FR2790171A1 - Digital signal transformation method, in which signal is processed by successive samples, such that calculations made on any series do not take into account samples in following series, and any series terminates in low frequency sample - Google Patents

Abstract

The digital signal filtering method involves analysis filtering and transforming a digital signal which processes the signal by blocks, whilst limiting the degradation of the reconstructed signal. Other processing are applied to the signal between transformation and its reconstruction. The signal is processed by successive series of samples, and the calculations made on any series do not take into account the samples in a following series, and any series terminates in a low frequency sample. The method involves analysis filtering of an original digital signal which includes original samples representing physical quantities, and in which original samples of the signal are transformed by successive calculations into high and low frequency output samples. Any sample calculated at a given step is calculated by a predetermined function of original samples, and/or previously calculated samples. The samples are ordered in increasing rank. The signal is processed by successive series of samples, and the calculations made on any series do not take into account the samples in a following series. Any series terminates in a low frequency sample. Independent claims are included for; a method of coding a digital signal including original samples representing physical quantities; method of synthesis filtering a digital signal including high and low-frequency interlaced samples; a device for analysis filtering of an original digital signal; digital signal coding device; a storage medium for a program for implementing the method of the invention; a computer program product for implementing the method of the invention.

Description

The present invention relates to digital signal filtering, such as

  transformation of digital signal into frequency sub-band signals. Many digital filtering methods and devices are known. We consider here, by way of example, analysis filtering and

  corresponding filtering of digital signal synthesis.

  These filterings are generally subsets integrated into the coding and / or decoding sets. They often require a large place in RAM or in buffer memory, to store the

data being processed.

  However, in practice, the size of the memory means is often less than the size which would be necessary to store an entire set of data, for example a digital image. It is therefore necessary to "cut" the signal into blocks and to process the blocks one after the other.

others.

  However, between an analysis and the corresponding synthesis of a signal, other processing operations, such as quantification or entropy coding, are generally applied to the latter. These treatments, combined with

  block processing, cause degradations in the reconstructed signal.

  The present invention provides a method and a device for transforming a digital signal which processes the signal in blocks, while limiting the degradations in the reconstructed signal, in the case where other processing

  are applied to the signal between its transformation and its reconstruction.

  To this end, the invention proposes a digital signal analysis filtering method comprising original samples representative of physical quantities, original samples of the digital signal being transformed into high and low frequency samples, on at least a resolution level, a high frequency sample of a given resolution level being calculated by an original sample function, a low frequency sample of the given resolution level being calculated by an original sample function and of high frequency samples of the given resolution level, the low frequency samples of the given level then serving as original samples for a possible lower resolution level, characterized in that the signal is processed by successive series of samples, the calculations carried out on any series not taking into account the samples of a following series ante, and in that the arbitrary series ends with a

low frequency sample.

  The invention also proposes a digital signal synthesis filtering method comprising interleaved samples of high and low frequency respectively, transformed samples being formed from high and low frequency samples, on at least one level of resolution, of the first samples. transforms of a given resolution level being calculated by a function of high and low frequency samples of samples, second samples of the given resolution level being calculated by a function of high and low frequency samples and first samples transformed from the given resolution level, the transformed samples from the given level then serving as low-frequency samples for a possible higher resolution level, characterized in that the signal is processed by successive series of samples, the calculations carried out on any series not taking in co mpte the samples of a following series, and in that the arbitrary series ends with a

low frequency sample.

  The invention also relates to a digital signal coding method which comprises - analysis filtering as defined above, - quantification of the previously filtered samples, and

  - an entropy coding of the previously quantified samples.

  According to this coding method, the signal is processed by successive series of samples, the calculations carried out on any series not taking into account the samples of a following series, and the series

  any one ends with a low frequency sample.

  The invention also proposes a method for decoding a coded digital signal according to the preceding coding method, comprising: - an entropy decoding of coded samples of the coded digital signal 1 5, - a dequantification of the previously decoded samples, - a synthesis filtering samples previously

  dequantified, as defined above.

  According to the decoding method, the signal is processed by successive series of samples, the calculations carried out on any series not taking into account the samples of a following series, and the series

  any one ends with a low frequency sample.

  Thanks to the invention, the degradations in the reconstructed signal are limited. In addition, the occupation in the buffer of the data being processed is optimized, since the signal is processed in blocks. Thus, complex filtering can be integrated into many devices, without

  that these do not require very large memories.

  According to a preferred characteristic, on synthesis, each series of samples ends after a last sample of a determined series

  during an analysis filtering as defined above.

  According to another preferred characteristic, both in analysis and in synthesis, the arbitrary series ends in a low frequency sample of the lowest resolution level. This configuration limits

  considerably degradations in the reconstructed signal.

  According to preferred characteristics, the digital signal is an image signal and the original samples are rows or columns of the image. The invention advantageously applies to an image signal, which generally requires a large memory space. This memory space is

reduced thanks to the invention.

  Correspondingly, the invention provides analysis filtering devices, synthesis filtering, coding and decoding, which comprise

  means adapted to bring the preceding characteristics.

  The invention also relates to a digital device including the

  previous device or means for implementing the previous method.

  The advantages of the device and the digital device are identical to those

previously exposed.

  A means of storing information, readable by a computer or by a microprocessor, integrated or not in the device, possibly removable,

  stores a program implementing the method according to the invention.

  The characteristics and advantages of the present invention will appear more clearly on reading a preferred embodiment illustrated by the attached drawings, in which: - Figure 1 schematically shows a data processing device according to the invention , - Figure 2 schematically shows another data processing device according to the invention, - Figure 3 shows an embodiment of the data processing device according to the invention, Figure 4 shows an embodiment of transformation circuit included in the data processing device of FIG. 1, - FIG. 5 is an image to be coded according to the invention, - FIG. 6 is a transformed image according to the invention, - FIG. 7 is a trellis representing the operation of a transformation circuit according to the invention, - Figure 8 is a trellis representing the operation of the reverse transformation circuit from that of FIG. 7, - FIG. 9 is a trellis representing the operation of a transformation circuit according to the invention, - FIG. 10 is a trellis representing the operation of the reverse transformation circuit from that of FIG. 9, - Figure 11 is a lattice representing the operation of a transformation circuit according to the invention, - Figure 12 is a lattice representing the operation of the reverse transformation circuit from that of Figure 11, - Figure 13 is a lattice representing the operation of a transformation circuit according to the invention, - Figure 14 is a trellis representing the operation of the reverse transformation circuit from that of Figure 13, - Figure 15 is a coding algorithm according to the present invention, - Figure 16 is a decoding algorithm according to the present invention. According to an embodiment chosen and shown in FIG. 1, a data processing device according to the invention is a data coding device 2 which has an input 24 to which a source is connected

1 of non-coded data.

  The source 1 comprises for example a memory means, such as random access memory, hard disk, floppy disk, compact disc, for memorizing non-coded data, this memory means being associated with a suitable reading means for reading the data there. A way to record

  data in the memory means can also be provided.

  We will consider more particularly below that the data to

  coding are a series of digital samples representing an IM image.

  The source 1 supplies a digital image signal SI to the input of the coding circuit 2. The image signal SI is a series of digital words, for example bytes. Each byte value represents a pixel of the IM image, here at 256 gray levels, or black and white image. The image can be a multispectral image, for example a color image having components in three frequency bands, of the red-green-blue or luminance and chrominance type. Each strip is then treated in a manner analogous to the image

monospectral.

  Means 3 users of coded data are connected at output

coding device 2.

  The user means 3 comprise for example means for storing coded data, and / or means for transmitting

coded data.

  The coding device 2 conventionally comprises, from the input 24, a transformation circuit 21, more particularly concerned with the present invention, and of which several exemplary embodiments will be detailed below. The transformations envisaged here are decompositions into signals of frequency sub-bands of the data signal, so as to

perform a signal analysis.

  The transformation circuit 21 is connected to a quantization circuit 22. The quantization circuit implements a quantification known per se, for example a scalar quantification, or a vector quantization, of samples, or of groups of samples, of signals of sub-bands of

  frequency supplied by circuit 21.

  The circuit 22 is connected to an entropy coding circuit 23, which performs an entropy coding, for example a Huffman coding, or a

  arithmetic coding, of the data quantified by the circuit 22.

  FIG. 2 shows another data processing device according to the invention, in the form of a data decoding device 5

coded by device 2.

  Means 4 users of coded data are connected at the input 54 of the decoding device 5. The means 4 comprise for example coded data memory means, and / or means for receiving the coded data which are adapted to receive the coded data transmitted by the transmission means 3. Means 6 users of decoded data are connected at the output of the decoding device 5. The user means 6 are for example means for viewing images, or means for restoring sounds, in

  depending on the nature of the data processed.

  The decoding device 5 globally performs operations opposite to those of the coding device 2. The device 5 comprises an entropy decoding circuit 51, which performs an entropy decoding corresponding to the coding of the circuit 23. The circuit 51 is connected to a circuit dequantification 52, corresponding to the quantization circuit 22. The circuit 52 is connected to a reverse transformation circuit 53, corresponding to the transformation circuit 21. The reverse transformation circuit 53 is more particularly concerned with the present invention. Several examples of implementation will be detailed below. The transformations envisaged here

  carry out a synthesis of the digital signal, starting from sub-signals

frequency bands.

  The coding device and / or the decoding device can be integrated into a digital device, such as a computer, printer, fax machine, scanner or digital camera, by

example.

  The coding device and the decoding device can be integrated into the same digital camera, for example a digital camera. In this case, the data processing device performs the coding and decoding of the data in a combined manner, as

exposed in the continuation.

  With reference to FIG. 3, an example of a device 10 implementing the invention is described. This device is suitable for transforming a digital signal, and according to the examples developed below, for analyzing it, or for synthesizing it. The device 10 is here a microcomputer comprising a communication bus 101 to which are connected: - a central unit 100, - a read-only memory 102, - a random access memory 103, - a screen 104, - a keyboard 114, - a disk hard 108, - a floppy drive 109 adapted to receive a floppy 110, - an interface 112 for communication with a communication network 113,

  - an input / output card 106 connected to a microphone 111.

  The hard disk 108 stores the programs implementing the invention, which will be described below, as well as the data to be coded and the data coded according to the invention. These programs can also be read on the floppy disk 110, or received via the communication network 113, or else

stored in read-only memory 102.

  More generally, the programs according to the present invention are stored in a storage means. This storage means can be read by a computer or by a microprocessor. This storage means is integrated or not to the device, and can be removable. For example, it may include a magnetic tape, a floppy disk or a CD-ROM (disk

compact with frozen memory).

  When the device is powered up, the programs according to the present invention are transferred into the random access memory 103 which then contains the executable code of the invention and registers containing the variables necessary for implementing the invention. RAM includes a

buffer memory.

  The device 10 can receive data to be coded from a peripheral device 107, such as a digital camera, or a

  scanner, or any other means of acquiring or storing data.

  The device 10 can also receive data to be coded from a remote device, via the communication network 113, and transmit coded data to a remote device, still via the communication network.

communication 113.

  The device 10 can also receive data to be coded from the

  microphone 111. These data are then a sound signal.

  The screen 104 allows a user in particular to view the

  data to be coded, and serves, with the keyboard 114, as a user interface.

  With reference to FIG. 4, the transformation circuit 21, or analysis circuit, is a dyadic decomposition circuit with two levels. The circuit 21 is, in this embodiment, a conventional set of filters, respectively associated with decimators by two, which filter the image signal in two directions, into sub-band signals of high and low spatial frequencies. The relationship between a high pass filter and a low pass filter is determined by the conditions for perfect signal reconstruction. Different examples of filters will be considered below. Note that the vertical and horizontal decomposition filters are not necessarily identical, although in practice this is generally the case. The circuit 21 here comprises two successive analysis blocks for decomposing the image IM

  into subband signals at two resolution levels.

  In general, the resolution of a signal is the number of samples per unit of length used to represent this signal. In the case of an image signal, the resolution of a subband signal is related to the number of samples per unit of length used to represent this subband signal horizontally and vertically. The resolution depends on the number of decimations performed, the decimation factor and the resolution

of the initial image.

  The first analysis block receives the digital image signal SI and applies it to two digital low-pass and high-pass filters 210 and 220 respectively which filter the image signal in a first direction, for example horizontal in the case of 'an image signal. After passing through decimators by two D210 and D220, the resulting filtered signals are respectively applied to two low-pass filters 230 and 250, and high-pass filters 240 and 260, which filter them in a second direction, for example vertical in the case an image signal. Each resulting filtered signal passes through a decimator through two respective D230, D240, D250 and D260. The first block outputs four signals of sub-bands LL1, LH1, HL1 and HH, of

  highest RES1 resolution in decomposition.

  The LL1 subband signal includes the components, or

  samples of low frequency, in both directions, of the image signal.

  The sub-band signal LH1 comprises the components of low frequency in a first direction and of high frequency in a second direction, of the image signal. The sub-band signal HL1 comprises the high frequency components in the first direction and the low frequency components in the second direction. Finally, the sub-band signal HH1 comprises the high-frequency components in the two directions. Each sub-band signal is a set of real samples constructed from the original image, which contains information corresponding to a respectively vertical, horizontal and diagonal orientation of the contours of the image, in a band of given frequency. Each signal from

  sub-band can be compared to an image.

  The sub-band signal LL1 is analyzed by an analysis block analogous to the previous one to supply four sub-band signals LL2, LH2,

  HL2 and HH2 of RES2 resolution level.

  Each of the RES2 resolution subband signals corresponds

  also to an orientation in the image.

  A digital IM image at the output of image source 1 is represented diagrammatically in FIG. 5, while FIG. 6 represents the IMD image resulting from the decomposition of the IM image, into seven sub-bands according to two resolution levels, by circuit 21. The IMD image contains as much information as the original IM image, but the information is

  frequently split according to two levels of resolution.

  Of course, the number of levels of resolution, and consequently of sub-bands, can be chosen differently, for example 10 sub-bands on three levels of resolution, or 13 sub-bands on four levels of resolution, for a bi signal. -dimensional such as an image. The number of sub-bands per resolution level can also be different. In addition, the decomposition may not be dyadic. Analysis and synthesis circuits

  are adapted to the size of the signal processed.

  In FIG. 6, the samples resulting from the transformation are arranged sub-band by sub-band. However, the IMD image can be represented in an equivalent manner according to a so-called interlaced mode, in which the samples of the various sub-band signals are grouped according to their spatial origin in the image. This representation has the advantage that the samples of the transformed image can be calculated on the spot, that is to say that a calculated sample is stored in memory in place of a sample used for its calculation. Note that on-site calculation is not essential

for the present invention.

  In the following, we will focus on interlaced representations. Transformation circuits to obtain an interlaced representation

  are shown as a trellis.

  FIG. 7 is a trellis showing the operation of a transformation circuit which performs a digital signal analysis according to a

  level of resolution, in one dimension.

  A portion of the signal to be transformed, here eleven samples, has been

  represented. It should be noted that each signal sample to be transformed can

  be a sample or may be a series of samples. According to an example, each sample is a line of a digital image. The filtering carried out by trellis is then a vertical filtering of the image. Alternatively, equivalently, the samples are the image columns and filtering is a

horizontal image filtering.

  The transformation circuit includes two associated filters H0 and Hi, low pass and high pass respectively. The filters chosen are the 5/3 filters, which can be represented by their samples: Ho = [- 1 2 6 2 -1] / 8 Hl = [- 1 2 -1] / 2 According to the so-called "lifting" method of Sweldens, the low frequency filter H0 can be expressed as a function of the high frequency filter H1, according to a type relation: Ho = [0 0 1 0 0] + a. [1 0 1] * H1 oo is a coefficient multiplicative, equal to 0.25 for a 5/3 filter, and "*" represents the convolution operation. This type of decomposition is said to be reversible. Consequently, the low frequency samples are calculated at

  from the high frequency samples and the original signal samples.

  In the following, we note: - x2i-1, x2i, x2i + 1, ... the samples of the signal to transform, where i is an integer. - Y2-1, Y2i, Y2i + 1, ... the samples obtained by transformation. The even index samples here are the low frequency samples, and the

  odd index samples are the high frequency samples.

  The index of a sample represents its rank in the ordered sequence

forming the signal.

  The calculations carried out in the transformation circuit are on-site calculations, that is to say that a calculated sample, of given rank, is stored in place of another sample of the same rank having been used for its calculation. In addition, the samples of the signal to be transformed are processed

  in an orderly fashion, in ascending order.

  The first line L1 of the trellis contains the samples {..., x2i, x2i + 1, ..}, where the rank of the samples varies in steps of one, from the original signal. These samples are stored in buffer memory 103 as and when

their usefulness in filtering.

  The second L2 lattice line has the high samples

  frequency {..., Y2i, Y2i + 1, ...}, where the rank of the samples varies in steps of two.

  The high frequency sample Y2i + 1 is obtained by the formula

Y2i + 1 = X2i + 1 - 0.5. (X2i + X2i + 2).

  After its calculation, this sample is stored in buffer memory

  103, in place of the sample of the same rank in the original signal x2i + 1.

  The third L3 lattice line contains the bottom samples

  frequency {..., Y2i, Y2i + 2, ...}, where the rank of the samples varies in steps of two.

  The low frequency sample Y2i is obtained by the formula

Y2i = X2i + 0.25. (Y2i-1 + Y2i + 1).

  After its calculation, this sample is stored in buffer memory

  103, in place of the sample x2i of the same rank in the original signal.

  The result of the transformation of the original signal {..., x2, x2i + l, ...

  by the filters 5/3 is an interlaced signal of the form {........ Y2i, Y2i + 1 .....}, that is

  that is to say comprising a succession of high frequency and low frequency samples. Of course, it is possible to perform similar operations on a different number of samples, on a different number of resolution levels, or to use other filters on one or more of the

resolution.

  In practice, only a maximum predetermined number of samples can be stored in memory 103. It is therefore necessary to cut the signal when this number is reached, to process the samples stored in memory 103, then to start again with the following series of samples. Calculations

  previously presented must be adapted accordingly.

  The inventors have found that the location of the border between two successive series of samples has an influence on the quality of reconstruction of the signal. More particularly, a border placed just after a low frequency sample limits the discontinuities that may appear

  during signal reconstruction.

  Indeed, the input signal is cut by the border F1, placed after the sample x2i, that is to say after the low frequency sample Y2i. Calculations

  previously presented are not affected until the Y2i-1 sample.

  To determine the sample Y2i, only samples up to the index 2i are available, the following samples being "unknown". The calculation of the Y2i sample is adapted so as to remove the branch coming from the Y2i + 1 sample. the sample Y2i is thus determined as a function of the samples Y2i-1 and x2i. To determine the Y2i sample, we can for example

  apply the principle of symmetrical reflection, that is: Y2i = x2i + 0.25. (2 x Y2i-1).

  When the next series of samples is processed, the samples are determined without the F1 border having any influence, i.e. no branch is deleted due to the presence of the F1 border ,

from sample Y2i + 1.

  FIG. 8 is a trellis representing the operation of the reverse transformation circuit, or synthesis circuit, corresponding to the trellis of FIG. 7. The samples to be filtered are here the high and low samples

  interlaced frequency obtained after filtering the analysis of a digital image.

  These samples were possibly modified by another treatment between

analysis and synthesis.

  The first line L10 contains the high frequency samples {....

  Y2i-1, y2i +, ....}, where the rank of the samples varies in steps of two, interlaced with the low frequency samples {... Y2i, Y2i + 2, ...} o the rank of

  samples varies in steps of two.

  The second line L11 includes the samples of even rank {.... x2 ;, X2i + 2, ...}, where the rank of the samples varies in steps of two, of the reconstructed signal. The sample of even rank x2; is obtained by the formula: X2i = Y2i - 0.25. (Y2i-1 + Y2i + 1).

  After its calculation, the sample x2i is stored in buffer memory

  103 in place of the Y2i sample.

  The third line L12 contains the samples of odd rank {....

  x2â1, x2. + 1, ...}, where the rank of the samples varies in steps of two, of the reconstructed signal. The sample of odd rank x2i + 1 is obtained by the formula:

X2i + l = Y2i + 1 + 0.5. (x2i + 2 + X2i).

  After its calculation, the sample x2i +, is stored in buffer memory

  103 in place of the sample Y2i + 1.

  As before, it is necessary to place a border F2 to process the signal by series of samples. The border F2 is placed after a low frequency sample Y2i. In addition, the location of the border F2 depends on that of the border F1, so as to adapt the calculations correspondingly to the analysis. In other words, the border F2 is placed here so as to delete a branch corresponding to the branch deleted in the previous figure, which ensures perfect reconstruction of the signal in

  the absence of treatment between analysis and synthesis.

  The calculation of x2i is thus adapted to the border F2, and the sample x2i only depends on the samples Y2i-1 and Y2i. The other samples are not affected. The reconstructed sample according to x2i + 1 depends in particular on the sample x2i, which limits the discontinuity at the border in the reconstructed signal. FIG. 9 is a trellis showing the operation of another transformation circuit which performs a digital signal analysis according to a level of resolution, in one dimension. The transformation circuit includes

  two associated filters H0 and H., low pass and high pass respectively.

  The input samples are processed in an orderly fashion, in ascending order. The filters chosen are 13/7 filters, for example having as

  low pass filter H0 and high pass filter H1 the following filters.

  Ho = [-1 0 18 -16 -63 144 348 144 -63 -16 18 0 -1] / 512

H1 = [1 0 -9 16 -9 0 1] / 16

  By performing calculations similar to those previously

  presented, the following relationships are obtained between the lattice samples.

  The first line L20 of the trellis contains the samples to be filtered {..

  x2i, x2i + 1, ....}, where the rank of the samples varies in steps of one. These samples are stored in buffer memory 103 as and when they are useful for

filtering.

  The second line L21 contains the high frequency samples {.., Y2i1, Y2i + 1, ...}, where the rank of the samples varies in steps of two, obtained by the formula: Y2i + 1 = x2i + 1 - (- x2i-2 + 9.X2i + 9.x2i + 2 - x2i + 4) / 16 After its calculation, the sample Y2i + 1 is stored in memory

  buffer, in place of the same rank original signal sample.

  The third line L22 contains the low frequency samples {.., Y2i, Y2i + 2, ...}, where the rank of the samples varies in steps of two, obtained by the formula: Y2i = x2i + (-Y2i-3 + 9.Y2i-1 + 9.Y2i + 1 - Y2i + 3) / 32 After its calculation, the sample Y2i is stored in buffer memory,

  in place of the original signal sample of the same rank.

  A border F3 is placed after the low frequency sample Y2i. The border F3 causes a modification of the calculation of the samples Y2i2, Y2i-1 and Y2i, which consists in removing the branches cut by the border F3, since the samples placed after the border are unknown during the calculation of the samples placed before the border. Thus, the sample Y2i-1 no longer depends on the sample x2i + 2, the samples Y2i-2 and Y2i no longer depend on

  the Y2i + 1 sample and the Y2i sample no longer depend on the Y2i + 3 sample.

  To the right of the border F3, the calculations are not modified by the

presence of the border.

  FIG. 10 is a trellis representing the operation of the reverse transformation circuit, or synthesis circuit corresponding to the trellis of the

figure 9.

  The first line L30 of the trellis contains the low frequency samples {..., Y2i, Y2i + 2, ...}, where the rank of the samples varies in steps of two, interleaved with the high frequency samples {..., Y2i -1, Y2i + 1, ...}, where the rank

  samples vary in steps of two, obtained by analysis filtering.

  The second line L31 of the trellis comprises the samples {..., x2i, X2i + 2, ...} of even rank of the reconstructed signal obtained by the formula:

  X2i = Y2i - (-Y2i-3 + 9.Y2i-1 + 9.Y2i + 1 - Y2i-3) / 32.

  After its calculation, the sample x2i is stored in the buffer memory, in place of the intermediate sample of the same rank. The third line L32 of the trellis comprises the samples {..., x2i.1, x2i + l ....} of odd rank of the reconstructed signal obtained by the formula:

  X2i + l = Y2i + 1 + (-x2i-2 + + 9.x2i + 2 - x2i + 4) / l 6.

  After its calculation, the sample x2i + 1 is stored in memory

  buffer, in place of the intermediate sample of the same rank.

  As before, a border F4 is placed after a low frequency sample Y2i. This causes a modification of the calculation of samples x2i-2, x2i-1 and x2i, which consists in removing the branches cut by the border F4. Thus, the sample x2i-2 no longer depends on the sample Y2i + 1, the sample x2- no longer depends on the sample x2i + 2 and the sample x2j does not

  no longer depends on samples Y2i + l and Y2i + 3.

  To the right of the border F4, the calculations are not modified by the

presence of the border.

  The reconstructed signal does not have any discontinuity, because the

  samples of the reconstructed signal are all connected to their neighbors.

  FIG. 11 is a lattice representing the operation of another transformation circuit which performs an analysis (dyadic decomposition) of digital signal according to three levels of resolution, in one dimension. The transformation circuit has two associated filters H0 and Hi, respectively

low pass and high pass.

  The input samples are processed in an orderly fashion, in ascending order. As in Figure 7, the filters chosen are 5/3 filters. By performing calculations analogous to those previously presented, we obtain

  the following relationships between lattice samples.

  The first line L40 of the trellis contains the samples to be filtered {...

  x2i, x2i + 1, ...}, where the rank of the samples varies in steps of one. These samples are stored in buffer memory 103 as and when they are useful for

filtering.

  The second line L41 of the trellis contains the high frequency samples of first resolution level {..., t2i-1, t2i + 1, ...}, where the rank of the samples varies in steps of two, obtained by the formula:

t2i + 1 = X2i + 1 - 0.5. (X2i + X2i + 2) -

  After its calculation, the sample t2i + 1 is stored in the buffer memory,

  instead of the sample of the same rank in the original signal.

  The third line L42 of the trellis comprises low frequency samples of first level of resolution {..., t2i2, t2i, ...}, where the rank of the samples varies in steps of two, obtained by the formula t2i = X2i + 0 , 25. (T2i-1 + t2i + 1) À After its calculation, the sample t2i is stored in buffer memory,

  instead of the sample of the same rank in the original signal.

  The fourth line L43 of the trellis comprises the high frequency samples of second resolution level {..., v2i-2, v2i + 2, ...}, where the rank of the samples varies in steps of four, obtained by the formula: v2i-2 = t2i-2 - 0.5. (t2i + t2i-4) After its calculation, the v2i-2 sample is stored in buffer memory, instead of the first level low frequency sample of

same rank.

  The fifth line L44 of the trellis contains the low frequency samples of second resolution level {..., v2i-4, v2i, ...}, where the rank of the samples varies in steps of four, obtained by the formula v2i = t2i + 0.25. (V2i-2 + V2i + 2) After its calculation, the sample v2i is stored in buffer memory,

  in place of the first level low frequency sample of the same rank.

  The sixth line L45 of the trellis comprises the high frequency samples of third resolution level {..., Y2i-4, Y2i + 4, ..}, where the rank of the samples varies in steps of eight, obtained by the formula: Y2i -4 = v2i-4 - 0.5. (V2i + V2i-8) 4 After its calculation, the sample Y2i-4 is memorized in buffer memory, in place of the low frequency sample of second level of

same rank.

  The seventh line L46 of the trellis contains the low-level third-level samples {..., Y2i, Y2i + 8, ...}, where the rank of the samples varies in steps of eight, obtained by the formula Y2i = v2i + 0 , 25. (y2i-4 + Y2i + 4) After its calculation, the sample Y2i is stored in buffer memory,

  in place of the second level low frequency sample of the same rank.

  As before, only a maximum predetermined number of samples can be stored in memory 103. It is therefore necessary to cut the signal when this number is reached, to process the samples stored in memory 103, then to start again with the following series

samples.

  The inventors have also noted here that the location of the border between two successive series of samples has an influence on the quality of reconstruction of the signal. More particularly, a border placed just after a low frequency sample of lower resolution level in the decomposition limits the discontinuities that may appear during the

signal reconstruction.

  Indeed, the input signal is cut by the border F5, placed after the sample x2i, that is to say after the low frequency sample of lower level Y2i. The calculations previously presented are not affected until

the sample of index 2i-1.

  To determine the samples t2i, v2i and Y2i, only samples up to the index 2i are available. The calculations of samples t2i, V2i and Y2i is adapted so as to remove the branches crossing the border F5. For example, the sample Y2i is thus determined only as a function of the

samples Y2i-4 and v2i.

  When the next series of samples is processed, the samples are determined without the F5 border having any influence, i.e. no branch is deleted due to the presence of the F5 border ,

  from the sample of index 2i + 1.

  FIG. 12 is a trellis representing the operation of the reverse transformation circuit, or synthesis circuit corresponding to the trellis of the

figure 11.

  The first line L50 of the trellis comprises the low frequency samples of third level of resolution {..., Y2i, Y2i + 8,}, where the rank of the samples varies in steps of eight and the high frequency samples of third level of resolution { ..., Y2i-4, Y2i + 4, ....}, o the rank of the samples

varies in steps of eight.

  The second line L51 of the trellis includes the samples of even rank {..., v2i-8, v2, ...}, where the rank of the samples varies in steps of eight, of the reconstructed low frequency signal, of second resolution level , obtained by

  formula: v2i = Y2i - 0.25. (y2i4 + Y2i + 4).

  After its calculation, the sample v2i is stored in buffer memory,

  instead of the same rank sample Y2i.

  The third line L52 of the trellis comprises the high frequency samples of second resolution level {..., v2i-2, v2i + 2, ...}, where the rank of the samples varies in steps of four, and the rank samples odd {..., v2i-4, v2 + 4, ...}, where the rank of the samples varies in steps of eight, of the reconstructed low frequency signal, of second resolution level, obtained by the formula: V2i-4 = Y2i-4 + 0.5. (V2i-8 + V2i) After its calculation, the sample v2i-4 is stored in memory

  buffer, in place of the same row sample Y2i-4.

  The fourth line L53 of the trellis includes the samples of even rank {..., t2i-4, t2i, ...}, where the rank of the samples varies in steps of four, of the reconstructed low frequency signal, of first resolution level , obtained by the formula: t2i = v2i- 0.25. (V2i-2 + V2i + 2) After its calculation, the sample t2i is stored in buffer memory,

* in place of the v2i sample of the same rank.

  The fifth line L54 of the trellis contains the first level high frequency samples {..., t2i-1, t2i + 1 ,, ...}, where the rank of the samples varies in steps of two, and the samples of odd rank {..., t2i-2, t2i + 2, ...}, where the rank of the samples varies in steps of four, from the reconstructed low-frequency signal, of first resolution level, obtained by the formula: t2 i-2 = V2i-2 + 0.5. (T2i-4 + t2i) À After its calculation, the sample t2i-2 is stored in buffer memory,

  in place of the v2i-2 sample of the same rank.

  The sixth line L55 of the trellis contains the samples of even rank {..., X2i, X2i + 2, ...} of the reconstructed signal obtained by the formula: X2i = t2i - 0.25. (T2i-1 + t2i + 1) After its calculation, the sample x2i is stored in the buffer memory,

  instead of the sample t2i of the same rank.

  The seventh line L56 of the lattice the odd-ranking samples {.., X2i-1, x2i + 1, ...} of the reconstructed signal obtained by the formula: X2i + 1 = t2i + 1 + 0.5. (X2i + X2i + 2) À After its calculation, the sample x2i + l is stored in memory

  buffer, in place of the sample t2i + l of the same rank.

  As before, a border F6 is placed after the low-frequency sample of lower level Y2i. The calculations of the samples v2i, t2i and x2i are adapted so as to remove, for each, the

  branch cut by the F6 border.

  Calculation of samples up to the index 2i-1, and from the index

  2i + 1 are not affected by the F6 border.

  The coefficients calculated in the second step of each level of resolution, that is to say here the coefficients calculated and represented in lines L52, L54 and L56 are connected by branches to their neighbors, none of these branches being deleted due to the presence of the F6 border. Thus, there is no discontinuity in the reconstructed signal due to the presence of the

border F6.

  Figures 13 and 14 are lattices identical respectively to those of Figures 11 and 12, except that the borders F7 and F8 are placed after a low frequency sample v2i-4 which does not belong at most

  low level of resolution, but at the next higher level.

  In FIG. 13, the lines L40 to L46 are identical to those of FIG. 11. The calculations of the samples t2i-4, v2i-4 and Y2i-4 are adapted to the presence of the border F7, so as not to hold counts the samples placed after the F7 border, i.e. here the samples with index greater than or equal to 2i-3. Likewise, in FIG. 14, the lines L50 to L56 are identical to those of FIG. 12. The border F8 is placed so as to cause modifications corresponding to those of the border F7. The calculations of samples v2-4, t2i-4 and x2i-4 are adapted to the presence of the border F8, so as to not take into account the samples placed after the border F8,

  either here the samples of index greater than or equal to 2i-3.

  The inventors have found that the signal reconstructed after analysis and synthesis according to the filters of FIGS. 13 and 14 has a little more distortion than the signal reconstructed after analysis and synthesis according to the filters

Figures 1 1 and 12.

  This is due to the fact that the samples calculated and represented on line L52 have a suppressed branch, unlike in the case of FIG. 12, this

  which generates distortions in the reconstructed signal.

  Figure 15 shows a signal coding algorithm

  digital according to the present invention.

  This algorithm, implemented in the coding device, comprises

steps E1 to E5.

  The coding algorithm can be stored in whole or in part in any information storage means capable of cooperating with the microprocessor. This storage means can be read by a computer or by a microprocessor. This storage means is integrated or not to the device, and can be removable. For example, it may include a magnetic strip, a

  floppy disk or CD-ROM (compact disk with frozen memory).

  Step E1 is the reading of a series of signal samples to be coded.

  The next step E2 is the transformation of the series of samples read. This transformation is for example an analysis filtering, as

previously described.

  Step E2 is followed by step E3, in which the series of samples

filtered is quantified.

  The next step E4 is the entropy coding of the data

previously quantified.

  Steps E1 to E4 are repeated for all series

samples of the signal to be encoded.

  Step E4 is followed by step E5 which is the use of coded data, for example their transmission. It should be noted that the series of coded samples can be transmitted as and when they are

  training, or when all signal series have been coded.

  Figure 16 shows a signal decoding algorithm

  digital according to the present invention.

  This algorithm, implemented in the decoding device,

includes steps El10 to E14.

  The decoding algorithm can be stored in whole or in part in any information storage means capable of cooperating with the microprocessor. This storage means can be read by a computer or by a microprocessor. This storage means is integrated or not to the device, and can be removable. For example, it may include a magnetic strip, a

  floppy disk or CD-ROM (compact disk with frozen memory).

  Step E10 is the reading of a series of samples to be decoded.

  The next step El is an entropy decoding of the data

previously read.

  The next step E12 is a dequantification of the data

  decoded in the previous step.

  The dequantized data then undergo a reverse transformation in step E13, for example a synthesis filtering, as

previously described.

  Steps E10 to E13 are repeated for all the series of samples to be decoded. Step E13 is followed by step E14 of using the data

  decoded, for example their display, in the case of an image signal.

  Of course, the present invention is in no way limited to the embodiments described and shown, but includes, on the contrary,

  any variant within the reach of the skilled person.

  In particular, the invention is not limited to the field of digital signal coding, but applies to all fields of signal processing, when it is sought to minimize the distortions of a transformed signal and then

rebuilt.

Claims (20)

  1. A digital signal analysis filtering method comprising original samples representative of physical quantities, original samples (x2) of the digital signal being transformed into high and low frequency samples (Y2i, Y2i + 1), on at least one resolution level, a high frequency sample of a given resolution level being calculated by an original sample function, a low frequency sample of the given resolution level being calculated by a sample function source and high frequency samples of the given resolution level, the low frequency samples of the given level then serving as original samples for a possible lower resolution level, characterized in that: the signal is processed ( E2) by successive series of samples, the calculations carried out on any series not taking into account the samples of a following series, and in that any series ends   by a low frequency sample (t2i-4, v2i-4, Y2i).   2. Digital signal synthesis filtering method comprising interleaved samples of high and low frequency respectively, transformed samples (x2i) being formed from the high and low frequency samples (Y2i, Y2i + 1), on at least one level resolution, first transformed samples of a given level of resolution being calculated by a function of samples of high and low frequency of samples, second samples of the given level of resolution being calculated by a function of samples of high and low frequency and first transformed samples of the given resolution level, the transformed samples of the given level then serving as low frequency samples for a possible higher resolution level, characterized in that: the signal is processed (E13) by successive series d '' samples, the calculations performed on any series not taking into account mpte the samples of a following series, and that any series ends   by a low frequency sample (t2i-4, v2i-4, Y2i).   3. A digital signal coding method comprising original samples representative of physical quantities, the coding comprising: analysis filtering (E2) of the digital signal according to which original samples (x2;) of the digital signal are transformed in high and low frequency samples (Y2i, Y2i + 1), on at least one level of resolution, a high frequency sample of a given level of resolution being calculated by an original sample function, a sample of low frequency of the given resolution level being calculated by a function of original samples and high frequency samples of the given resolution level, the low frequency samples of the given level then serving as original samples for a possible lower resolution level, - quantification (E3) of previously filtered samples, and - entropy coding (E4) of previously quantified samples és, characterized in that: - the signal is processed by successive series of samples, the calculations carried out on any series not taking into account the samples of a following series, and in that the arbitrary series ends in a   low frequency sample (t2i-4, v2i-4, y2i).   4. A method of decoding a coded digital signal according to the method of claim 3, comprising: - an entropy decoding (Ell) of coded samples of the coded digital signal, - a dequantification (E12) of the previously decoded samples, - a filtering of synthesis (E13) of the previously dequantized samples, comprising interleaved samples of high and low frequency respectively, transformed samples (x2i) being formed from the high and low frequency samples (Y2i, Y2i + 1), on at least one level of resolution, first transformed samples of a given level of resolution being calculated by a function of high and low frequency samples, second samples of the given level of resolution being calculated by a function of high and low samples frequency and first samples transformed from the given resolution level, the samples transformed més of the given level then serving as low frequency samples for a possible higher resolution level, characterized in that - the signal is processed by successive series of samples, the calculations carried out on any series not taking into account the samples d 'a following series, and in that the arbitrary series ends with a   low frequency sample (t2i-4, v2i-4, Y2i).   5. Method according to claim 2 or 4, characterized in that each series of samples ends after a last sample in a series   determined during an analysis filtering according to claim 1.   6. Method according to any one of claims 1 to 5,   characterized in that the random series ends with a sample of   low frequency of the lowest resolution level (Y2i).   7. Method according to any one of claims 1 to 6,   characterized in that the digital signal is an image signal (IM) and in that   that the original samples are lines from the image.   8. Method according to any one of claims 1 to 6,   characterized in that the digital signal is an image signal (IM) and in that   that the original samples are columns of the image.   9. A digital signal analysis filtering device comprising original samples representative of physical quantities, the device comprising means (21) for transforming the original samples (x2i) of the digital signal into high and low frequency samples (Y2i, Y2i + 1), on at least one resolution level, a high frequency sample of a given resolution level being calculated by an original sample function, a low frequency sample of the given resolution level being calculated by a function of original samples and high frequency samples of the given resolution level, the low frequency samples of the given level then serving as original samples for a possible lower resolution level, characterized in what: the transformation means (21) are adapted to process the signal by successive series of samples, to perform the calculations on a s series one by not taking into account the samples of a next series, and finish the one set by a low frequency sample (t2i-4, v2-4, y2i).   10. A digital signal synthesis filtering device comprising interleaved samples of high and low frequency respectively, the device comprising means (53) of reverse transformation adapted to form transformed samples (x2i) from high and low frequency samples ( Y2i, y2i + 1), on at least one resolution level, first transformed samples of a given resolution level being calculated by a function of samples of high and low frequency of samples, second samples of the resolution level given being calculated by a function of high and low frequency samples and first transformed samples of the given resolution level, the transformed samples of the given level then serving as low frequency samples for a possible higher resolution level, characterized in that : the transformation means (53) are adapted to process the sig nal by successive series of samples, to carry out the calculations on any series by not taking into account the samples of a following series, and to end any series by a sample of low frequency (t2i-4, V2i-4 , Y2i). 11. A digital signal coding device comprising original samples representative of physical quantities, the device comprising: - means (21) for filtering analysis of the digital signal to transform original samples (x2i) of the digital signal in high and low frequency samples (Y2i, Y2i + 1), on at least one resolution level, a high frequency sample of a given resolution level being calculated by an original sample function, a low sample frequency of the given resolution level being calculated by a function of original samples and high frequency samples of the given resolution level, the low frequency samples of the given level then serving as original samples for a possible level of lower resolution, - means (22) for quantifying the previously filtered samples, and - means (23) for entropy coding of the samples previously quantified ons, characterized in that: - the device is adapted to process the signal by successive series of samples, to carry out the calculations on any series by not taking into account the samples of a following series, and to complete series   any by a low frequency sample (t2i-4, V2i-4, Y2i).   12. Device for decoding a coded digital signal according to the device of claim 11, comprising: - means (51) for entropy decoding of coded samples of the coded digital signal, - means (52) for dequantizing the previously decoded samples, - Means (53) for synthesis synthesis of the previously dequantized samples, these samples comprising interleaved samples of high and low frequency respectively, to form transformed samples (x2i) from high and low frequency samples (Y2i, Y2i + 1 ), on at least one resolution level, first transformed samples of a given resolution level being calculated by a function of samples of high and low frequency of samples, second samples of the given resolution level being calculated by a function of high and low frequency samples and first transformed samples of the level of given resolution, the transformed samples of the given level then serving as low frequency samples for a possible higher resolution level, characterized in that - the device is adapted to process the signal by successive series of samples, to perform the calculations on a any series by not taking into account the samples of a following series, and ending the series   any by a low frequency sample (t2i-4, v2i-4, Y2i).   13. Device according to claim 10 or 12, characterized in that it is adapted to complete each series of samples after a last sample   of a series determined during an analysis filtering according to claim 1.   14. Device according to any one of claims 9 to 13,   characterized in that it is suitable for ending any series with a   low frequency sample of the lowest resolution level (Y2i).   15. Device according to any one of claims 9 to 14,   characterized in that it is suitable for processing a digital signal which is a signal   image (IM) and original samples that are lines of the image.   16. Device according to any one of claims 9 to 14,   characterized in that it is suitable for processing a digital signal which is a signal   image (IM) and original samples that are columns of the image.   17. Device according to claim 9 or 10, characterized in that the transformation means are incorporated in: - a microprocessor (100), - a read only memory (102) comprising a program for filtering the signal, and - a random access memory ( 103) with registers adapted to   save variables modified during the execution of said program.   18. Device according to claim 1 1 or 12, characterized in that the filtering means are incorporated in - a microprocessor (100), - a read only memory (102) comprising a program for filtering the signal, and a random access memory (103 ) with registers adapted to   save variables modified during the execution of said program.   19. Digital apparatus (10) including means of implementation   of the method according to any one of claims 1 to 8.   20. Digital apparatus (10) including the device according to one   any of claims 9 to 18.