EP1454297A1

EP1454297A1 - Noise reduction in a digital image by factorial analysis of correspondences

Info

Publication number: EP1454297A1
Application number: EP02804609A
Authority: EP
Inventors: Pascal Hannequin
Original assignee: Individual
Current assignee: Individual
Priority date: 2001-12-12
Filing date: 2002-12-12
Publication date: 2004-09-08
Also published as: US20050036703A1; FR2833445B1; US7376283B2; FR2833445A1; CA2469915A1; WO2003050760A1

Abstract

The invention concerns a method which consists in processing in a central unit (4) the digitized image (1) obtained by sensing noisy radiation. The image (1) is considered as a table of pixel intensity values, which is broken down into p elementary tables of n pixels so as to subsequently order them into a processing table with p lines of n columns; applying to said table a factorial analysis method, to deduce therefrom the n significant factors; then reconstituting a reconstructed processing table taking into account the most significant factors, and in deducing therefrom a reconstituted image wherein the high-frequency noise is reduced, maintaining a satisfactory contrast.

Description

NOISE REDUCTION IN A DIGITAL IMAGE BY FACTOR CORRESPONDENCE ANALYSIS

TECHNICAL FIELD OF THE INVENTION The present invention relates to methods and devices for filtering digital images, in particular methods and devices for eliminating noise in a digital image.

Some images are very noisy, which reduces readability. Such is the case, for example, of images obtained from low level signals, in which the useful signals are strongly disturbed by parasites and other physical phenomena which alter the transmission of the signals.

This is also the case with certain medical imaging images, such as scintigraphic images. The nuclear medicine scintigraphy technique involves injecting patients with biological molecules labeled with gamma-emitting radioactive isotopes. Gamma photons are detected using a gamma camera.

Gamma photons _. are emitted randomly by emitting particles injected into the human body. The signals received depend on the one hand on the quantity of emissive particles in a given area, and on the other hand on the emission hazards of each particle. In a scintigraphic image, which is the image of the distribution of gamma photons coming from an organism, each element of the image or pixel is an integer which is the number of particles, i.e. the number of photons detected in front of it. We see that these integer values are distributed around an average value, according to Poisson's law.

The distribution of Poisson's law follows the formula: μ ^k e ^{~ μ}

Pr (X = k) = k! Pr (X = k) is the probability for the pixel X to take the value k. μ is the mean value of the distribution. Figure 1 gives an example of a Poisson distribution for an average μ = 5.

Another distribution case according to Poisson's law is the distribution of X photons such as those used in CT scan which consists of visualizing the anatomical structures of an organism using the differences in attenuation of X-rays by biological tissues.

In all cases, the images are tainted with fish noise, resulting from the random nature of the emissions, and this noise is of relative importance the greater the smaller the number of events detected. Indeed, the relative error of the measurement is given by the formula: Relative error = [(variance) (X)] ¹² / mean (X)] = μ / μ = 1 / Vμ The relative error therefore varies in direction inverse of the number of events detected.

To improve the readability of an image, we are therefore naturally led to reduce noise, and for this to increase the number of events detected. A first way is to acquire the images for a longer time. But it can be difficult when the subject is moving, for example in radiology because of respiratory and cardiac movements. In addition, the increase in acquisition times immobilizes the detection devices longer, which poses significant scheduling problems in medical imaging.

A second way to increase the number of photons detected is to increase the flux of the particles. In medical imaging, this involves increasing the radioactive dose injected or the flow of X photons. But this will increase the radiation dose received by the patient by the same amount, which is in contradiction with the principles of radiation protection.

Finally, one can imagine using more efficient detection devices, but this immediately poses cost problems.

To illustrate the influence of the increase in the number of photons detected on the quality of the image, a real scintigraphic image of a subject has been reproduced in FIG. 2, obtained by using the signals received for three different durations: l image on the left corresponds to a reception for one minute, the image in the middle corresponds to a reception for five minutes, and the image on the right corresponds to a reception for ten minutes. The quality of the image on the right is much higher.

It is understood that the fish noise consists of a random variation between a pixel and the adjacent pixels, a variation which is not linked to the actual difference in concentration of emissive particles between the area facing the pixel considered and the areas facing the adjacent pixels. It is thus a high frequency noise, that is to say introducing sudden variations from one pixel to another in the sequence of pixels of an image.

As it is often very difficult to increase the number of photons detected, the invention proposes to reduce the high frequency noise contained in an image by the use of a particular filtering device. It has already been proposed to filter the images, in order to reduce the influence of noise. Many filters have been proposed.

The simplest and best known filter is to replace the value of each pixel by the average of the values of the adjacent pixels. The Gaussian filter has also been proposed, consisting in giving a weight of Gaussian spatial distribution to the different neighboring pixels, and by replacing the central pixel by a linear combination of the neighboring pixels.

An example is described in document WO 01/72032, which defines particular coefficients allowing both filtering, and preserving if possible a certain contrast of the image.

This document also expresses the problem of all weighted or unweighted filters: all these filters improve the signal / noise ratio, but at the cost of a sharp degradation in spatial resolution and image contrast. Indeed, it is easily conceivable that a filter carrying out a weighted average between several neighboring pixels necessarily reduces the sudden variations in intensity between the neighboring pixels, and therefore reduces the effects of contrast. By way of example, FIG. 3 illustrates the processing of a real scintigraphic image by two filters: the view on the left is the raw unfiltered image; the middle view is 1 image filtered by a 3 x 3 weighted filter; the right view is the image filtered by a 3 x 3 median filter, which therefore replaces each pixel with the median of the adjacent pixels. We can see, on the filtered images, that the contours are not very sharp, due to a reduction in spatial resolution and contrast.

It has also been proposed to filter images by multivariate statistical analysis methods applied to an array of numbers each expressing the degree of brightness of a corresponding pixel in a digitized image. Document XP 002212651 AEBERSOLD, STADELMANN,

ROUVIERE describes a processing of images from electron microscopes. This processing is carried out by means of a factorial analysis of correspondences, applied to a table consisting of the pixels of the digitized image. The analysis is applied to the entire digitized image, by searching on this entire image for the most representative correspondence factors of the image, that is to say those which correspond to the largest eigenvalues, then by reconstructing the image from these representative factors alone. If in theory the method makes it possible to obtain good quality filtering of a given image, in practice it does not make it possible to adapt the filtering to the structure of the image to be filtered, so that the result remains disappointing.

Document XP 001074312 HANNEQUIN, LIEHN, VALEYRE, proposes to apply the factorial analysis of correspondences to a series of whole scintigraphy images, and suggests using the likelihood ratio test to determine the correspondence factors to be used for reconstruct the series of images. The method is applied again to all of the images. The filtering result is slightly improved, but remains disappointing for certain image structures to be filtered.

The same difficulties are found in documents XP 008007773 and XP 008007666, which apply statistical processing to the whole of an image.

It ^'is therefore a need for a more effective filtering device, for removing high frequency noise without substantially reducing the resolution or contrast of one image. A problem common to all filtering devices is the difficulty of adapting the filtering to the structure of the image to be filtered. Indeed, the images do not all have the same structure, this structure differing depending on the subject observed. It appears that the filters can generally be well suited to a particular image, but are then poorly suited to very different images. Attempts have been made to adapt the filters according to the variations of the pixels, but these tests are not satisfactory. STATEMENT OF THE INVENTION

The object of the present invention is therefore to allow efficient filtering, producing good quality images, using particularly inexpensive means.

According to one particularly advantageous embodiment, the invention therefore proposes to adapt the filtering not only to the general structure of an image, but also and above all to the individual structure of elementary parts of the image to be processed. . It is understood that this can thus significantly improve the contrast of the image. In addition, according to the invention, this adaptation is preferably automatic, making it possible to reduce the loss of information resulting from filtering as much as possible.

To achieve these and other aims, the invention provides a method of processing a digitized image consisting of a table T of numbers X (i _j j each expressing the degree of brightness of a pixel of rank i, j corresponding (for example the number of particles detected in the corresponding pixel), the method comprising the reduction of high frequency noise (for example a statistical fish noise) by the following steps: a) decomposing the table T into a continuous sequence of p elementary arrays of the same dimension each having n pixels, b) order the data of the sequence of elementary arrays into a processing table X of p rows and n columns, each row i being formed of the ordered sequence of pixels of the elementary array of rank i, d) perform on the treatment table X a multivariate analysis statistical treatment, considering that the n columns are the variables, in order to extract the n representative factors therefrom, f) generate a reconstructed treatment table XR of numbers xr _{(i; j} j using only the first q representative factors and restoring the absolute brightness degrees, then generating a reconstituted table TR constituting the reconstituted digitized image in which the high frequency noise has thus been reduced, during step f), the reconstituted treatment table XR is reconstituted by independently reconstructing each line i taking into account only the factors having a significant weight with the line i.

In the present description and in the claims, the expression “statistical processing of multivariate analysis” is used to generally designate all the methods of statistical analysis such as in particular principal component analysis with or without normalization, factor analysis with or without normalization, factor analysis of correspondences. Thanks to line by line reconstruction, the invention adapts the filtering to each subset of the image, which considerably improves the result obtained.

According to an advantageous embodiment, the method uses a factorial correspondence analysis method, according to which: dl) the transposed matrix XN ^T is calculated, d2) the square matrix is calculated by the product of the normalized matrix XN and its transposed XN ^T , d3) we diagonalize the square matrix XN ^T XN to extract the n eigenvectors u _k (k from 1 to n) associated with the n eigenvalues vp _k , d4) we calculate the coordinates of the p lines of the matrix normalized XN on the n eigenvectors, d6) we calculate the coordinates of the n columns on the n eigenvectors.

It can advantageously be provided that: - during a step d5) the square cosines of the lines on the n factor axes are calculated,

- the square cosines are used as a test of the weight of the representative factors. In this case, after step b), it is advantageously possible to provide for a normalization step c) in order to obtain a normalized matrix XN in which each element xn.i _j of row i and of column j is weighted by a TN transform using the mean. of the values of the elements of line i and the average of the elements of column j, step during which: cl) the sum fi of each line of the processing table X is calculated, c2) the sum f _j of each is calculated column of the treatment table X, c3) we calculate the total sum f _tot of the table, c4) we use a normalization transform consisting in replacing each element xi _j of the table by the normalized value equal to Xi _j divided by the product of the roots squares of f _± and f _j .

According to an advantageous embodiment, the invention provides a method allowing one self-adaptation of the reconstruction, in order to best eliminate the high frequency noise without affecting the quality of the image. The means used is to keep only the variance of the signal by eliminating the variance of the noise. For this, according to the invention, the reconstruction of a line of the reconstructed table XR is stopped as soon as a sufficient number of factors has been used so that the variance of the reconstructed line is greater than the variance of the initial signal from which one subtracted the estimated variance of the noise.

The test applies particularly well for example to the processing of a fish noise image. In this case, a property of Poisson's law is that its mean is equal to its variance: variance (X) = mean (X) = μ

It follows that a good estimate of the variance of the noise consists in calculating the average of the signals of line i. According to another aspect, the invention provides a device for processing digital images, comprising a memory, a calculation unit, an input-output device for receiving the data constituting the digital image to be processed, display means. and / or printing to view the processed image, and a program stored in memory and suitable for implementing the method as defined above.

The invention applies in particular to a medical imaging installation comprising such a device. SUMMARY DESCRIPTION OF THE DRAWINGS

Other objects, characteristics and advantages of the present invention will emerge from the following description of particular embodiments, given in relation to the attached figures, among which: - Figure 1 illustrates a Poisson distribution of average 5; FIG. 2 illustrates the improvement of an image during the increase in the duration of observation of a fish phenomenon;

- Figure 3 illustrates the results obtained by weighted or median filters of the prior art;

- Figure 4 illustrates the result that can be obtained with a filter according to an embodiment of one invention;

- Figure 5 illustrates the main steps of a filtering method according to the present invention; - Figure 6 illustrates a shift principle used to limit side effects according to the method of one invention; and

- Figure 7 schematically illustrates an imaging installation incorporating an image processing device according to the invention.

DESCRIPTION OF THE PREFERRED EMBODIMENTS First of all, we will consider FIG. 7 where we schematically illustrated a medical imaging installation comprising a gamma ray sensor 1 such as a gamma camera moving in two directions facing the subject 2 to be observed, and capturing the gamma rays 3 coming from the radio-emissive particles previously injected into the patient's body 2. The gamma ray sensor 1 sends to a computing unit 4 the sequence of image signals of the photons received on each elementary area or sensor pixel gamma ray 1, the calculating unit 4 memorizing in a memory 5 the numbers of photons of each pixel, corresponding to the intensity of the pixel. We thus find in memory 5 a digitized image consisting of a table T of numbers x (i, j) each expressing the number of detected photons (or degree of brightness) of a pixel of line i and of column j of the observed area 1. The installation further comprises, according to the invention, a program stored in memory 5 and making it possible to control the computing unit 4 to filter the image thus scanned and to produce on a display device or printing 6 a filtered image of good quality and from which the high frequency noise has been extracted.

We will now describe an image filtering method according to an embodiment of the present invention, in relation to FIG. 5. We find the table T, constituting the digitized image.

In practice, scanned images contain a large number of pixels. For the simplicity of the presentation, we consider an image constituted by 8 x 8 pixels, of square shape, each pixel being illustrated by a small square. The first operation a) of the noise reduction method according to the invention consists in decomposing the table T into a continuous series of p elementary tables of the same dimension each having n pixels. In the example illustrated in FIG. 5, four elementary arrays T1, T2, ^' T3 and T4 are considered, each having 16 pixels.

Then, according to a step b), the data of the sequence of elementary arrays T1-T4 is ordered into a processing array X of p rows and n columns, each row i being formed of the ordered sequence of pixels of the elementary array of rank i. We thus find, on the first line of table X, the pixels 1 to 16 of table Tl, arranged in order. Similarly, we will find in the second row of table X the pixels arranged in order of table T2, and so on. In the example, the treatment table X thus has four rows of 16 columns. In the example of FIG. 5, the table T has been broken down into four elementary square tables T1-T4. We can however, without departing from the scope of the invention, decompose the table T into a series of rectangular tables of the same dimension.

Then, according to a step c) the processing table X is normalized to obtain a normalized matrix Xn in which each element xiiy of row i and of column j is weighted by a transform using the mean of the values of the elements of row i and the mean elements of column j. An example of a TN normalization transform will be described later.

Then, according to step d), a statistical processing of factorial analysis AFC is performed on the normalized matrix XN, considering that the j columns are the variables, in order to extract n representative orthogonal factors.

For example, we use a factorial correspondence analysis method, according to which: dl) we calculate the transposed matrix XN ^T , d2) we calculate the square matrix by the product of the normalized matrix XN and its transposed XN ^T , d3 ) we diagonalize the square matrix XN ^T XN to extract the n eigenvectors u _k (k from 1 to n) associated with the n eigenvalues vp _k , d4) we calculate the coordinates of the p lines of the normalized matrix XN on the n eigenvectors, d5) we calculate the square cosines of the p lines on the n factor axes, d6) we calculate the coordinates of the n columns on the n eigenvectors.

During a step e), the n factors are then classified in descending order according to their respective weight.

During a step f), a reconstructed processing table XR of numbers xr (i, j) is generated by using only the first q representative factors and by restoring the initial values of the pixels by an inverse transform of the normalization transform. TN.

Finally, a reconstituted table TR is generated, constituting the reconstructed digital image, in which the noise at high frequency, for example the statistical fish noise, has been reduced. According to one embodiment, step c) can perform normalization by the steps: cl) the sum fi of each row of the treatment table X is calculated, c2) the sum f _j of each column of the treatment table is calculated X, c3) we calculate the total sum f _tot of the table, c4) we use a normalization transform consisting in replacing each element Xi _j of the table by the normalized value equal to xy divided by the product of the square roots of fj _. and f _j .

In practice, step d4) of calculating the coordinates of the p lines of the normalized matrix XN on the n eigenvectors can be carried out by calculating the coordinate c _k (i) of the line i on

1 axis k generated by the eigenvector u _k by the formula nx ^ c _k (i) = f _tot ^{1 2} ∑ u _k (j) j = l (fi fj ^1/2 in which u _k (j) is the j ^th coordinates of the eigenvector u _k . According to step d5), we can calculate the square cosine by the formula: cos ² _k (i) = c _k (i) c _k (i)

The coordinates of the n columns on the n eigenvectors can be calculated during a step d6) by the coordinate d _k (j) of column j on the eigenvector of axis k according to the formula:

1 pi _j d _k (j) = Σ c _k (i) vp _k ι = lf _j vp _k being the eigenvalue associated with the eigenvector u _k .

During step e), it is advantageous to classify the n factors as a function of their square cosine by applying the formulas above.

According to the invention, the reconstitution of the reconstructed processing table xr is carried out line by line, independently, taking into account only the q factors having the maximum square cosine for line i. Assuming that the first q factors are taken into account, the reconstructed value xr _y (q) of the element of the reconstructed processing table XR of row i and column j is calculated by the formula: fi f _j qc _k ( i) d _k (j) xr _{± j} (q) ≈ Σ fto k = l vp _k ^ι

From the reconstructed processing table XR, in FIG. 5, the reconstruction of the reconstituted table TR is carried out line by line, the first line of the reconstituted processing table XR constituting the pixels of the first elementary table TRI, and so on.

According to the invention, it is sought to automate the adaptation of the filtering device to the content of the image. This automation is done for each zone of the image each corresponding to one of the elementary arrays Tl to T4. For this we reconstruct the reconstituted table XR line by line. We perform the calculation of the reconstructed values xr _Aj of a line i of elements of the reconstructed array XR by a step-by-step calculation: - we successively calculate the value of the elements r _j for increasing q values of the number of factors taken into account ,

- the residual variance of line i is calculated each time, - the residual variance is compared to the estimated variance of the noise to be reduced,

- And we stop the calculation of the line i when the residual variance of the line i is no longer statistically greater than the estimated variance of the noise of the line i in the starting image, thus obtaining an estimated final image Im_finale.

In practice, the residual variance var_res (q) is calculated by difference between the initial variance of line i of the treatment table X and the reconstructed variance var_rec (q) or variance of line i of the reconstituted treatment table XR: var_res ( q) = var_ini - var__rec (q)

The comparison test for the residual variance and the estimated noise variance can advantageously be carried out by: a) calculating the variable t by the formula t = (Var_bruit) xhi (ddl) / ddl in which xhi (ddl) is the value given by the table of χ ² for a risk of 5% and a number ddl of degrees of freedom, ddl is the number of degrees of freedom , with ddl = nq-1 q being the number of factors taken into account, b) stop the reconstruction when the residual variable Var_res (q) is less than t.

In the case where the method is applied to the processing of an image having a noise which follows a Poisson law, the estimated variance of the noise of line i is taken equal to the average of the elements Xi _j of line i of treatment table X.

In order to reduce the influence of noise on the results, the procedure described above is repeated several times on the same image, each time shifting the division into elementary arrays by one pixel. Figure 5 illustrates the first procedure for an offset of 0 in x and 0 in y. 6 illustrates the second procedure for a shift of 1 pixel x and pixel 0 are: elemental T'1 table is shifted one pixel to the right in _^ the table T. For example, for cutting a square 4 4, the procedure will be carried out 16 times, with x shifts going from 0 to 3 and y shifts going from 0 to 3. The final image

(Im_finale), estimated without noise, will be the average of the sixteen result images. In this average, the number of times each pixel of the image can actually be included in the factor analysis analysis of AFC correspondence can be taken into account, so as not to cause edge effects. Another advantage of repetition is to get rid of geometric artefacts which can appear due to the division into elementary rectangles.

According to an advantageous embodiment, the invention also makes it possible to choose the noise elimination level, by subtracting from the original image only part of the noise image, in order to obtain a so-called reduced image im_reduced. The noise image is the original image subtracted from the final image. So, a reduced image Im_reduced is produced in which the noise is partially eliminated by the steps:

- calculate the noise image Im_bruit by difference of the original image and the final image: Im_bruit = Im_originale - Im_finale

- partially add the image of the noise to the final image: Im_ reduced = Im_finale + α Im_noise α can go from 0 (total noise elimination) to 1

(no noise elimination). Figure 4 illustrates the result of a filtering according to

1 invention: the left view is the original image; the middle view is the final image with optimum filtering; the view on the right is the reduced image, with α = 1/3.

The present invention is not limited to the embodiments which have been explicitly described, but it includes the various variants and generalizations thereof contained in the field of claims below.

Claims

CLAIMS 1 - Method for processing a digitized image consisting of a table T of numbers x ₍ i _j ) each expressing the degree of brightness of a corresponding pixel (i, j), the method comprising reducing noise at high frequency by the following steps: a) decompose the table T into a continuous sequence of p elementary arrays of the same dimension each having n pixels, b) order the data of the sequence of elementary arrays into a processing table X of p rows and n columns, each row i being formed from the ordered sequence of pixels of the elementary array of rank i, d) perform on the processing table X a statistical processing of multivariate analysis, considering that the n columns are the variables, in order to extract the n representative factors, f) generate a reconstructed processing table XR of numbers xr ₍ i, _j ) using only the first q representative factors and restoring the degrees of lumi absolute number, then generate a reconstituted table TR constituting the reconstructed digital image in which the high frequency noise has thus been reduced, characterized in that, during step f), the reconstituted processing table XR is reconstituted by reconstructing independently each line i taking into account only the factors having a significant weight with line i. 2 - Method according to claim 1, characterized in that step d) uses a factorial analysis method of correspondences, according to which: dl) the transposed matrix XN ^T is calculated, d2) the square matrix is calculated by the product of the normalized matrix XN and its transpose XN, d3) we diagonalize the square matrix XN ^T XN to extract the n eigenvectors u _k (k from 1 to n) associated with the n eigenvalues vp _k , d4) we calculate the coordinates of the p rows of the normalized matrix XN on the n eigenvectors, d6) the coordinates of the n columns on the n eigenvectors are calculated. 3 - Method according to claim 2, characterized in that:

- during a step d5) the square cosines of the lines on the n factor axes are calculated, - the square cosines are used as a test of the weight of the representative factors in line i.

4 - Method according to claim 3 characterized in that, after step b), there is provided a normalization step c) to obtain a normalized matrix XN of which each element ni _j of row i and column j is weighted by a transform TN using the average of the values of the elements of line i and the average of the elements of column j, step during which: cl) we calculate the sum fi of each line of the treatment table X, c2) we calculate the sum f _j of each column of the treatment table X, c3) we calculate the total sum f _tot of the table, c4) we use a normalization transform consisting in replacing each element x _± of the table by the normalized value equal to x _{± j} divided by the product of the square roots of fi and f _j .

5 - Method according to claim 4 characterized in that:

- step d4) calculates the coordinate c (i) of line i on the axis k generated by the eigenvector u _k by the formula n ^χ ij

where u _k (j) is there; ^th coordinate of the eigenvector u _k ;

- step d5) calculates the square cosine by the formula: cos ² _k (i) = c _k (i) c _k (i)

- step d6) calculates the coordinate dk _(j ) of column j on the eigenvector of axis k by the formula

1 px _{± j} d _k (j) = Σ c _k (i) vp _k i = lf _j vp _k being the eigenvalue associated with the eigenvector u.

6 - Method according to claim 5 characterized in that the reconstructed value xr ₁₃ (q) of the element of the reconstructed treatment table XR of line i and column j taking into account the q appropriate factors is calculated by the formula: xr ₁₃ (q) = Σ f _to tk = l vp _k ^{1 2}

7 - Method according to any one of claims 1 to 6, characterized in that one performs the calculation of the reconstructed values xr _1D of a line i of elements of the reconstructed table XR by a stepwise calculation, by successively calculating the value of the elements of the line for increasing q values, by calculating each time the residual variance of the line i (var_res (q)), by comparing it to the estimated variance of the noise to be reduced, and by stopping the calculation of the line when the residual variance of the line is no longer statistically greater than the estimated variance of the noise of line i in the starting image, thus obtaining a final image (Im_finale) estimated without noise. 8 - Method according to claim 7 characterized in that the residual variance Var_res (q) of the line i reconstituted with the q factors is calculated by difference of the initial variance Var_ini of line i of the treatment table X and the reconstituted variance Var_rec (q) or variance of line i of the reconstructed treatment table XR.

9 - Method according to claim 7 characterized in that the comparison test of the residual variance and the estimated variance of the noise is carried out by: a) calculating the variable t by the formula t = (Var_bruit) xhi (ddl) / ddl in which xhi (ddl) is the value given by the table of χ ² for a risk of 5% and a number ddl of degrees of freedom, ddl is the number of degrees of freedom, with ddl = nq-1 q being the number factors taken into account, b) stop the reconstruction when the residual variable Var res (q) is less than t. 10 - Method according to any one of claims 7 to 9 applied to the processing of a noise image according to a Poisson law, characterized in that the estimated variance of the noise of the line i is taken equal to the average of the elements x _{± j} from line i of processing table X.

11 - Method according to any one of claims 7 to 10, characterized in that a reduced image (Im_reduced) is produced in which the noise is partially eliminated, by the steps:

- calculate the noise image (Im_bruit) by difference between the original image and the final image:

Im_bruit = Im_originale - Im_finale

- partially add the noise image to the final image: Im_reduced = Im_finale + α Im_noise.

12 - Method according to any one of claims 1 to 11 characterized in that the method is applied several times to the same image by shifting each time by one pixel the division into elementary arrays, and by calculating the average of the reconstituted images thus obtained.

13 - Device for processing digital images, comprising a memory, a calculation unit, an input-output device for receiving the data constituting the digital image to be processed, display and / or printing means for viewing the processed image, and a program recorded in memory and adapted to implement the method according to claims 1 to 12.

14 - Medical imaging installation comprising a device according to claim 13.