Abstract
A system and method for denoising experimental data originating from multiple acquisitions by a magnetic resonance imaging device, by analysis of selected principal components, to obtain a better compromise between the efficiency of the denoising and retention of the relevant information in the experimental data under consideration during their reconstruction to produce denoised experimental data. A selection criterion is based on the informative indicators quantifying the spatial information contained in images of scores associated with said principal components. The invention also provides for the capability to apply an adaptive filtering excluding the persistent spatial noise associated with each component selected.
Claims
1. A system for attenuating the noise in experimental data originating from multiple acquisitions by a nuclear magnetic resonance imaging device pertaining to an elementary volume of interest, hereinafter named “voxel” of interest, among a plurality of voxels, said system comprising a processor configured to implement the following operations: acquiring said experimental data pertaining to the plurality of voxels; projecting the experimental data into a base of functions or vectors to produce a set of q components as well as their respective scores for the plurality of voxels, said scores corresponding to the projection of said experimental data onto said q components; selecting k components among the q components produced, wherein the selection of the k components includes: producing score images of the components for the plurality of voxels and informative indicators quantifying the spatial information contained in said images of the scores associated with said components in the form of a rate of decrease of the values of a determined characteristic of said scores before and after application of a smoothing filter to said scores, said determined characteristic of the scores for a plurality of voxels belonging to a set of characteristics, alone or in combination, including variance, standard deviation, median and mean, and determining the k components on the basis of said informative indicators; projecting said experimental data onto the selected k components and producing noise-attenuated experimental data pertaining to the elementary volume; and generating a human-perceptible representation of a physiological signal based upon the noise-attenuated experimental data
2. The system of claim 1, wherein: the production of q components as well as their respective scores for the plurality of voxels produces an ordered set of q components according to a determined order relation; and the determination of the k components comprises determining the rank k in order to select the first k components on the basis of said informative indicators.
3. The system of claim 2, where the production of q components as well as their respective scores for the plurality of voxels comprises implementing a principal component analysis to produce an ordered set of q principal components according to their respective eigenvalues.
4. The system according to claim 1, wherein: the experimental data pertaining to the plurality of voxels result from a multiphase diffusion imaging acquisition by the magnetic resonance imaging device; and the production of q components as well as their respective scores for the plurality of voxels comprises implementing a spherical harmonic decomposition.
5. The system according to claim 1, wherein: the experimental data pertaining to the plurality of voxels result from a multiphase acquisition by a functional magnetic resonance imaging device; and the production of q components as well as their respective scores for the plurality of voxels comprises implementing a Fourier transform decomposition.
6. The system of claim 2, wherein the determination of the rank k comprises calculating the mathematical difference between values of said informative indicators which are ordered in accordance with the q components, the rank k being that of the component for which said mathematical difference falls below, or becomes equal to, a determined threshold.
7. The system of claim 2, wherein the determination of the rank k comprises detecting a plateau described by the values of the informative indicators which are ordered according to the q components, from the informative indicator of the component of rank q to the informative indicator of the component of rank 1, the rank k being that of the first component the value of the informative indicator which deviates from said plateau.
8. The system of claim 1, wherein the determination of the k components comprises calculating the mathematical difference between successive values of said informative indicators which are ordered according to a determined order relation, the k components selected being those for which said mathematical difference between the values of their informative indicators remains above a determined threshold.
9. The system of claim 2, wherein the determination of the k components comprises detecting a plateau described by the values of the informative indicators which are ordered according to an order relation, the k components selected being those for which their respective informative indicators deviate from said plateau.
10. The system of claim 1, wherein the processor is further configured to apply a filtering operation of the selected k components, the filtering intensity of which is specific to each of the selected k components and proportional to the informative indicator thereof.
11. The system according to claim 10, wherein the filtering operation comprises the use, alone or in combination, of a Gaussian filter, a mean filter, a median filter, an anisotropic diffusion filter.
12. A non-transitory computer-readable storage medium including one or more program instructions that can be interpreted by the processor of said system, said program instructions being capable of being loaded in non-volatile storage of said system, wherein the execution of said instructions by said processor causes the implementation of the operations set forth in claim 1.
13. A method for attenuating the noise in experimental data originating from multiple acquisitions by a nuclear magnetic resonance imaging device pertaining to an elementary volume of interest, hereinafter named “voxel” of interest, comprising: acquiring said experimental data pertaining to the plurality of voxels; projecting the experimental data into a base of functions or vectors to produce a set of q components as well as their respective scores for the plurality of voxels, said scores corresponding to the projection of said experimental data onto said q components; selecting k components among the q components produced, wherein the selection of the k components includes: producing score images of the components for the plurality of voxels and informative indicators quantifying the spatial information contained in said images of the scores associated with said components in the form of a rate of decrease of the values of a determined characteristic of said scores before and after application of a smoothing filter to said scores, said determined characteristic of the scores for a plurality of voxels belonging to a set of characteristics, alone or in combination, including variance, standard deviation, median and mean, and determining the k components on the basis of said informative indicators; projecting said experimental data onto the selected k components and producing noise-attenuated experimental data pertaining to the elementary volume; and generating a human-perceptible representation of a physiological signal based upon the noise-attenuated experimental data.
14. A system for attenuating the noise in experimental data originating from multiple acquisitions by a medical imaging device pertaining to an elementary volume of interest, hereinafter named “voxel” of interest, among a plurality of voxels, said system comprising a processor configured to implement the following operations: acquiring said experimental data pertaining to the plurality of voxels; projecting the experimental data into a base of functions or vectors to produce a set of q components as well as their respective scores for the plurality of voxels, said scores corresponding to the projection of said experimental data onto said q components; selecting k components among the q components produced, wherein the selection of the k components includes: producing score images of the components for the plurality of voxels and informative indicators quantifying the spatial information contained in said images of the scores associated with said components in the form of a rate of decrease of the values of a determined characteristic of said scores before and after application of a smoothing filter to said scores, said determined characteristic of the scores for a plurality of voxels belonging to a set of characteristics, alone or in combination, including variance, standard deviation, median and mean, and determining the k components on the basis of said informative indicators; projecting said experimental data onto the selected k components and producing noise-attenuated experimental data pertaining to the elementary volume; and generating a human-perceptible representation of a physiological signal based upon the noise-attenuated experimental data.
15. A method for attenuating the noise in experimental data originating from multiple acquisitions by a medical imaging device pertaining to an elementary volume of interest, hereinafter named “voxel” of interest, comprising: acquiring said experimental data pertaining to the plurality of voxels; projecting the experimental data into a base of functions or vectors to produce a set of q components as well as their respective scores for the plurality of voxels, said scores corresponding to the projection of said experimental data onto said q components; selecting k components among the q components produced, wherein the selection of the k components includes: producing score images of the components for the plurality of voxels and informative indicators quantifying the spatial information contained in said images of the scores associated with said components in the form of a rate of decrease of the values of a determined characteristic of said scores before and after application of a smoothing filter to said scores, said determined characteristic of the scores for a plurality of voxels belonging to a set of characteristics, alone or in combination, including variance, standard deviation, median and mean, and determining the k components on the basis of said informative indicators; projecting said experimental data onto the selected k components and producing noise-attenuated experimental data pertaining to the elementary volume; and generating a human-perceptible representation of a physiological signal based upon the noise-attenuated experimental data.
Description
[0069] Other characteristics and advantages will become more clearly apparent on reading the following description and on examining the figures which accompany it, in which:
[0070] FIG. 1, already described, shows a simplified depiction of a system for analysing images obtained by magnetic resonance;
[0071] FIG. 2, already described, shows a simplified depiction of a variant of a system for analysing images obtained by magnetic resonance;
[0072] FIG. 3, already described, shows an example of a Z-spectrum in the form of a set of samples Zi(Δω) according to relative frequency shifts Δω with respect to the frequency of water, such shifts Δω being expressed in ppm;
[0073] FIG. 4, already described, shows the principle of principal component analysis consisting of transforming variables or data associated with one another (also described as “correlated” in statistics) into new variables or data that are decorrelated from one another;
[0074] FIG. 5, already described, shows a known method for denoising a noisy Zi-spectrum resulting from a CEST acquisition according to the state of the art;
[0075] FIG. 6, already described, shows the experimental data projected onto different principal components extracted from a CEST data set after remodelling in their origin space;
[0076] FIG. 7 shows an example functional algorithm of a denoising method according to the invention;
[0077] FIG. 8 shows an example calculation of a principal component informative indicator specific to the invention;
[0078] FIG. 9 shows an example selection of principal components according to the invention;
[0079] FIG. 10 shows an example attenuation of the noise in HARDI diffusion experimental data for different phases;
[0080] FIG. 11 shows an example of noise removed by implementation of the invention from such HARDI data for different phases;
[0081] FIG. 12 shows an example of use and the benefit resulting from such a use of data denoised by virtue of the invention in the field of tractography;
[0082] FIG. 13 shows an example attenuation of the noise in experimental perfusion data for different phases;
[0083] FIG. 14 shows an example of noise removed by implementation of the invention from such perfusion data for different phases;
[0084] FIG. 15 shows an advantageous embodiment of a method according to the invention making it possible to adjust the weights specific to the different principal components selected prior to the projection of the noisy experimental data onto them.
[0085] A method 100 for attenuation of the noise in medical images, according to the invention and shown in FIG. 7, is advantageously expressed in the form of a computer program product the program instructions of which are intended to be installed in the program memory of an element of a medical imaging system, such as the system S in FIGS. 1 and 2, for example a computer or a computer system server or, more generally, any electronic object having a sufficient computation power available.
[0086] FIG. 7 thus shows a method 100, according to the invention, for attenuation of the noise in experimental data originating from multiple acquisitions by an imaging device, for example a magnetic resonance imaging device, such as the device 1 of the medical analysis system S shown in FIGS. 1 and 2, pertaining to a plurality of n voxels. Such a method includes some common steps with the method 100 according to FIG. 5. Thus, a “denoising” method 100 according to the invention can include, if necessary, a step 110 of collection or acquisition of noisy experimental data pertaining to or concerning said plurality of voxels V1 to Vn. Such experimental data can consist of curves such as Z1- to Zn-spectra following an acquisition of the CEST type, like the example referenced in FIGS. 3 and 5 or, more generally, any experimental data for a set of voxels or pixels pertaining to a volume or a slice of an organ concerned by a plurality of m acquisitions according to different instants or different phases for example. Such experimental data could thus, non-exhaustively, result from a multiphase high angular resolution diffusion imaging (HARDI) acquisition, concern the field of perfusion imaging by scanning or magnetic resonance imaging.
[0087] By way of preferred but non-limitative example, like FIG. 5, FIG. 7 depicts experimental data Zi pertaining to a voxel of interest among the n voxels acquired. FIG. 7 shows experimental data Zi, in the form of a noisy spectrum identical to that shown in FIG. 5. Such a noise is expressed by more or less pronounced discontinuities or oscillations according to the frequency shifts concerned, as evidenced by the partial enlargement of said Zi-spectrum. In order to attenuate this phenomenon, like the known method 100 and shown in FIG. 5, a method 100 according to the invention includes a step 120 of implementing a principal component analysis to produce or calculate q principal components, said step being similar to step 120 of the known method 100 according to FIG. 5. Such a step 120 consists of determining q principal components respectively symbolized by or associated with eigenvalues λ1, . . . , λq or with singular values s.sub.1 to s.sub.q forming an ordered set of principal components the rank of which is determined according to a set of decreasing scalar values, such as the eigenvalues Λ={λ1, . . . , λq} or the singular values S. In a variant, such principal components could be ordered according to any other order relation or even not be ordered. Such a method 100 according to the invention also includes a step 130 of determining or selecting k principal components among the q produced, i.e. the principal components of ranks 1 to k when these latter are ordered according to a determined order relation, to determine a smaller set of principal components. The selection 130, according to the invention and shown in FIG. 7, is clearly differentiated from the approach described in the great majority in the state of the art based on eigenvalues A. Such a step 130 specific to the invention will be detailed hereinafter. A method 100 according to the invention also includes, like the known methods 100 as shown in FIG. 5, a step 140 of projecting the noisy experimental data Zi onto the k principal components selected in step 130 and producing noise-attenuated, or “denoised”, experimental data Zi′ pertaining to an elementary volume of interest. It is possible to observe the increased efficiency of a method 100 according to the invention, by virtue of an improved selection, or a modification of the k principal components, prior to said projection 140, by examining the denoised Zi′-spectrum describing a particularly smooth curve with respect to the one described by the Zi-spectrum of origin. Like the one shown in FIG. 5, step 140 of the method 100 according to the figure consists of projecting the noisy experimental data set Z1, . . . , Zi, . . . , Zn onto the k principal components selected, and producing noise-attenuated experimental data Z1′, . . . , Zi′, . . . , Zn′ for the voxels of interest V1 to Vn. Thus, optionally and advantageously, such a method 100 according to the invention can include a step 150 of joint use of the denoised experimental data Z1′, . . . , Zi′, . . . , Zn′ for all or part of a plurality of said voxels of interest V1 to Vn. Such a use can for example consist of counting fibres in tractography on the basis of HARDI diffusion experimental data, as will be discussed with reference to FIGS. 10 to 12.
[0088] In a variant, step 120 for producing a set of q components can result from the implementation of techniques other than principal component analysis. Such a step 120 consists more generally of a decomposition or projection of the signal or of the experimental data into a base of functions or vectors. Thus, such a step 120 can consist for example, when the experimental data result from a multiphase diffusion imaging acquisition by a magnetic resonance imaging device, of implementing a spherical harmonic decomposition. Similarly, such a step 120 could, instead of principal component analysis, consist of implementing a Fourier transform decomposition, for example by Fast Fourier Transformation, of experimental data resulting from a multiphase acquisition by a functional magnetic resonance imaging device, a technique also known as fMRI.
[0089] The invention is thus differentiated mainly by the implementation of step 130 making it possible to select the relevant components, i.e., making it possible to optimize the attenuation of the noise without losing relevant items of spatial information. Thus, as shown in FIG. 7, such a step 130 includes a sub-step 131 of producing informative indicators, referenced σ1.sup.r, . . . , σq.sup.r in FIG. 7, calculated respectively for the q principal components produced of ranks 1 to q in step 120 when the latter consists of a decomposition by principal component analysis. Such a set Σ.sup.r of informative indicators σ1.sup.r to σq.sup.r is an alternative to the set Λ of the eigenvalues λ1 to λq used directly by the known methods for selecting k principal components among the q extracted. Such an informative indicator σj.sup.r characterizes the capacity of a principal component of rank j to express relevant spatial information. It can advantageously consist of a rate of decrease of the values of a determined characteristic of the scores of said principal component pertaining to the plurality of voxels V1 to Vn under consideration or of interest, before and after application of a smoothing filter to said scores. Such an operation 131a is shown in FIG. 8. This depicts, for the principal component of rank 3, two images PC3a and PC3b showing the scores of said principal component of rank 3 for the set of voxels under consideration. The image PC3a depicts said scores before application 131a of a smoothing filter and the image PC3b depicts these same scores after said application 131a of the smoothing filter. This latter thus appears more blurred with respect to the image PC3a in FIG. 8. Such an operation 131a can advantageously consist of applying a Gaussian filter of Factor F having a predetermined value, optionally configurable.
[0090] By way of preferred but non-limitative example, said determined characteristic can consist of the standard deviation of said scores. The informative indicator σj.sup.r of a principal component of rank j can then be calculated in an operation 131b such that:
[00006]
[0091] where σj.sup.a is the standard deviation of the scores of the principal component of rank j before application 131a of the smoothing filter and σj.sup.b is the standard deviation of said scores after application 131a of said smoothing filter.
[0092] In this case, in FIG. 8, the informative indicator σ3.sup.r of the principal component of rank 3 is such that:
[00007]
[0093] Similarly, FIG. 8 shows the calculation of the informative indicator σ9.sup.r of the principal component of rank 9 is such that:
[00008]
[0094] or also of the informative indicator σ29.sup.r of the principal component of rank 29 is such that:
[00009]
[0095] In this way, the set Σr of the informative indicators of the q principal components of ranks 1 to q produced in step 120 and ordered according to their respective eigenvalues A or singular values S can be constituted at the end of implementation of the sub-step 131. In a variant, this set Σr of the informative indicators of the q principal components can be ordered according to the numerical values of said informative indicators or according to any other order relation.
[0096] In a variant or in addition, such a determined characteristic σjr could, instead of standard deviation, make use of the variance, entropy, median or also the mean of said scores of the principal component of rank j, or also result from a combination of all or some of these.
[0097] Once the set Σ.sup.r of the informative indicators has been calculated, step 130 of a method 100 according to the invention includes a sub-step 132 of determining the rank k in order to select the first k principal components (symbolized by the set of eigenvectors ϕ′={φ1, . . . , φk} or the matrix U′={u.sub.1, . . . , u.sub.k} in FIG. 7) on the basis of said set Σ.sup.r of said informative indicators. The implementation of such a sub-step 132 is shown in FIG. 9. The latter shows, with reference to the q=29 principal components of ranks 1 to 29, the scores PC1 to PC29 of which for a plurality of voxels of interest are shown in FIG. 6, the set Σ.sup.r of the informative indicators calculated in 131b and ordered according to the respective ranks of the q=29 principal components produced in step 120. The values of said informative indicators describe a curve “σj.sup.r” substantially increasing when the rank of the principal components increases, to reach a plateau σp.sup.r of the order of ninety percent in the example shown in FIG. 9 starting from rank 12. The value of convergence or of a plateau σp.sup.r depends on the power of the smoothing that was applied to the score images in FIG. 8 and on the characteristic used to produce the informative indicators. As previously noted with reference to FIG. 6, the component of rank j=1 seems to express more items of spatial information than the components of ranks j greater than 10. Step 132 thus makes it possible, according to different embodiments, to objectivize the selection of the first k principal components in order to obtain the compromise sought. Thus, according to a first embodiment, such a sub-step 132 can consist of calculating the mathematical difference between values of said informative indicators Σ.sup.r={σ1.sup.r, . . . , σq.sup.r} when these latter are ordered in accordance with the ranks j of the q principal components produced. The rank k can be determined based on such a difference between two informative indicators of consecutive ranks. Thus, as soon as said difference falls below, or becomes equal to, (in absolute value) a determined threshold, for example a threshold of a value below three hundredths, the rank k sought is that of the principal component of the rank immediately below that of the principal component for which the informative indicator is substantially equal (difference substantially zero or below said threshold) to that of the principal component of the rank which is immediately above it. Such an approach is relevant when the informative indicators, ordered according to the ranks of the principal components that are respectively associated therewith, describe a curve “σj.sup.r” that is substantially increasing until reaching a plateau σp.sup.r. In a variant or in addition to the calculation of a mathematical difference between two informative indicators of consecutive ranks, the invention provides for the possibility of calculating a mean mathematical difference between an enhanced collection of consecutive indicators, a difference between the informative indicators of rank(s) lower and/or higher than a given informative indicator or any other equivalent technique. However, as indicated by the curve “σj.sup.r” shown in FIG. 9, the latter can have one or more level sections. In this case, a first level section is depicted by the values of the informative indicators σ7.sup.r and σ8.sup.r of the principal components of ranks 7 and 8. A second level section is depicted by the values of the informative indicators σ12.sup.r to σ29.sup.r of the principal components of ranks greater than or equal to 12. So as not to determine a rank k that is too low pertaining to the existence of an intermediate level section for which the derivative of the curve “σj.sup.r” is substantially zero, such a calculation of the derivative can be accompanied by or combined with the calculation of a deviation (depicted by the curve “σp.sup.r-σj.sup.r” in FIG. 9) with the informative indicator associated with the principal component of the highest rank, in this case the rank q=29, or the informative indicator of maximum value. If said deviation “σp.sup.r-σj.sup.r” is very low (for example less than three hundredths), then step 132 considers that the curve has reached the asymptote or the plateau σp.sup.r. The rank k is thus determined as being that of the principal component of the rank immediately below. This is for example the case of the component of rank k=11, which is the last having an informative indicator σ11.sup.r “escaping” the plateau σp.sup.r or, more specifically, the value of which deviates substantially from the value σp.sup.r of said plateau. On the other hand, if said deviation “σp.sup.r-σj.sup.r” is significant, for example greater than ten percent of the value σp.sup.r, (the case of the principal component of rank 7 the informative indicator σ7.sup.r of which is substantially equal to that, σ8.sup.r, of the principal component of the rank immediately above in the example shown in FIG. 9), then such a level section of the curve “σj.sup.r” is disregarded.
[0098] In a variant, such a sub-step 132 can consist of the detection of a plateau σp.sup.r, as mentioned above, described by the values of the informative indicators σj.sup.r (j being comprised between 1 and q), passing through these latter from the highest rank of the principal components, in this case the rank q=29, to the rank 1. By assumption, such a plateau σp.sup.r exists for the principal components of the highest ranks, in this case in FIG. 9, the plateau σp.sup.r is of the order of ninety percent. The rank k sought is determined as being that of the first principal component the value of the informative indicator σk.sup.r of which deviates significantly from said plateau σp.sup.r (i.e. beyond a predetermined threshold, for example five percent of the value of said plateau). In this case, the informative indicator σ11.sup.r is the first to describe such a value sufficiently distinct from the value of said plateau σp.sup.r. The rank k sought is thus that of said principal component of rank k equal to eleven.
[0099] The invention is not to be considered limited by such operations implemented within the context of the sub-step 132 for detecting the value of the rank k on the basis of the ordered set of the informative indicators Σ.sup.r.
[0100] As mentioned above, the informative indicators of the components can be ordered according to an order relation independent of the ranks or an ordering according to an order relation specific to the components produced. In this case, the sub-step 132 of determining k components can consist of calculating the mathematical difference between successive values of said informative indicators of the components and selecting only the k components the mathematical difference of which between the values of their respective informative indicators remains above a determined threshold. Similarly, according to this variant according to which the informative indicators of the components are ordered according to an order relation specific to them, the sub-step 132 can consist of selecting the k components for which their respective informative indicators deviate from a plateau such as the aforementioned plateau σp.sup.r.
[0101] The invention also provides for the capability to modify the k components thus selected in step 130 (symbolized by the vector ϕ′ in FIG. 7), prior to the implementation of step 140, whether said components were produced in step 120 by a principal component analysis or by an alternative technique (spherical harmonics, Fourier transform, etc.). In the case of an implementation of a principal component analysis, the q components produced are known hereinafter as “principal components”. The objective is to increase the contributions of the most “informative” principal components (the ranks of which are the lowest) with respect to those the respective capacities of which to express items of spatial information are lower, those of higher ranks. To this end, such a step 130 can also include a sub-step 133 of applying an operation of filtering the k principal components selected, the filtering intensity of which is specific to each of the k principal components of ranks 1 to k (less than or equal to q) selected and proportional to the informative indicator σ1.sup.r to σk.sup.r thereof. Such a filtering operation 133 can consist of the use, alone or in combination, of a Gaussian filter, a mean filter, a median filter, an anisotropic diffusion filter, a wavelet filter, or any filter, spatial or other, capable of being used in this context. By way of preferred but non-limitative example, such a sub-step 133 can consist of the adjustment of weights wj.sup.r specific to the principal components of ranks j carried out on the basis of the values σj.sup.r. In this example, the weights can be multiplied linearly by the power A of a Gaussian filter. Each component selected, i.e. of rank j, j being less than or equal to k, is filtered by a factor of wj.sup.r×A. In a variant, or in addition to the linear multiplication, the weights can be expressed beforehand in the form of inputs of a logarithmic, exponential or polynomial function f. In this way, each selected score image of PCj, i.e. of rank j, j being less than or equal to k, can be filtered by a factor defined by f(wj.sup.r)×A. Finally, the “filtered” score images are used to reproduce the matrix of scores U. As shown in FIG. 15, such a weight wj.sup.r can be calculated on the basis of the curve “σj.sup.r” or shown in FIG. 9, as follows:
[00010]
where σj.sup.r is the value of the informative indicator of the principal component of rank j, σ1.sup.r is the value of the informative indicator of the principal component of rank 1 and σp.sup.r the value of the plateau of the curve “σj.sup.r” described by said informative indicators Σ.sup.r. Thus, such a weight wj.sup.r is comprised between w1.sup.r=0 and wp.sup.r=1 (i.e. when the curve “σj.sup.r” has reached a plateau σp.sup.r).
[0102] The invention is not to be considered limited to only these examples of calculations of the weights wj.sup.r of the sub-step 133.
[0103] FIGS. 10 to 12 make it possible to show the benefit resulting from the implementation of a method for attenuating the noise in experimental data originating from multiple acquisitions by a magnetic resonance imaging device in the HARDI diffusion imaging field. Such an acquisition of experimental data can thus bear on a plurality of slices, in this case a human brain, for a plurality of phases. FIG. 10 thus shows the raw data, for a given slice, of phases two, twelve, twenty-two, thirty-two, forty-two, fifty-two and sixty-two, respectively referenced P2, P12, P22, P32, P42, P52 and P62 in FIG. 10. The first series of images referenced L1 show the raw, therefore noisy, experimental data for a plurality of voxels and respectively for the different phases P2 to P62 mentioned above. The second and third series of images L2 and L3 show said experimental data denoised by the implementation of the invention, according to which the k principal components selected were subjected to a filtering (step 133 of a method according to FIG. 7) prior to (L3) or not prior to (L2) the projection of the experimental data onto said k principal components. The increasing enhancement contributed by the invention can be noted visually from series L1 to series L3.
[0104] In addition, the performances of a method 100 according to the invention can be shown in FIG. 11, which depicts the noise removed in step 140 of a method according to the invention, for the different phases referenced P2, P12, P22, P32, P42, P52 and P62 in FIG. 10, pertaining to the denoised experimental data of series L2 and L3 in FIG. 10. It is clear that such noise does not reveal any spatial information of interest.
[0105] FIG. 12 depicts the use of HARDI diffusion data described with reference to FIG. 10 in the context of tractography. FIG. 12 shows three colour images 11, 12, 13, expressed in grayscale, for a given slice, as well as a partial enlargement P11, P12 and P13 of each image I1, I2, I3. These latter were produced in a step 150 on the basis of respectively raw experimental data (series L1 in FIG. 10), data denoised by implementation of the invention and as shown by the series L2 in FIG. 10, and by the series L3 in said FIG. 10. Said enlargements P11, P12 and P13 make it possible to see with the naked eye an increasing highlighting of fibres. In the enlargement P11, an area (circled in white) of the organ could be considered to be dead, which is not the case in the enlargements P12 and P13. Moreover, such a use makes it possible to count such fibres. On the basis of the raw data of series L1 in FIG. 10, it is possible to count of the order of twenty-seven thousand fibres. These are of the order of thirty-four thousand if denoised data forming the series L2 in FIG. 10 are used, and over thirty-seven thousand if the denoised data forming the series L3 in FIG. 10 are used. A denoising of experimental data according to the invention thus contributes a particularly significant enhancement.
[0106] FIGS. 13 and 14, like FIGS. 10 and 11, show the enhancement contributed by the invention on the basis of perfusion data. Thus, the acquisition of experimental data bears on a plurality of slices, in this case a human brain, for a plurality of phases. FIG. 13 thus shows the raw data, for a given slice, of phases one, five, ten, fifteen, twenty, twenty-five, thirty, thirty-five and forty, respectively referenced P1, P5, P10, P15, P20, P25, P30, P35 and P40 in FIG. 13. The first series of images referenced L1 show the raw, therefore noisy, experimental data for a plurality of voxels and respectively for the different phases P1 to P40 mentioned above. The second and third series of images L2 and L3 show said experimental data denoised by the implementation of the invention, according to which the k principal components selected were subjected to a filtering (step 133 of a method according to FIG. 7) prior to (L3) or not prior to (L2) the projection of the experimental data onto said k principal components. The increasing enhancement contributed by the invention can be noted visually from series L1 to series L3. This enhancement is even more noteworthy when, in said FIG. 13, the spectrum of the experimental data is examined, for a voxel V of interest, respectively raw (A), denoised by the implementation of the invention when the k principal components selected were not subjected to a filtering (B) and when said filtering has been carried out (C). It is notable that the curves respectively described by said spectra are increasingly smooth.
[0107] In addition, the performances of a method 100 according to the invention can be shown in FIG. 14, which depicts the noise removed pertaining to the series L2 and L3 in FIG. 13. It is clear that such a noise does not reveal any spatial information of interest.
[0108] In the foregoing description, the concepts that underlie the invention have been described through an exemplary implementation applied to data obtained by magnetic resonance imaging. It will be appreciated, however, that these concepts can be equally applied to other types of medical imaging, such as CT scans and sonograms. Moreover, they are not limited to medical imaging data. They could be utilized in other fields of application from the point at which noisy images or volumes of noisy images are acquired repetitively or sequentially, such as for example the cinema, identity control, etc.
