WO1993002526A1

WO1993002526A1 - Method for compressing digital image sequences

Info

Publication number: WO1993002526A1
Application number: PCT/CH1992/000148
Authority: WO
Inventors: Murat Kunt; Frédéric DUFAUX; Iole Moccagatta; Touradj Ebrahimi; George Campbell; Alexander Geurtz
Original assignee: Laboratoire De Traitement Des Signaux
Priority date: 1991-07-19
Filing date: 1992-07-16
Publication date: 1993-02-04

Abstract

A method comprising an image decomposition step using multiresolution pyramidal Gabor transformation. The transformed image data arranged in a pyramid of sub-bands are then selected in three groups according to the spatial frequency level of the sub-band data, wherein the sub-band data of each group are coded by a respective one of three coding operations which are performed in parallel and each of which has a specific performance matching the properties of the data in each group. A reverse transformation operation is then performed to recreate the images. The method uses movement-compensation prediction to reduce the time correlation between the two images without movement vector transmission to the receiver being absolutely necessary. The method further uses filters providing decomposition into sub-bands which only comprise value coefficients that are powers of two or the sum of or difference between two powers of two. A previous step allows the data for processing to be converted from interlaced (CCIR 601 format) to progressive modes, based on a movement-compensated interpolation. A final progressive to interlaced mode conversion step may be provided in the decoder.

Description

Method for compressing digital image sequences

The use of image sequences is becoming increasingly important in modern imaging applications, such as high definition television (HDTV), teleconferencing, multi-media applications, medical imaging, robotics , satellite imagery, interactive video and entertainment.

The influence of the imagery field, in technology, in politics, in society, in the economy, as well as in art and culture, makes this use of image sequences even more important. This is why a large number of companies and organizations, national and international, have invested in the various aspects of the science of imagery.

In high-definition television, for example, significant efforts are being made to define new standards. Japanese efforts in this area are not new. Already in the 1970s, the company NHK (Nippon Hoso Kyokai) began its preparatory research with eleven Japanese television manufacturers. The result of these efforts, MUSE (Multiple sub-nyquist sampling encoding) is a high-definition analog system. The introduction of this system has already started on a small scale in Japan. Europe followed Japan with another analog system, HD-MAC (High Definition Multiplexed Analog Components). The first commissioning of this system is planned for 1995. Other intermediate systems such as D-MAC or D2-MAC are already available. Many American companies and universities are also working to introduce a high definition analog or digital television system. These include MIT-RC and MIT-CC from the Massachusetts Institute of Technology, 3XNTSC from Zénith and HDS-NA from North American Philips.

Other applications of digital video coding include may quote recommendation H261 CCITT (International Telegraph and Telephone Consultative Committee) for video telephony and video conference which is a digital coding system, and also the coding system for interactive video (ISO / IEC JTC1 / SC2 / G11) proposed by MPEG (Motion Picture Expert Group).

A method of compressing digital images comprising a step of decomposing images by transformation into sub-bands is described in "International Conférence on

Acoustics, Speech and Signal Processing, Albuquerque, 3-6 April, 1990, vol. 4, IEEE (New York, US), M. Antonini et al: Image coding using vectόr quantization in the wavelet transform domain, pp. 2299-2300 ". This is an application of vector quantization to compress a multiresolution data structure. The described method only reduces redundancies within each sub-band, but does not take account for the dependence between the sub-bands. Furthermore, vector coding is applied to all the sub-bands, regardless of the importance of the spatial frequency of the data of the sub-bands. However, the characteristics of the sub-bands being different according to the importance of the spatial frequency, the proposed method does not make the most of these differences. On the other hand, this method makes no difference between the analysis filters and the synthesis filters as to their complexity, which implies that the cost of a decoder implementing this method is as high as that of the coder.

The aim of the present invention is to provide a method of compressing digital images intended for video-digital transmissions or for digital storage on media such as compact disks or optical disks, so as to obtain average transmission rates. of the order of 1 to 10 Mb / s with higher quality compared to known systems, such as for example H261 CCITT or MPEG mentioned above, and with a relatively simple implementation. To this end, the invention relates to a method for compressing sequences of digital images comprising a step of decom¬ position the images by transformation into sub-bands, as defined in claim 1. It also relates to a device for setting implementation of the method, as defined in claim 12, as well as a filter bank for implementing the method, as defined in claim 13, and a filter bank intended for rapid multiresolution transformation for compression digital images, as defined in claim 15.

The method of the invention makes it possible in particular to take into account the redundancy not only inside a sub-band, but also the dependence between the sub-bands, which leads to a higher efficiency than that of the methods. known. The method of the invention has the advantage of being very simple for its implementation. It uses very little memory while being very efficient. Furthermore, the precision of the motion vectors is only limited by the arithmetic precision of the elementary operations of the space-time constraint.

On the other hand, the structure of the synthesis filters much less complex than that of the analysis filters makes it possible to simplify the decoding operation, which is vital to lower the cost of the decoder. The proposed filters can be implemented effectively in terms of polyphase components thanks to the structures of the QMF (quadrature mirror filter) type contained in the synthesis analysis parts. The structure of the filter bank allows a VLSI implementation with a clock frequency half as low as that proposed so far, the filters being obtained by optimization of a localization function both in image space and in the 'frequency space.

As shown in FIGS. 1 and 3, the multi-resolution organization of the data is taken into account by three different coding techniques, each giving rise to specific performances adapted to the properties of the respective data classes.

The average frequencies are coded by a vector quantization (VQ) with a pyramidal structure. The latter eliminates linear and non-linear spatial correlation, as well as linear and non-linear correlation across sub-bands. As shown in Figure 4, this pyramid structure consists of a low resolution image in one level of the pyramid and detail images in the other levels. The resulting pyramid transformation provides information at different levels of resolution.

A pseudo-random scanning of the high-frequency sub-bands minimizes the visual distortion due to the overflow of the buffer memory by distributing it over the entire surface of the image. Pseudo-random is understood here in a sense analogous to that of the randomize function of a computer.

The spatial sub-band of the continuous component is coded by a conventional technique of pulse code modulation.

The special shape of the synthesis and analysis filters leads to efficient implementation, while maintaining maximum localization in both the spatial and spatial frequency domains.

This process can be used to encode among others the ISO / CCIR 601 and CCITT / CIF formats. For the data to be processed which are in the CCIR 601 format, one proceeds beforehand in the coder to a conversion from interlaced to progressive (figure 1), then in the decoder to a conversion from progressive to interlaced (figure 2), in order to restore the original format. These conversions are based on an interpolation with motion compensation. They are not necessary for progressive scan formats. The use of the Gabor decomposition was chosen on the one hand because the Gabor functions, which are Gaussian functions modulated by complex exponentials, have an optimal location in the joint spatial / spatial frequency domain. On the other hand, according to recent experiences, the majority of the receptive field profiles of the mammalian visual system can be modeled by this type of function. The partitioning of the spatial frequency domain into octave bands is motivated by natural image statistics and also by the sensitivity of the human visual system.

The main disadvantage of Gabor functions is that they do not form an orthogonal basis. Consequently, there is not a priori a direct method to compute the transformation, as one can do it in an orthogonal case by simple scalar products. A method has already been proposed for carrying out the Gabor pyramid transformation. This technique is based on the criterion of adjustment by the method of least squares. The solution to the problem of the method of least squares shows that the coefficients of weighting can be extracted by simple multiplication between a matrix and a vector of data. If the set of Gabor functions is chosen independently of the image, the multiplicative matrix is constant. The reconstructed data are obtained by another multiplication between the matrix of Gabor functions and the vector of the weighting coefficients. A parallel implementation of the transformation is therefore carried out to carry out the transformation in real time.

The chrominance is undersampled in the transform domain by eliminating the higher frequency components from the pyramid (Figure 4). This process does not deteriorate the visual quality of color images.

The spatial continuous component (low resolution image, see Figure 3) is coded using modulation by coded pulses (PCM). The average levels of the pyramid are coded using a hierarchical vector quantization (VQ) with a tree structure, as represented in FIG. 4. The highest spatial frequencies are selected adaptively and scalarly quantized (SQ / RL). The position information and the amplitude of the coefficients are coded separately. The adaptive quantization step and a variable length entropy encoder are controlled using a feedback strategy based on the occupation of the buffer memory.

In order to exploit the temporal correlation (inter-images) between the coefficients of each image, a differential inter-image technique is used. Using two previous images, the current image is predicted by a motion compensated extrapolation, and only the prediction error is coded and transmitted. The motion vectors are estimated hierarchically (pairing of blocks or spatio-temporal constraint). These same vectors are also used when converting from progressive to interlaced. In order to avoid an accumulation of channel errors, an intra-image technique is applied in a fixed interval to completely update all the coefficients. This mechanism is also restarted after each scene change.

The features and advantages of the invention will emerge clearly from the description which follows, given by way of example, and which refers to the accompanying drawings.

Figure 1 is a block diagram of a coding device operating according to the method of the invention.

Figure 2 is a block diagram of a decoding device operating according to the method of the invention.

Figure 3 illustrates the three different data regions according to the three coding strategies. FIG. 4 illustrates the implementation of the vectors of vector quantization.

Figure 5 is a block diagram of motion compensation.

FIG. 6 shows an example of impulse response of a filter from the analysis filter bank.

FIG. 7 shows an example of impulse response of a filter from the synthesis filter bank.

FIG. 8 gives a representation in the frequency domain of the filters of the analysis filter bank.

FIG. 9 gives a representation in the frequency domain of the filters of the bank of synthesis filters.

Conversions from interlaced to progressive and from progressive to interlaced

The system can be used to encode the two formats ISO / CCIR 601 (interlaced) and CCITT / CIF (progressive). The ISO / CCIR 601 format consists of 288 by 720 interlaced images at a frequency of 50 fields per second for 625-line systems. The CCITT / CIF format consists of 288 by 360 progressive images at a frequency of 25 images per second. When the input image is in an interlaced format, a first block (Figures 1) performs the conversion from interlaced to progressive. This first conversion is based on a spatial interpolation with motion compensation. A final block on decoding (Figure 2) allows you to find the initial format by converting from progressive to interlaced. This second conversion uses time interpolation with motion compensation.

In order to be able to convert 50 interlaced fields per second into 25 progressive images per second and vice versa, the following steps are implemented. An image is generated for each field using spatial interpolation. This leads to 50 frames per second. The image sequence is sub-sampled in the time domain, so as to preserve only 25 images per second. Transformation and coding can then be performed. In the decoder, a temporal interpolation is executed. This leads to 50 frames per second. Finally, we only keep the even or odd lines of the images, so as to generate 50 fields per second.

The following technique is used for this conversion. The missing lines are obtained by using a space-time interpolation with compensation for movement between the two neighboring lines existing on either side of the missing line. This makes it possible to go from an image frequency of 25 images per second to an image frequency of 50 progressive images per second. A time compensated motion interpolation is used. The movement between two consecutive images is estimated by a hierarchical technique. These same motion vectors are also used for motion compensation prediction, and they are obviously only calculated once. These two techniques have already been widely studied by many authors, for example in the articles by M. Bierling,

"Displacement estimation by hierarchical blockmatching", SPIE Visual Communications and Image Processing '88' vol. 1001, 1988, pp. 942-951 and by M. Bierling and R. Thoma "Motion co pensating field interpolation using a hierarchically structured displacement estimator". Signal Processing 11 (1986) 387-404.

Gabor's pyramid transformation

Subband decomposition and transform coding as a subset of subband decomposition are very popular for data compression, thanks to the good quality of the results obtained for a rate of compression given by comparison with other techniques.

The transformation used in the present system is a Gabor pyramid transformation with multi-resolution. In recent years, numerous studies have shown that multiresolution techniques are very effective for image analysis and coding; as for example SG Mallat, "A Theory for Multirésolution Signal Décomposition: The avelet Representation", pami IEEE, volume 11, number 7, July, pages 674-693, 1989, and Rosenfeld, A., "Multirésolution Image Processing and Analysis" , Springer-Verlag, 1984, Berlin, Germany.

The choice of the Gabor functions for the basis of the transformation (or for the impulse response of the synthesis filters) is motivated by the fact that these functions have an optimal localization in the joint spatial / spatial frequency domain. In other words, the Gabor functions are the only ones to reach the lower limit of Heisenberg uncertainty in the space of signals. This principle states that the product of the extent of a signal in the spatial domain with its extent in the frequency domain is always greater than or equal to a constant. The minimum is reached precisely, when the signal is a Gabor function. On the other hand, as recent experiments have shown, the majority of receptive field profiles of the mammalian visual system can be modeled by this type of function. In addition, the power spectrum of natural images decreases exponentially as the spatial frequency increases. This motivates the choice of a decomposition into octave bands of the frequency domain. In addition, measurements made on the cells of the receptive field of the visual cortex of mammals have shown that each of them is sensitive to frequencies located in a sub-band whose bandwidth corresponds to one octave.

The design of analysis and synthesis filters (or equivalent way the basic functions of the transformation and of the bi-orthogonal functions to these) is performed using the least squares solution. This solution shows that the transformation coefficients can be extracted by a simple matrix product A ^T FA which is equivalent to a filtering and a subsampling, where A is the matrix of the analysis filters and F the matrix of the image. Similarly, the inverse transformation is obtained using another product of matrix GXG ^T which implements oversampling and inverse filtering, where G is the matrix of the synthesis filters and X the matrix of the coefficients of the transformation, and where

when it comes to square matrices, as described in the article by T. Ebrahimi, T. Reed, and M. Kunt, "Sequence coding by Gabor Décomposition", Signal

Processing V, Proceedings of Ensipco 90, Pages 769-772, 1990.

For practical questions, such as the possibility of implementation for real-time application, an approximation of the Gabor functions is used to generate the basic functions of the transformation. The synthesis filters are designed to contain only coefficients which are a sum or a difference of two powers of two at most. Several methods have been proposed to approximate a given filter, for example by a method based on min-max or least squares criteria by linear or quadratic programming (see the article by YC Lim and SR Parker, "FIR Filter Design over a discrete powers-of-two coefficient space ", IEEE transactions on ASSP Vol. 31 No. 3, 1983, Pages 583-591), and by a method based on simulated annealing (see the article by N. Benvenuto, M. Marchesi and A. Uncini, "Results on the application simulated annealing algorithm for the design of digital filters.with powers-of-two coefficients", IEEE proceedings 1990, Pages 1301-1304). It is also possible to approximate a given filter by several filters cascaded. This approximation allows reverse transformation to be carried out very quickly using only some addition and shift operations. All filtering operations are performed on a highly parallel architecture ASP (Associative String Processor). (See: Lea RM, ASP: parallel Computing technology, SPIE Visual communication and image processing 90, vol 1360,

Lausanne, Switzerland p. 78-91). The complexity is however moved in the analysis filters. However, it is also possible to approximate these filters by a sum or a difference of powers of two. After this last operation, the perfect reconstruction property is no longer checked. Nevertheless, results show an almost perfect quality of the reconstructed images, with a signal to reconstruction error ratio exceeding 46 dB. An example of a filter bank having power coefficients of two, approximating Gabor filters, is given in FIGS. 6 to 9. In FIGS. 7 and 9, the curves in dashed lines 1 represent ideal filters, the curves in dotted line 2 being those of the filters obtained, easy to implement.

The coefficients of the prototype filter (Figure 6) of the analysis filter bank are as follows:

f (l) = f (10) = 2- ^" f (2) = f (9) = 0

f (4) = f (7) = - 2- ⁷ f (5) = f (6) = 2 °

The coefficients of the prototype filter (Figure 7) of the synthesis filter bank are as follows:

g (D = g (6) = 2- '

g (3) = g (4) = 2 °

For practical implementation, the coefficients of these filters are programmed in a special chip according to a poly-phase structure.

Demultiplexing is achieved by simple addressing of the memory.

Quantification

The coefficients of the transformed image are coded according to three different methods depending on the spatial frequency to which they belong. These coding classes are shown in Figure 3.

a) Pulse code modulation (PCM)

The spatial sub-band of the continuous component is coded by a conventional technique of pulse code modulation. This technique is relatively robust in the presence of noise.

b) Hierarchical vector quantification (DV)

It is well known how vector quantization (VQ) can improve performance compared to scalar quantization (SQ). (JS Lim, "Two-dimensional signal and image processing", pp. 589-611, Prentice-Hall ed., 1990, and RM Gray, "Vector Quantization", IEEE ASSP Mag., Vol 1, pp. 4-29 , April 1984). The most important feature of vector quantization is how to exploit the statistical dependence among scalars in the quantization block. Using vector quantization, it is possible to take into account the linear and non-linear dependence between scalars (elements in the block forming a quantization vector).

Different quantization procedures can be applied to the coding of the sub-bands generated by the Gabor transformation. In order to take into consideration tion the obvious correlation that exists between the different bands, a more efficient coding can be obtained by replacing scalar quantization by vector quantization. (See in this regard the article by G. Galand, E. Lacson, G. Furland and J Menez, "Subband coding of images using adaptive VQ, and Entropy Coding", Image'com 90, pp. 106-110, Bordeaux , Nov. 1990). Vector quantization is used in the mid-frequency region, where the correlation is higher and where vector quantization is most effective. In the domain of the transform, the elements of the vectors are chosen in accordance with the pyramidal structure described above (Figure 4).

A relevant parameter is the size of the vectors, in that the larger they are, the better the exploitation of the correlation between coefficients. By increasing the size of the dictionary, we increase the duration of the dictionary construction. For this reason and for strict implementation conditions (real-time processing, amount of memory), it is advantageous to use a small to medium size of vectors, depending on the number of levels in the quantified pyramid using vector quantization.

The chrominance coefficients are also included in the vectors, along with those of luminance (Figure 4). Based on experimental results described in the recommendation "Encoding parameters for digital television for studios"

CCIR Recommendation 601-1 XVIth Plenary Assembly Dubrovnik 1986, Vol. XI, Part 1, pp. 319-328, it can be shown that the use of chrominance coefficients only in low to medium frequencies does not significantly deteriorate the visual quality. From the point of view of implementation, control of the buffer memory is avoided by adopting vector quantization with exhaustive search / tree structure, using a fixed length code assigned to each element. We thus defined a system giving a minimum required quality. The bit rate corresponding to the above quality will always remain below the channel capacity, while the remaining available bit rate can be used to improve the quality of high frequency band information. Finally, the dictionary is defined a priori and known to both the transmitter and the receiver.

Scalar quantization, variable length code, buffer check (SQ / RL)

The highest level of the pyramid is scanned using a Peano-Hilbert scan in sub-blocks of the image in a pseudo-random order. This scan converts two-dimensional image subbands into a one-dimensional number chain. This chain is then quantified using standard scalar quantization (SQ). The result is a string of numbers with only a small number of bits. These numbers are then compared to a threshold and set to zero if they are below the threshold. The vast majority of the coefficients will be smaller than the threshold. This chain is then divided into two chains, one being a sequence of non-zero coefficients and the other being a binary chain where the value represents the position of a non-zero coefficient and a zero represents a zero coefficient. The binary chain is coded using a range coding (RL) based on the Capon model (see in this regard the thesis of M. Kunt, "Comparison of coding techniques for the reduction of redundancy of facsimile images to two levels ", thesis Nr. 183, LTS-DE, EPFL, 1974). The non-zero coefficients are coded using a Huffman code. In order to produce an output which is always below the maximum authorized data rate, a feedback from the buffer is used to define the threshold. If the data rate exceeds the maximum, the data flow is truncated and the threshold is lowered for the next image. Due to the pseudo-random order of the scanned sub-blocks, the visual effect of truncation is minimized.

Multiplexing is carried out by simple addressing of the memory, then an inverse pyramidal transformation is carried out.

Motion compensation prediction

The method described here uses motion compensation prediction to reduce the time correlation between the images. Studies have shown that this method is very effective in reducing temporal redundancy (see on this subject the articles by A. Puri, HM Hang and DL Schilling, "An Efficient Block-Matching Algorithm for Motion-Compensated Coding", ICASSP, April 1987, pages 25.4.1-4, and by AN Netravali and JD Rob ^' bins, "Motion Compensated Television Coding-Part I", journal Bell Systems Technical Journal, volume 58, number 3, 1979, pages 629-668.). The same displacement vectors obtained are also used for the conversion from progressive to interlaced and for slow motion with good rendering of the movement. In these two cases, a temporal interpolation with motion compensation is involved (Figure 5). The multiresolution structure of the pyramidal transform is used to find the movement in two consecutive images. In FIG. 5, Fι (m, n) and F _a (m, n) represent the two images used for the motion estimation, which can be either the two previous images, or a previous image and the image

__ Λ current, V (m, n) representing the field of motion, F (m, n) the predicted image and F (m, n) the interpolated image, and where m and n are the indices of the rows and columns of the image. We first use a block matching algorithm, or spatio-temporal constraint, on the highest level of the pyramid with the lowest resolution. The results are then projected downwards as an initial condition in the lower levels and refined each time. The final results are then used to predict the current image. The entire motion estimation method is performed on quantized images, so that the receiver can reconstruct the images without having received the motion vectors. This method can thus be used when no movement information is necessary for the decoding of the movement vector.

As mentioned above, two modes of motion estimation are considered here. In the event that there is little movement in the scene, the movement estimation is carried out on the basis of the two previous images. Thus, as said above, no additional information is required. In the case where there is a lot of movement in the scene, the motion estimation is performed based on the current image and the previous image. In this case, a better estimate is obtained, but additional information on the motion vectors is to be sent through the channel.

Claims

1. A method of compressing sequences of digital images, comprising a step of decomposing the images by transformation into sub-bands, characterized in that the decomposition operation is carried out according to the diagram of a pyramidal transformation at multiresolution, in that the data of the transformed image, organized in sub-bands in pyramidal form, are then selected in three groups according to the importance of the spatial frequency of the data of the sub-bands, the data of the sub- bands of each group being respectively coded using three different coding operations executed in parallel, each of these operations having specific performances adapted to the properties of the data of each group, and in that an inverse transformation operation is then executed to reconstruct the images.

2. Method according to claim 1, characterized in that the reverse transformation operation is of less complexity than that of the direct transformation.

3. Method according to one of claims 1 or 2, characterized in that the decomposition operation is carried out using a Gabor pyramid transformation with multiresolution.

4. Method according to one of claims 1 to 3, characterized in that it comprises filters for performing the decomposition into sub-bands comprising only coeffi¬ cients of values being powers of two or the sum or the difference of two powers of two.

5. Method according to one of claims 1 to 4, characterized in that it comprises an operation of coding the spatial sub-band of continuous component using a pulse code modulation technique, an operation of coding the sub- medium frequency bands in using a hierarchical vector quantization with tree structure and an operation of adaptive selection of the sub-bands of higher frequencies and scalar quantization of the selected sub-bands.

6. Method according to claim 5, characterized in that the scalar quantization operation of the higher frequency sub-bands comprises a Peano-Hilbert scan in sub-blocks of the image according to a pseudo-random order.

7. Method according to one of the preceding claims, characterized in that it uses a motion compensation prediction to reduce the time correlation between two images, without it being absolutely necessary to transmit the motion vectors to the receiver

8. Method according to one of the preceding claims, characterized in that it comprises a prior step of converting the data to be processed which is in the CCIR 601 format, this step comprising an operation of conversion from interleaved to progressive, based on interpolation with motion compensation.

9. Method according to one of the preceding claims, characterized in that it comprises a final stage of conversion of the data which are in a progressive format in CCIR 601 format, this stage comprising an operation of progressive conversion to interlaced, based on an interpolation with motion compensation.

10. Method according to one of claims 5 to 9, characterized in that the information of the position and the amplitude of the coefficients of the quantization are coded separately.

11. Method according to claim 10, characterized in that the adaptive step of the quantification is controlled and a variable length entropy coder using a feedback strategy based on the occupation of the buffer memory.

12. Device for implementing the method according to one of claims 1 to 11, characterized in that it comprises first means for decomposing the images into sub-bands according to the diagram of a pyramidal transformation. in multiresolution, second means for selecting the data of the transformed image, organized in sub-bands in pyramidal form, in three groups according to the importance of the spatial frequency of the data of the sub-bands, of the third, fourth and fifth means intended for the respective respective coding of the data of the sub-bands of each group, each of said third, fourth and fifth means being arranged so as to provide specific performances adapted to the properties of the data of each group, and of the sixth means for carrying out a transformation reverse in order to reconstruct the images.

13. Filter bank for implementing the method according to one of claims 1 to 11, characterized in that it comprises a set of filters of the type with almost perfect reconstruction, each filter containing a number of coefficients in powers of two less than twenty and in multiresolution structure.

14. Filter bank according to claim 13, characterized in that the number of said filters is between six and ten.

15. Filter bank intended for a rapid multiresolution transformation for the compression of digital images, characterized in that it comprises a set of filters of the quasi-perfect reconstruction type, each filter containing a number of coefficients in powers of two less than twenty and in multiresolution structure.

16. Filter bank according to claim 15, characterized in that the number of said filters is between six and ten.