finding an excitation profile can employ, for example, iterative methods. Methods and apparatus for determining an excitation profile according to an embodiment will be described with reference to FIG 4 - 6 described in more detail.

4 is a flowchart representation of a method 50 according to an embodiment. The procedure can be done with the MR system 1 be performed, wherein the computing device 19 is set up for the determination of the excitation profile.

at 51 a first MR data acquisition is carried out on the examination object, at which a later reduced-noise MR data acquisition is to be performed in the ROI. The first MR data acquisition at 51 can be carried out with a homogeneous excitation. The suggestion at 51 may be limited to a slice of the examination subject and is homogeneous in the sense that the amplitude of the r.f. pulse within the slice does not or only slightly varies. The first MR data acquisition can be performed so that a lower number of k-space points is scanned than in the later MR data acquisition, in which a spatially variable excitation profile is used. In this way, for the first MR data acquisition at 51 required time, but also the time required for the computational definition of the excitation profile can be shortened.

at 52 the k-space covariance matrix C can be determined. The k-space covariance matrix C can be determined mathematically from the k-space points acquired with the L receiver coils.

rechnerisch bestimmt. So lange sich die Codiermatrix E und die k-Raum-Kovarianzmatrix C nicht ändert, kann die bestimmte Matrix

bei der nachfolgenden Ermittlung eines geeigneten Anregungsprofils weiterverwendet werden, ohne dass eine erneute Berechnung der Matrix erforderlich ist.at 53 becomes the matrix

calculated. As long as the coding matrix E and the k-space covariance matrix C do not change, the particular matrix

be used in the subsequent determination of a suitable excitation profile, without a re-calculation of the matrix is required.

at 54 the inverse covariance matrix of the prior information, C ₀ ^-1 , is set equal to zero, and at 55 the assigned image space covariance matrix is calculated. In the determination of C _ρ = (E ^† C ^-1 E) ^-1 (20) with C ₀ ^-1 = 0 at 54 is considered that for a homogeneous excitation a priori is not known in advance, which voxels provide no signal amplitude.

at 56 becomes a nominal covariance matrix in the image space D _ρ equals that at 55 determined matrix C _ρ set.

at 57 Main diagonal elements of the desired covariance matrix in the image space D _ρ , which correspond to voxels in the RoI, are changed. In particular, the main diagonal elements D _{ρ m, m} for voxels m lying in the RoI can be reduced to a value smaller in magnitude. Through the steps 55 and 56 a desired covariance matrix is generated, which is derived from an actually determined image space covariance matrix C _ρ , so that the associated covariance matrix C _{0 is} also close to the constraints imposed by technical conditions. Adjusting the main diagonal elements of D _{ρ forces} the noise in the image data for the RoI to be reduced compared to homogeneous excitation.

at 58 the covariance matrix C _{0 of} the prior information or its inverse is calculated, which corresponds to that at 56 and 57 determined set covariance matrix in the image space, D _ρ , leads. The determination of the covariance matrix C ₀ or of the inverse matrix C ₀ ^-1 can be carried out according to equation (1).

at 59 The covariance matrix C ₀ or its inverse C ₀ ^{-1 can} be changed so that it satisfies the constraints imposed on it. For example, the inverse of the covariance matrix C ₀ ^{-1 can} be changed such that it does not have large values in the main diagonal elements corresponding to the RoI. This ensures that the signal amplitude from the RoI is not suppressed. Alternatively or additionally, the extra-diagonal elements of C ₀ ^{-1 can be set} equal to 0. It can thereby be taken into account that a priori no correlations between voxels are assumed.

Optionally available at 59 further constraints are imposed. For example, if the later performed MR data acquisition is such that large intensity variations in the RoI are undesirable, it may be imposed as a further constraint that the major diagonal elements of C ₀ ^-1 corresponding to voxels of RoI do not vary significantly. A suitable suitable threshold comparison can be used.

at 60 a new image space covariance matrix C _{ρ is} calculated. The calculation can be carried out according to equation (3), now using the non-zero inverse C ₀ ^{-1 of} the matrix C ₀ , which is used in steps 58 and 59 was generated.

at 61 it is checked whether an abort criterion is met. In one embodiment can be checked to see if at 60 the image space covariance matrix C _ρ satisfies a predetermined condition or whether the changes in the image space covariance matrix C _ρ have become smaller than a threshold value from iteration to iteration.

The given condition, its fulfillment at 61 can be checked, for example, that the sum of the diagonal elements of the image space covariance matrix C _ρ after a projection in the space corresponding to the voxels in the RoI is less than a threshold. In this case, the constraint condition can be imposed that the signal contribution from the RoI is not suppressed. This condition can be expressed as Tr (RC _ρ R ^† ) <SW. (21)

When checking equation (21), it can be taken into account as a constraint that the reduction of signal contributions from voxels outside the RoI is desired, but not a reduction of the signals from the RoI.

Here, in equation (21), the matrix R is an M _R × M matrix, where M _{R is} the number of voxels in the RoI. The matrix entries of the matrix R are only 1 or 0 and select from the image space covariance matrix C _ρ those entries which are assigned to a voxel of the RoI. The matrix R is defined so that RR ^† = I (22) is where on the right side of equation (22) I is an M _R × M _R unit matrix.

If at 61 if it is determined that the termination criterion is not met, the method returns for another iteration 56 back.

If at 61 is determined that the termination criterion is met, an excitation profile is determined, which corresponds to the last determined matrix C ₀ .

at 62 Then, an MR data acquisition is performed, in which a spatially non-homogeneous excitation profile is generated. The excitation profile is chosen so that the expected noise for voxels in the RoI is reduced without reducing the signal of the voxels of the RoI. This is achieved by choosing the excitation profile according to the matrix C ₀ , which was determined in the iterative method.

For MR data acquisition at 62 Different pulse sequences can be used. Advantageously, the method for determining the excitation profile for MR data acquisition at 62 can be used, are determined in the echo time-dependent quantities. An example of such a measurement is the creation of T ₂ * cards.

The MR data acquisition at 62 performed with the non-homogeneous excitation profile can be performed so that a higher resolution than with the first MR data acquisition at 51 is achieved.

The termination criterion used in the process 50 at step 61 can be checked, will be explained in more detail for an embodiment. Various termination criteria can be used which result in a reduction of noise in the RoI by suppressing the signals from voxels outside the RoI. For better illustration, it is assumed that in vectors and matrices in the image space the first M _R voxels correspond to the RoI. This assumption does not limit the generality of the representation, since it can always be achieved by a corresponding renumbering of the coordinates.

wobei X1 eine M_R×M_R-Matrix und X2 eine (M – M_R)×(M – M_R)-Matrix ist. M_R bezeichnet dabei weiterhin die Anzahl der Voxel in der RoI. Die Matrizen X1 und X2 sind diagonal und weisen positive Matrixelemente entlang der Hauptdiagonalen auf. Die Matrixelemente liegen jeweils im Intervall von einschließlich 0 bis einschließlich 1.Assuming that the extra-diagonal elements of C ₀ ^-1 are 0, then

where X1 is an M _R × M _R matrix and X2 is an (M-M _R ) × (M-M _R ) matrix. M _R continues to denote the number of voxels in the RoI. The matrices X1 and X2 are diagonal and have positive matrix elements along the main diagonal. The matrix elements each lie in the interval from 0 to 1 inclusive.

definiert werden, wobei F11 eine M_R×M_R-Matrix, F21 eine M_R×(M – M_R)-Matrix, F12 eine (M – M_R)×M-Matrix und F22 eine (M – M_R)×(M – M_R)-Matrix ist.It can be a block representation of the matrix

where F11 is an M _R × M _R matrix, F21 is an M _R × (M-M _R ) matrix, F 12 is an (M-M _R ) × M matrix, and F22 is an (M-M _R ) × (M - M _R ) matrix.

It can be a block representation of the selection matrix R R = (I 0) (25) in equation (25) I is an M _R × M _R unit matrix and 0 is an M _R × (M-M _R ) zero matrix.

Using the block representation, the matrix on the right side of equation (21) can be represented as

The track over this size is given by Tr (F11X1F11 ^† + F21X2F21 ^† ) = Tr (F11X1F11 ^† ) + Tr (F21X2F21 ^† ), (27) where the first term on the right side of equation (27) is contributions to the noise in the RoI caused by voxels from the RoI and the second term on the right side of equation (27) contributions to the noise in the RoI, of voxels outside the RoI.

A reduction of the first term on the right of equation (27) is generally undesirable because it would result in a reduction of the signal from the RoI. However, the second term on the right side of equation (27) can be reduced to reduce the noise of the image data in the RoI.

wobei κ_n = ΣF21_m,nF21*_m,n. (29) The condition that the trace of equation (27) becomes minimum without decreasing the first term on the right side of equation (27) can be represented as

in which κ _n = ΣF21 _{m, n} F21 * _{m, n} . (29)

The quantity κ _n represents a weighting for the contribution that the nth voxel, which lies outside the RoI, to the noise in the image data in the RoI (calculated here according to equation (21)).

The quantities κ _n depend on the coding matrix C and the k-space covariance matrix C via equation (24). To select a suitable excitation pattern, therefore, the variables κ _n can be calculated automatically after a user-defined selection of the RoI. The quantities κ _n can be output graphically in order to allow the user to select a suitable excitation profile in which voxels can be suppressed depending on their associated κ _n . Alternatively, a fully automatic selection of an excitation profile can be made dependent on the κ _n .

While referring to 4 An iterative method for determining an excitation profile has been described, modifications of the method can be realized. For example, different termination criteria can be used. Depending on the application of the subsequent MR data acquisition, different constraints can be imposed on the matrix C ₀ ^-1 .

While an iterative method for determining an excitation profile can be used, in further embodiments sequentially several excitation profiles can be evaluated by calculation. An evaluation of the influence that an excitation profile has on the resulting noise in image data can be made by equation (3).

5 is a flowchart representation of a method 70 according to an embodiment. The procedure can be done with the MR system 1 be performed, wherein the computing device 19 is set up for the determination of the excitation profile.

bei 53 können wie bei dem Verfahren 50 von 4 durchgeführt werden.The MR data acquisition at 51 , the determination of the k-space covariance matrix C at 52 and the mathematical determination of the matrix

at 53 can as in the process 50 from 4 be performed.

at 71 an image space covariance matrix C _ρ expected for homogeneous excitation is calculated according to equation (20).

at 72 are determined based on the image space covariance matrix C _ρ voxels outside the RoI, which strongly contribute to the signal noise in the RoI. The determination of such voxels can be done in different ways. For example, all voxels k outside the RoI can be identified for which for at least one voxel j within the RoI the extradiagonal element of the image space covariance matrix C _{ρ is} greater than a threshold value SW1, | C _{ρ k, j} | > SW1. (30)

In another embodiment, all voxels outside of the RoI for which the weighting factor κ _n defined in equation (29) that quantifies the contribution of the voxel n outside the RoI to the noise of the image data in the RoI is greater than a threshold ,

at 73 may depend on the at 72 determined voxels outside the RoI be selected an excitation profile. The excitation profile can be selected so that the amplitude of the excitation profile of the at 72 detected voxels outside the RoI is suppressed. The excitation profile at 72 can be chosen under different constraints. For example, it can be imposed as a constraint that the amplitude of the excitation profile in the RoI must not have a zero.

at 74 is calculated, the image space covariance matrix C _ρ determined for the at 73 selected excitation profile would result. The mathematical determination of the image space covariance matrix C _ρ can be carried out according to equation (3).

at 75 it is checked whether an abort criterion is met. The review at 75 can like step 61 of the procedure 50 from 4 be performed. In particular, at 75 check whether the contribution of voxels outside the RoI to the signal noise of voxels within the RoI is less than a threshold.

If at 75 If it is determined that the termination criterion is not fulfilled, the method returns 73 back.

If at 75 it is determined that the termination criterion is met, is at 76 performed an MR data acquisition, in which the spatially non-homogeneous excitation profile is generated. The excitation profile is chosen so that the expected signal noise for voxels in the RoI is reduced, without the signal contribution from the RoI itself being reduced. For MR data acquisition at 75 Different pulse sequences can be used. Advantageously, the method for determining the excitation profile for MR data acquisition at 62 can be used, are determined in the echo time-dependent quantities. An example of such a measurement is the MR data acquisition for the creation of T ₂ * cards.

In the process of 5 the selection of the excitation profile is heuristically guided by the extradiagonal elements of the image space covariance matrix C _ρ . These allow the detection of voxels outside the RoI that significantly increase the noise for voxels in the RoI. In further embodiments, a group of possible excitation profiles may be computationally evaluated without voxels in advance can significantly increase the noise for voxels in the RoI. The evaluation can again include the computational determination of diagonal elements of the image space covariance matrix C _ρ .

The group of functions which are evaluated in terms of the resulting noise in image data of the RoI can be selected in consideration of the arrangement of the excitation coils. For example, sinusoidal or cosinusoid varying functions may be evaluated as a function of location. In k-space, such functions with which the excitation amplitude is locally modulated can be represented as a pair of excitations at the wave vectors k ₁ and k ₂ = -k ₁ . The set of excitation profiles to be tested can be further reduced by considering constraints. For example, the excitation profile should have no root within the RoI. This determines a lower bound for k ₁ . Similarly, a lower bound for k _{1 may} result from the constraint that the amplitude of the excitation profile across RoI has a relative change less than a threshold. Additionally or alternatively, it may be required that the modulation vectors k ₁ and k ₂ = -k _{1 are} parallel to the phase encoding direction.

6 is a flowchart representation of a method 80 according to an embodiment. The procedure can be done with the MR system 1 be performed, wherein the computing device 19 is set up for the determination of the excitation profile.

The MR data acquisition at 51 and the determination of the k-space covariance matrix C at 52 can as in the process 50 from 4 be performed.

at 81 a modulation vector or a pair of modulation vectors is chosen which define the local sinusoidal or cosine modulation of the excitation profile. The selection of the modulation vector or of the modulation vectors can be effected as a function of constraints. In this case, the selection of the modulation vector or of the modulation vectors can take place in such a way that the excitation profile has no zero point within the RoI. The selection of the modulation vector or of the modulation vectors can be carried out in such a way that the amplitude of the excitation profile has a relative change over the RoI which is smaller than a threshold value. The selection of the modulation vector or of the modulation vectors can be carried out such that the modulation vector or the modulation vectors are parallel to the phase coding direction.

at 82 the matrix C ₀ or its inverse C ₀ ^{-1 is} determined 81 corresponds to selected excitation profile.

at 83 is calculated, the image space covariance matrix C _ρ determined that would result for the excitation profile. The mathematical determination of the image space covariance matrix C _ρ can be carried out according to equation (3).

at 84 it is checked whether an abort criterion is met. The review at 84 can like step 61 of the procedure 50 from 4 be performed. In particular, at 84 check whether the contribution of voxels outside the RoI to the signal noise of voxels within the RoI is less than a threshold.

If at 84 If it is determined that the termination criterion is not fulfilled, the method returns 81 back.

If at 84 it is determined that the termination criterion is met, is at 85 performed an MR data acquisition, in which the spatially non-homogeneous excitation profile is generated. The excitation profile is with the at 81 last selected vector is modulated sinusoidally or cosinusoidally. The excitation profile is chosen so that the expected signal noise for voxels in the RoI is reduced, without the signal contribution from the RoI itself being reduced. For MR data acquisition at 85 Different pulse sequences can be used. Advantageously, the method for determining the excitation profile for MR data acquisition at 85 can be used, are determined in the echo time-dependent quantities.

While methods and devices have been described in accordance with embodiments, modifications may be made in other embodiments.

For example, in other embodiments, other groups of excitation profiles may be evaluated as sinusoidal or cosinusoid modulated profiles with respect to the resulting noise of the image data. It is also possible, in a first step, to perform a heuristic determination of voxels to be suppressed, as with reference to FIG 5 described and then the information thus obtained for selecting a group of excitation profiles to be tested according to the method of 6 or as information for use in the iterative method of 4 use.

While exemplary embodiments for determining an excitation profile for the subsequent use in the measurement of echo-time-dependent variables have been described, in other exemplary embodiments the methods and devices can also be set up for determining an excitation profile for use with other MR sequences.

Claims (19)

Method for specifying excitation parameters, in particular for specifying an excitation profile ( 41 ), for an MR imaging in which a parallel excitation with several transmission channels ( 15a . 15b . 16 ) and parallel data acquisition with multiple receive channels ( 22 - 25 ), wherein elements of a k-space covariance matrix for signal noise in k-space data, which in a data acquisition at an examination object ( 11 ) with the plurality of receiving channels ( 22 - 25 ), characterized in that for a plurality of voxels ( 32 ) of the examination subject ( 11 ) computationally elements of at least one image space covariance matrix are determined as a function of the k-space covariance matrix, and that the excitation parameters ( 41 ) are determined depending on the determined elements of the at least one image space covariance matrix. Method according to claim 1, wherein the excitation parameters prior to MR data acquisition represent or influence known prior information on which the image space covariance matrix depends, wherein the excitation parameters are determined so that the elements of the image space covariance matrix satisfy a predetermined condition. Method according to Claim 2, in which covariances of the prior information are determined in order to determine the excitation parameters such that geometry factors for voxels in a region of interest, RoI, ( 32 ) of the examination subject ( 11 ) are reduced compared to a homogeneous excitation. The method of claim 2 or 3, wherein for determining the excitation parameters, a covariance matrix of the prior information is determined for which the elements of the image space covariance matrix are reduced compared to a homogeneous excitation. The method of claim 4, wherein determining the covariance matrix of the prior information results in solving the equation

where C ₀ denotes the covariance matrix of the prior information, E the coding matrix, C the k-space covariance matrix, D _ρ a picture space covariance matrix whose elements satisfy a predetermined condition, and I denotes a unit matrix. Method according to one of claims 2-5, wherein covariances of the prior information are determined in an iterative method. Method according to one of claims 2-6, wherein covariances of the prior information under compulsory conditions are determined automatically by calculation. Method according to one of the preceding claims, wherein, for several sets of excitation parameters, the components of the image space covariance matrix associated with the corresponding set of excitation parameters are computationally determined, wherein the excitation parameters for the MR imaging are determined as a function of the elements of the image space covariance matrix respectively determined for the several sets of the excitation parameters. The method of claim 8, wherein the plurality of sets of excitation parameters are multiple excitation profiles ( 41 ), in particular a plurality of excitation profiles modulated sinusoidally or cosinusoidally as a function of the location. Method according to one of the preceding claims, wherein extra-diagonal elements of the at least one image space covariance matrix are determined and from them voxels ( 33 ) of the examination subject ( 11 ) whose contribution to the noise in image data for voxels of a region of interest, RoI, ( 32 ) of the examination subject ( 11 ) exceeds a threshold. Method according to one of the preceding claims, wherein the definition of an excitation profile ( 41 ) comprises determining excitation parameters such that one of diagonal elements of the image space covariance matrix, the voxels of a region of interest, RoI, ( 32 ) of the examination subject, dependent evaluation function is minimized. The method of claim 11, wherein defining an excitation profile ( 41 ) determining an excitation profile ( 41 ) such that the evaluation function evaluated for several excitation profiles4 Tr (RC _ρ R ^† ) where Tr denotes the track operator, C _ρ denotes the image space covariance matrix for the respective excitation profile and R denotes a projection operator for the RoI, the minimization taking place under the constraint that signals from the RoI ( 32 ) can not be reduced. Method according to one of the preceding claims, wherein the determined elements of the k-space covariance matrix covariances of different receiving coils ( 22 . 23 ) comprise k-space data. Method according to one of the preceding claims, wherein with the method the excitation profile ( 41 ) for MR imaging for measuring echo-time dependent quantities, in particular for a multi-echo imaging sequence. Method according to one of the preceding claims, wherein the excitation parameters are determined so that different portions of the detected MR image are suppressed for different echo times. Device for determining excitation parameters, in particular for determining an excitation profile ( 41 ), for an MR imaging in which a parallel excitation with several transmission channels ( 15a . 15b . 16 ) and parallel data acquisition with multiple receive channels ( 22 - 25 ), comprising: an interface ( 26 ) for receiving at a data acquisition on an examination object ( 11 ) with the plurality of receiving channels ( 22 - 25 ) recorded k-space data, and an electronic computing device ( 19 ), which is set up - to include elements of a k-space covariance matrix for signal noise in the multi-channel (s) ( 22 - 25 ) to determine acquired k-space data, - for several voxels ( 32 ) of the examination subject ( 11 ) computationally determine elements of at least one image space covariance matrix as a function of the k-space covariance matrix, and - automatically determine the excitation parameters as a function of the determined elements of the at least one image space covariance matrix. Apparatus according to claim 16, arranged for carrying out a method according to any one of claims 2-15. Magnetic resonance system for MR imaging, comprising - an excitation device ( 15a . 15b . 16 ) with several transmission channels ( 15a . 15b . 16 ) for the controllable generation of a spatially varying excitation profile ( 41 ), - a receiving device ( 22 - 25 ) with several receiving channels ( 22 - 25 ) for MR data acquisition after an excitation, and - one with the excitation device ( 15a . 15b . 16 ) coupled device ( 18 . 19 ) according to claim 16 or 17 for controlling the excitation means. Computer program, which directly into a memory of a programmable device ( 18 . 19 ) of a magnetic resonance system ( 1 ), the computer program being a sequence of control commands when executed by the device ( 18 . 19 ) cause the magnetic resonance system, the apparatus for performing a method according to any one of claims 1-15.

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