Method for measuring the quality of a reconstructed image

Abstract

The invention relates to a method for measuring the quality of a reconstructed image, the method comprising: 1) constructing (52) a residual image from the difference between the pixel values of an original image and the reconstructed image; and 2) for a plurality of regions of the residual image, calculating (54) a coefficient C(Pk) representative of the correlation between the pixels of this region in the residual image and the pixels of the same region in the original image, wherein the size and the shape of each region are the same for all of the calculated correlation coefficients, and wherein the predetermined size of each region is greater than nine pixels; 3) constructing (56) a measurement of the quality of the reconstructed image on the basis of the coefficients calculated in step 2).

Description

[0001] Method for measuring the quality of a reconstructed image

[0002] [1] The invention relates to a method for measuring the quality of a reconstructed image as well as:

[0003] - a method for automatically learning optimal values ​​for parameters of an image quality optimizer and an information recording medium for implementing this method,

[0004] - a method of manufacturing a device for reconstructing an image from a degraded set of data, and

[0005] - an imaging system.

[0006] [2] Hereinafter, a "reconstructed image" refers to an image that has been reconstructed from a degraded data set. The degraded data set encodes a degraded image that is of lower quality than the reconstructed image.

[0007] [3] Even when a powerful image reconstruction algorithm is used, the reconstructed image may have defects compared to an original image. Hereinafter, the term "original image" refers to the image with the maximum quality.

[0008] [4] The quality of a reconstructed image is all the better when the reconstructed image is similar to the original image and therefore free from defects such as reconstruction artifacts.

[0009] [5] The objective measurement of the quality of a reconstructed image is therefore an important topic in the field of image processing and analysis because it has important applications in many aspects of image processing. In particular, such image quality measures are used in the field of medical imaging and, for example, in the field of magnetic resonance imaging.

[0010] [6] Because of this, many methods have been developed to measure the quality of a reconstructed image. These methods generally deliver a single numerical value, called an "index", which represents the quality of the reconstructed image. Examples of such known indices include the following:

[0011] - the PSNR index (“Peak Signal to Noise Ratio”),

[0012] - the NRMSE index (Normalized Root Mean Square Error),

[0013] - the NMAE (Normalized Mean Absolute Error) index, and

[0014] - the SSIM (“Structural SI M ilarity”) index.

[0015] [7] Also known from the state of the art are CN109285146B, US2017 / 042496A1 and CN113469998A as well as the following articles:

[0016] - Marius PEDERSEN: “Full-Reference Image Quality Metrics: Classification and Evaluation”, Foundations and trends in computer graphics and vision, vol. 7, n°l, 1 / 01 / 2011, pages 1-80, and

[0017] - ZHOU WANG and Al: “Means squared error: Love it or leave it? A new look at signal fidelity measurements”, IEEE Signal Processing Magazine, USA, vol. 26, n°l, 1 / 01 / 2009, pages 98-117.

[0018] [8] In particular, the index described in patent CN109285146B consists of calculating for certain blocks, called smooth, of the original and reconstructed images, an index similar to the PSNR index and for other blocks, called structured, an index similar to the SSIM index. Then, these different indices are combined to form a single global index. In particular, in the method described in patent CN109285146B, no similarity coefficient between the original image and a residual image is calculated.

[0019] [9] However, these known methods for measuring the quality of a reconstructed image are insufficiently sensitive to small reconstruction defects introduced by the reconstruction algorithm implemented. In particular, the known methods are insufficiently sensitive to the absence of a small structured pattern in the reconstructed image while this small structured pattern exists in the original image. They are also insufficiently sensitive to the presence of a small structured pattern in the reconstructed image which does not exist in the original image. Because of these deficiencies, it is difficult to improve image reconstruction methods and therefore to obtain reconstructed images with fewer defects.

[0020]

[0010] The invention aims to remedy this drawback by proposing an improved method for measuring the quality of a reconstructed image.

[0021]

[0011] The invention is set forth in the attached set of claims.

[0012] The invention will be better understood upon reading the following description, given solely by way of non-limiting example and with reference to the drawings in which:

[0022] - Figure 1 is a schematic illustration of the architecture of an imaging system,

[0023] - Figure 2 is a flowchart of a method for measuring image quality,

[0024] - figure 3 is an original image of a section of a brain,

[0025] - figures 4 to 6 are reconstructed images of the image in figure 3,

[0026] - Figure 7 is a flowchart of a method for learning the values ​​of the parameters of an image quality optimizer implemented in the system of Figure 1,

[0027] - Figure 7 is a flowchart of a manufacturing and operating process of the system of Figure 1,

[0028] - Figure 8 is a flowchart of a manufacturing process of the system of Figure 1.

[0029]

[0013] In this description, the terminology, conventions and definitions of the terms used in this text are introduced in a chapter I. Then, detailed examples of embodiments are described in a chapter II with reference to the figures. In a chapter III, variants of these embodiments are presented. Finally, the advantages of the different embodiments are specified in a chapter IV.

[0030]

[0014] Chapter I: Definitions, terminologies and conventions:

[0031]

[0015] In the figures, the same references are used to designate the same elements.

[0032]

[0016] In the remainder of this description, the characteristics and functions well known to those skilled in the art are not described in detail.

[0033]

[0017] The symbol “*” denotes scalar multiplication.

[0034]

[0018] An image is a digital file containing a matrix of pixels. Each pixel contains a numerical value representing a color or a gray level. The position of this pixel in the image is encoded by the position of this pixel in the matrix. The position of a pixel defines its relative position with respect to the other pixels contained in the same image.

[0035]

[0019] The sizes of an image and a region of this image are equal to the number of pixels contained, respectively, in this image and in this region.

[0020] The Icob index is a measure of the perceptual quality of an image compared to an original image. The method for measuring the Icob index of an image is described with reference to Figure 2. The quality of an image is better when the Icob index is small.

[0036]

[0021] The original image is the image whose quality is maximum and therefore for which the Icob index is zero.

[0037]

[0022] A dataset is a set of data that encodes an image. A dataset can be presented directly in the form of a matrix of pixels or in an equivalent form. A form is equivalent to a matrix of pixels if there exists a predetermined mathematical function FT that allows this dataset to be transformed into a matrix of pixels. For example, in the field of MRI (Magnetic Resonance Imaging), the k-space is a dataset because the k-space is transformable by a predetermined function FT into a matrix of pixels.

[0038]

[0023] A degraded data set is a data set that encodes a degraded image. A degraded image is an image whose Icob index is greater than zero. For example, the degraded data set does not contain enough data to encode all of the information contained in the original image, such as after downsampling or lossy compression, methods known to those skilled in the art, or because of the presence of artifacts.

[0039]

[0024] By "artifact" is meant in particular the fact that an image contains a structured pattern which is not found in the original image or the fact that there is a structured pattern in the original image which cannot be found in the degraded image.

[0040]

[0025] Chapter: Example of embodiment

[0041]

[0026] Figure 1 represents a system 2. Here, the system 2 is described in the particular case where it is a magnetic resonance imaging (MRI) system used in the medical field. Such a system 2 makes it possible to visualize the structures of the soft tissues of a human or animal body. In addition, this system 2 has the advantage of not using ionizing radiation for this and is not invasive.

[0042]

[0027] In the field of MRI, the acquired images are first encoded into the inverse image space better known as "k-space". The k-space refers to a data matrix containing the raw MRI data. This data is subjected, for example, to a mathematical function called an "FT transform" to generate the final image. The FT transform is usually a discrete or fast Fourier transform. For two-dimensional imaging, each point in the k-space corresponds to a specific spatial frequency along two directions generally called "frequency encoding direction" and "phase encoding direction" (x,y coordinates) and information about the amplitude and phase of the signal for that spatial frequency. The FT transform is applied after the k-space acquisition to transform the k-space into a final image.Each pixel in the final image is the weighted sum of all individual points in k-space. Therefore, perturbing any point in k-space results in some form of distortion of the final image, determined by the frequency and phase data stored in that particular point. In general, the central regions of k-space encode information about the contrast of the final image, and the peripheral regions of k-space encode the spatial resolution of the final image.

[0043]

[0028] Obtaining an image by MRI can take time. However, there are situations, such as dynamic angiography, perfusion MRI or cardiac function imaging, where it is necessary to accelerate the obtaining of the final image. To reduce this obtaining time, new acceleration strategies have been developed. For example, parallel imaging is today one of the most common acceleration strategies. In parallel imaging, the magnetic resonance signal is acquired simultaneously with several small independent receiving coils (called phased arrays).

[0044]

[0029] Furthermore, in the case of parallel imaging, the k-space is undersampled, i.e., points are missing in the k-space. Thus, the initially acquired data set, i.e., here, the undersampled k-space, is a degraded data set since the undersampled k-space does not contain all the information necessary to obtain the final image. In particular, the absence of points in the undersampled k-space results in the fact that many artifacts are present in the corresponding degraded image. Therefore, to improve the quality of the final image, it is necessary to construct the final image by interpolation from the data contained in the undersampled k-space or from the pixels of the degraded image. The final image is therefore a reconstructed image. Therefore, hereinafter, the terms “final image” and “reconstructed image” designate the same image and are equivalent.

[0045]

[0030] Improving the quality of the final image can be achieved in the k-space, i.e. in the frequency domain and therefore before the FT transform is applied to obtain the final image. In this case, this consists of interpolating the missing points of the sub-sampled k-space from the points present in this sub-sampled k-space to obtain a complete interpolated k-space. These missing points which have been generated by interpolation are called "interpolated missing points". The complete interpolated k-space is identical to the under-sampled k-space except that it also includes the interpolated missing points. The complete interpolated k-space is an improved data set which encodes the final image. Indeed, in this case, the final image is obtained by applying the FT transform to the complete interpolated k-space. However, the FT transform does not create any new information compared to that already contained in the complete interpolated k-space.Improving the quality of the final image can also be achieved in the image domain, i.e. by working on the pixels of the degraded image, i.e. in this case on the pixels of the image obtained after the FT transform has been applied to the sub-sampled k-space.

[0046]

[0031] Here, system 2 implements parallel imaging and achieves improvement in the quality of the final image in the frequency domain.

[0047]

[0032] The following explanations are given in the particular case where the images are in gray level so that each image corresponds to a matrix of pixels and each pixel has a value, for example, between 0 and 4095.

[0048]

[0033] System 2 includes in particular:

[0049] - a measuring device 4,

[0050] - an electronic image processing unit 6, and

[0051] - a human-machine interface 8.

[0052]

[0034] In the case of MRI, the apparatus 4 is the part of the system 2 which measures the electromagnetic waves and generates, from these measurements, the corresponding sub-sampled k-space. The apparatus 4 notably comprises sensors which measure a physical characteristic of the environment at different locations and which generate, from these measurements, the degraded data set. In the case of the system 2, the environment comprises the body of a patient and the sensors are coils for measuring a magnetic field called “radiofrequency antennas” in the case of MRI. In the context of MRI, the apparatus 4 also comprises the various elements which make it possible to emit the appropriate excitation sequences of the body to generate the sub-sampled k-space. Such sequences are known. By way of illustration, the apparatus 4 makes it possible to implement the sequence known by the acronym FLAIR (“Fluid Attenuated Inversion Recovery”).

[0053]

[0035] Furthermore, in the particular case described here, the apparatus 4 is also capable of directly generating a complete measured k-space, that is to say a k-space comprising all the points of the k-space. The complete measured k-space is therefore not sub-sampled. The complete measured k-space makes it possible to directly obtain the final image without having to construct, by interpolation, missing data from a sub-sampled k-space. Thus, when the measured k-space is complete, in the final image, the values ​​of all the pixels are directly obtained from the data measured by the apparatus 4 without going through a step of interpolating missing measurements.

[0054]

[0036] More precisely, here, it is possible to set a factor R for accelerating the generation of the final image. If the factor R is set to one, the space k measured by the apparatus 4 is complete and no interpolation is implemented to obtain the final image. In return, the time taken to obtain the final image is maximum. If the factor R is set to N a , where N a is a number greater than one, the time to obtain an image is equal to Tmax / N a , where Tmax is equal to the maximum acquisition time. To reduce the acquisition time by the factor R, the device 4 only performs part of the measurements necessary to fill the k-space. This results in the k-space being undersampled. The larger the factor R, the more the k-space is undersampled and the faster the final image is obtained.

[0055]

[0037] Unit 6 corresponds to the part of system 2 which constructs the final image from the sub-sampled k space measured by the apparatus 4. For this, unit 6 comprises an electronic computer 20. Typically, computer 20 comprises a microprocessor 24 capable of executing instructions and a memory 26 comprising the instructions and data necessary for the operation of unit 6. Thus, in particular, memory 26 comprises:

[0056] - the executable code of an optimizer 28 configured to construct a complete interpolated k-space from a sub-sampled k-space measured by the apparatus 4,

[0057] - the executable code of the FT transform, - the executable code of a control module of the human-machine interface 8, and

[0058] - the executable code of a machine learning module 30.

[0059]

[0038] When the executable code of the optimizer 28 is implemented in a computer, it forms with the latter what is subsequently called “a reconstruction device”.

[0060]

[0039] When the executable code of the module 30 is implemented in a computer, it forms with this electronic computer a device subsequently called a “learning device”. Thus, in this embodiment, the unit 6 comprises both a reconstruction device and an automatic learning device.

[0061]

[0040] The optimizer 28 comprises numerous parameters 0j whose values ​​can be determined by implementing an automatic learning phase. The parameters 0j are adjustable parameters of the optimizer 28 which make it possible to adjust the process of developing, by the optimizer 28, an improved data set from a degraded data set. Thus, the improved data set developed by the optimizer 28 varies both as a function of the degraded data set and the values ​​of the parameters 0j. The parameters 0j are parameters specific to the optimizer 28 and independent of the degraded data sets processed by this optimizer 28. In other words, once adjusted, the values ​​of the parameters 0j no longer vary and, in particular, do not vary as a function of the degraded data sets processed by the optimizer 28. Here, the values ​​of the parameters 0j are determined as described with regard to the method of FIG. 7.For this purpose, the executable code of the optimizer 28 is designed so that it is possible to change the values ​​of the parameters 0j without having to compile the source code of the optimizer 28 in order to obtain a new executable code in which the parameters 0j have new values. For example, the current values ​​of the parameters 0j are recorded in a file 32 stored in the memory 26.

[0062]

[0041] In this embodiment, the optimizer 28 comprises at least one artificial neural network. This network comprises the parameters 0j. Typically, in the field of MRI, the optimizer 28 comprises a convolutional neural network known by the acronym CNN (“Convolutional Neuronal Network”). For example, the convolutional neural network is that described in one of the following articles:

[0063] - Akçakaya Mehmetet AL : « Scan-specific robust artificial-neural-networks for k-space interpolation (RAKI) reconstruction: Database-free deep learning for fast imaging », Magnetic Resonance in Medicine. 2019;81(l), pages 439-453, - Dawood Peter et al : « Iterative training of robust k-space interpolation networks for improved image reconstruction with limited scan specific training samples », Magnetic Resonance in Medicine. 2023;89(2), pages 812-827.

[0064]

[0042] The learning module 30 is configured to execute the learning phase which makes it possible to determine the values ​​of the parameters 0j of the optimizer 28. In addition, here, the module 30 is also capable of constructing, by controlling the apparatus 4, a database 34 containing the data sets necessary to carry out the automatic learning of the values ​​of the parameters 0j. In this embodiment, the base 34 contains sub-sampled k spaces representative of the sub-sampled k spaces that the optimizer 28 is likely to receive when it is operated. For each of these sub-sampled k spaces, the base contains a complete measured k space, that is to say a k space which has not been sub-sampled. The complete measured k space corresponds here to at least one original data set encoding an original image.

[0065]

[0043] The human-machine interface 8 typically comprises a screen on which the final images constructed by the unit 6 are displayed. The human-machine interface 8 may also comprise a printer for printing the final images and buttons for controlling the operation of the system 2.

[0066]

[0044] Figure 2 represents the method of measuring the quality of an Irec image compared to an original lorg image. These steps are executed by an electronic computer such as the computer 20. The measurement method is described in the particular case of a two-dimensional image.

[0067]

[0045] During a step 50, the electronic computer acquires the Irec and lorg images. The Irec and lorg images are of the same size.

[0068]

[0046] During a step 52, a residual image 1res, of the same size as the images Irec and lorg, is constructed. For this, the value of each pixel k of the residual image is calculated using the following relation: lres(P k ) =lorg(P k ) - lrec(P k ), Or :

[0069] - P k are the coordinates of pixel k, pixel k being located at the same position in the Irec, lorg and 1res images,

[0070] - lres(P k ) is the value of the pixel of the residual image located at position P k ,

[0071] - lorg(P k ) is the value of the pixel of the original image located at position P k ,

[0072] - lrec(P k ) is the value of the pixel of the reconstructed image located at position P k .

[0047] In the case of a two-dimensional image, the position P k corresponds to the x,y coordinates of pixel k in this image.

[0073]

[0048] Then, during a step 54, for each pixel k of the residual image 1res, a coefficient C(P k ) correlation is calculated. The coefficient C(P k ) is representative of the correlation between the pixels of a region R k of the 1res image and the pixels of the same region R k in the image lorg. The R region k is centered on pixel k. Here, the region R k is for example a square of 11 pixels by 11 pixels centered on pixel k so that its size is equal to 121 pixels. The size and shape of this region R k is the same for all pixels k.

[0049] Here, each coefficient C(P k ) is calculated from the covariance between the pixels of the region R k of the 1res image and the pixels of the R region k of the lorg image. For this, in this embodiment, the 121 pixels of the R region kare aligned one behind the other so as to obtain a series of 121 consecutive values. Subsequently, the series of values ​​thus obtained from the image lorg is noted o k and each value of this series is noted o k (i), where i is the order number of this value in this series. The series of values ​​obtained from the Irec image is noted r k and each value of this series is noted r k (i). The coefficient C(P k ) is then calculated using the following relationships:

[0074] where: - S is the number of values ​​in series o k and r k ,

[0075] - Om, k and r m , k are the arithmetic means of the values ​​contained, respectively, in the series o k and r k ,

[0076] - Cov(P k ) is the covariance between the series o k and r k, estimated in an unbiased manner,

[0077] - Oorg(P k ) and Ores(P k ) are the standard deviations of the values ​​of the series, respectively, o k and r k estimated in an unbiased manner.

[0078] - £ is a small positive number to avoid dividing by zero, e.g. 10 -9 .

[0079]

[0050] Then, during a step 56, the measurement of the quality of the image Irec is constructed from the coefficients C(P k ) calculated during step 52. In this exemplary embodiment, the measurement of the image quality Irec is constructed solely from the coefficients C(P k ). Moreover, here, the measurement of image quality is expressed in the form of a single value called the "Icob index". For this purpose, the Icob index is taken equal to an Lp norm of the vector formed by all the coefficients C(P k) calculated during step 54. Thus, the Icob index is calculated using the following relationship: Or :

[0080] - p is a predetermined integer greater than or equal to one,

[0081] - Ti is the size of the Irec and lorg images.

[0082]

[0051] Here, p is chosen equal to one. Since the norm Lp is here normalized by the size Ti, in this embodiment, the index Icob can only vary between zero and one. When the quality of the 1res image is maximum, that is to say that the images Irec and lorg are identical, the index Icob is equal to zero. The worse the quality of the 1res image, the closer the index Icob is to one.

[0083]

[0052] It has been demonstrated, by numerous experiments, that the Icob index is a measure of the quality of an image which is more sensitive to the presence of artifacts than the other known indices used to measure the quality of an image. In particular, it has been verified that the Icob index is a more sensitive measure of the quality of an image than the following known indices: the SSIM index, the NRMSE index, the NMAE index, the PSNR index, the EQM index (“Mean Square Error”) also known by the English acronym MSE (“Mean Square Error”). This is illustrated on a particular example using figures 3 to 6.

[0084]

[0053] Figure 3 shows an original image 60. This image 60 corresponds to a section of a brain obtained using system 2 using the FLAIR excitation sequence. To obtain image 60, the acceleration factor R was set to one so that image 60 is constructed from a complete measured k-space and therefore corresponds to the original image.

[0085]

[0054] Figure 4 shows an image 70 of the same brain slice as shown in image 60 except that it was obtained by choosing an acceleration factor R greater than one. Thus, a subsampled k-space was acquired. Then, image 70 was constructed from this subsampled k-space using the crRAKI (“complex residual RAKI”) reconstruction algorithm to interpolate the missing points from the subsampled k-space. The crRAKI algorithm was described in the following presentation: Nimje S, de Rochefort L, Artières T: “Accelerating Phase and Quantitative susceptibility mapping with Scan-Specific Complex Convolutional Neural Networks”, ISMRM. Toronto, Canada; 2023. p. 3882. (https: / / www.ismrm.org / 23 / program-files / D-174.htm).

[0086]

[0055] Figures 5 and 6 represent, respectively, images 80 and 90 constructed from the same subsampled k-space as that used to construct image 70 except that the reconstruction algorithms used are, respectively, rRAKI (“residual RAKI”) and GRAPPA (“Generated Autocalibrating Partially Parallel Acquisitions”). The rRAKI reconstruction algorithm is described in the following article: Zhang Chi et al: “Residual RAKI: A hybrid linear and non-linear approach for scanspecific k-space deep learning”. NeuroImage, 2022, vol. 256, 119248. The GRAPPA reconstruction algorithm is described in the following article: Griswold Mark A et al.: “Generalized autocalibrating partially parallel acquisitions (GRAPPA)”, Magnetic Resonance in Medicine. 2002;47(6), pages 1202-1210

[0087]

[0056] Figures 4 to 6 also represent images 70r, 80r and 90r which correspond, respectively, to the amplitude of the residual images constructed between the following pairs of images: (60, 70), (60, 80) and (60, 90).

[0088]

[0057] For each of the images 70, 80 and 90, the Icob index and the SSIM, NRMSE, NMAE, PSNR indices were constructed. The SSIM, NRMSE, NMAE, PSNR indices indicate that the image with the best quality is image 80, only the Icob index indicates that it is image 70. A visual examination of the residual images confirms that it is indeed image 70 which presents the least artifacts, with a level of residues which is spatially more random, and with a lesser intensity. An example of an artifact visible on the residual image 80r is pointed by the arrow 80c.

[0089]

[0058] The Icob index also proved to be more sensitive than the SSIM, NRMSE, NMAE, PSNR indices in the following situations:

[0090] - relative to the original image, the pixels of the reconstructed image are moved by a translation in a particular direction,

[0091] - relative to the original image, the pixels of the reconstructed image are moved by a rotation of a particular angle around an axis perpendicular to the image plane,

[0092] - compared to the original image, the pixels of the reconstructed image are obtained after applying a Gaussian blur.

[0093]

[0059] A method for automatic learning of optimal values ​​0j, op t for the parameters 0j of the optimizer 28 is now described with reference to figure 7. This method is implemented by the automatic learning device of the system 2, that is to say by the module 30 executed by the computer 20.

[0094]

[0060] This method begins with a step 100 of providing the database 34. For this, in this embodiment, the procedure is as follows:

[0095] - a body is placed inside the system 2, then - the module 30 controls the apparatus 4 so that it generates an original set of data, that is to say a complete measured k-space, corresponding to a section of the body, then

[0096] - the module 30 controls the apparatus 4 so that it generates a degraded set of data, that is to say a sub-sampled k space, corresponding to this same particular section of the body, possibly using a different excitation sequence,

[0097] - the original game and the degraded game thus generated are recorded in the database 34 and associated with each other.

[0098]

[0061] For example, to generate a full measured k-space, module 30 sets the acceleration factor R to the value one. Conversely, to generate a sub-sampled k-space, the acceleration factor R is set to a value greater than one.

[0099]

[0062] In order to populate the database 34 with N o different original data sets, what has just been described is carried out for several different sections and / or several different bodies and / or several different excitation sequences. Typically, the number N o depends on the spatial coverage desired by the user and requested from the system 4. In general, the number N o is either equal to 1 when imaging a single slice, or greater than eight or ten and, sometimes, greater than one hundred for multi-slice imaging.

[0100]

[0063] Once step 100 is completed, the automatic learning of the optimal values ​​0j, opt for the parameters 0j of the optimizer 28 begins. The optimal values ​​0j,opt are determined to minimize a cost function Fc. What characterizes the automatic learning carried out by the module 30 is that the value of the function Fc is calculated from measurements of the quality of the images carried out in accordance with the method of fig. 2. Thus, all conventional methods of learning the optimal values ​​0j, op t for the parameters 0j of a convolutional neural network can be used except that the cost function of this method is modified to also vary according to Icob indices. Therefore, subsequently, only the main steps of machine learning are summarized.

[0101]

[0064] During an initialization step 102, the module 30 chooses initial values ​​for each parameter 0j of the optimizer 28. For example, these initial values ​​are chosen randomly. They are recorded in the file 32 as current values ​​0j, t parameters 0j.

[0065] Then, during an optimization step 104, the module 30 determines new values ​​for the parameters 0j, which decrease the value of the function Fc.

[0102]

[0066] For this, during this step 104, the value of the function Fc, corresponding to current values ​​0j, t of the parameters 0j of the optimizer 28, is calculated by performing the following operations.

[0103]

[0067] During an operation 106, the module 30 sets the optimizer 28 with the current values ​​0j, tparameters 0j then commands the optimizer 28 thus parameterized so that it develops, for each degraded set of data contained in the database 34, an improved set of data, that is to say here a complete interpolated k-space. In addition, in the particular case described here, the reconstruction device also generates the reconstructed image corresponding to each of these complete interpolated k-spaces generated using the FT function.

[0104]

[0068] Then, during an operation 108, for each improved data set, the module 30 measures the quality, relative to the original image, of the reconstructed image coded by this improved set. The original image is that coded by the original data set associated, by the database 34, with the degraded data set that the optimizer 28 received to generate this improved data set. To do this, the module 30 executes the method of FIG. 2. Thus, an Icob index is measured for each reconstructed image.

[0105]

[0069] During an operation 110, the module 30 calculates the value of the function Fc from the measured Icob indices. In this exemplary embodiment, the value of the function Fc depends only on the measured Icob indices. More precisely, here, the value of the function Fc is simply the arithmetic mean of the Icob indices measured during the operation 108. In other words, since the Icob indices are positive, the value of the function Fc is equal to the L1 norm of the Icob indices measured for each reconstructed image.

[0106]

[0070] During a step 114, the module 30 verifies that the current values ​​of the parameters 0j determined during step 104 correspond to a value of the function Fc close to its minimum. To do this, the module 30 verifies whether a stopping criterion is satisfied. The stopping criterion can be the following but many other stopping criteria are possible:

[0107] OR

[0108] - Npa is equal to the number of parameters 0j of the optimizer 28,

[0109] - 0d, t are the current values ​​of parameters 0 and

[0110] - 0j,M are the previous values ​​of the parameters 0j, i.e. those obtained at the end of the previous iteration of step 104.

[0111]

[0071] If the stopping criterion is not satisfied, the method returns to step 104. If, on the contrary, the stopping criterion is satisfied, during a step 116, the optimal values ​​0 j, op t determined for each parameter 0j are taken equal to the current values ​​0j, t corresponding. The values ​​0j, op t are recorded in file 32.

[0112]

[0072] A method of manufacturing and operating the system 2 will now be described with reference to FIG. 8.

[0113]

[0073] The method begins with a phase 130 of manufacturing the system 2.

[0114]

[0074] During a step 132, the apparatus 4, the computer 20 and the human-machine interface 8 are provided and assembled together.

[0115]

[0075] During a step 134, the optimizer 28 and the module 30 are also implemented in the computer 20. Typically, for this, the executable codes of the optimizer 28 and the module 30 are recorded in the memory 26.

[0116]

[0076] At this stage, the file 32 is blank or contains values ​​for the parameters 0j which are not necessarily optimal. Thus, to obtain a reconstruction device capable of correctly reconstructing an image from a degraded set of data acquired by the apparatus 4, a machine learning step 136 is executed. Here, during this step 136, the method of FIG. 7 is executed by the module 30.

[0117]

[0077] Finally, during a step 138, a value for each of the parameters 0j is implemented in the calculator 20. Here, the value of each parameter 0j is between 0.95*0j, op t and l,O5*0j, op t, and, preferably, between 0.99*0j, op t and l,Ol*0j. op t., where 0j, op t is the optimal value determined during step 136. Here, the values ​​of the parameters 0j implemented in the calculator 20 are equal to the optimal values ​​0j, op t. In this exemplary embodiment, the implementation of the values ​​of the parameters 0j in the calculator 20 consists of recording them in the file 32.

[0118]

[0078] From this moment, the manufacture of the image reconstruction device is completed. The manufacture of the system 2 is then also completed.

[0119]

[0079] Then, during a phase 150, the system 2 is operated. During this operating phase, the apparatus 4 generates only a degraded set of data so as to accelerate the time to obtain an image. The reconstruction device then constructs the reconstructed image from this degraded set of data generated by the apparatus 4. For this, the optimizer 28 first develops an improved set of data from the degraded set of data and then the FT function is applied to the improved set of data to obtain the reconstructed image. This reconstructed image is then displayed on the screen of the human-machine interface 8.

[0120]

[0080] During the operating phase, steps 136 and 138 can be executed again to automatically recalibrate the optimizer 28.

[0121]

[0081] Chapter III: Variants:

[0122]

[0082] Variants of the coefficients C(P k ) :

[0123]

[0083] Other relationships can be used to obtain a coefficient C(P k ) representative of the correlation between the pixels in the residual image and the pixels in the same region in the original image. For example, the number £ is omitted. In this case, a preliminary check must be performed to avoid dividing by zero and division by zero is treated differently. Each coefficient C(P k ) can also be calculated using the following relation: C(P k ) = Cov(P k ). In the latter case, the coefficients C(P k ) are not standardized and the calculation of standard deviations o0r g (P k ) and o r es(P k ) can be omitted.

[0124]

[0084] It is also possible to calculate each coefficient C(P k ) by adding the coefficient C N (P k ) calculated using the following relationship: Or :

[0125] - S is the number of values ​​in series o k and r k ,

[0126] - N org (P k ) and N res (P k ) are the L2 norms of the values ​​of the series, respectively, o k and r k .

[0127] - £ is a small positive number to avoid dividing by zero, e.g. 10 -9 .

[0128] - a is a positive number, preferably equal to 1.

[0129]

[0085] Other sizes are possible for the R region k used. In practice, the size of the region R k is greater than sixteen or thirty-six pixels and, often, less than a thousand pixels. The R region k is not necessarily a square but can also have other shapes. For example, the region used can be a rectangle longer than it is wide or have a cross or disc shape.

[0130]

[0086] Alternatively, an area of ​​interest is defined in the reconstructed image. For example, this area of ​​interest surrounds the portion of the image that is of interest to the user and excludes other portions of the image. In the case of a medical image, the area of ​​interest excludes portions of the image that do not correspond to a portion of a human or animal body. In this alternative, instead of calculating a coefficient C(P k ) for all pixels of the image, the coefficients C(P k) are calculated only for the pixels located inside the area of ​​interest.

[0087] Everything previously described in the particular case of a two-dimensional image also applies to the case of an N-dimensional image, where N is an integer greater than two. In particular, what has been described also applies to the case of a three-dimensional image commonly called a "3D image". In the case of a 3D image, the position of a pixel of this 3D image is identified by x,y,z coordinates of an orthogonal reference frame. In this case, the measurement of the quality of an image is carried out as previously described except that the region R k used to calculate the coefficient C(P k ) is a three-dimensional volume, such as a cube, centered on the pixel at position P k .

[0131]

[0088] Variants of the construction of the quality measure:

[0132]

[0089] The Icob index can be calculated using a standard other than the L1 standard. For example, the L2 standard or any of the other Lp standards is used.

[0133]

[0090] The Icob index may also not be normalized, i.e. C(P k ) is then not divided by the standard deviations.

[0134]

[0091] Alternatively, the quality measurement is not simply taken equal to the Icob index. For example, during step 56, one or more other loth indices are calculated. Then, the image quality measurement is taken equal to a combination, for example linear, of the values ​​of the different calculated indices including the Icob index. As examples of other loth indices representative of the quality of an image, the following known indices may be cited: the NRMSE index, the NMAE index, the PSNR index, the EQM index, the SSIM index. The loth index may also correspond to the average of C N (P k) for the pixels of the image, or for an area of ​​interest identical to that used to calculate Icob.

[0135]

[0092] In another variant, during step 56, in addition to or instead of constructing the index Icob, an image in which the value of each pixel k is calculated from the value of the coefficient C(P k ), is constructed and then displayed on an electronic screen. For example, the value of each pixel in this image is taken equal to the value of the coefficient C(P k ) or to F(C(P k )), where F is a predefined continuous function. For example, the function F is a bijective function such as an affine function. This constructed image indicates the locations where the artifacts are located in the reconstructed image and is a measure of the quality of the reconstructed image.

[0136]

[0093] Variants of the reconstruction device:

[0094] Other embodiments of the FT transform are possible. For example, the FT transform can also be a “Hartley” transform.

[0137]

[0095] Many different embodiments are possible for the optimizer 28. In particular, the optimizer does not necessarily comprise a convolutional neural network. For example, as a variant, the optimizer 28 is configured to implement the GRAPPA (“Generated Autocalibrating Partially Parallel Acquisitions”) reconstruction algorithm. In the latter case, the parameters 0j whose values ​​are determined during the learning phase are the parameters of the convolution filters known as the GRAPPA kernel and discussed in the following article: Nana, R., Zhao, T., Heberlein, K., LaConte, SM and Hu, X: “Cross-validation-based kernel support selection for improved GRAPPA reconstruction”, 2008, Magn. Reson. Med., 59: 819-82.

[0138]

[0096] In fact, the teaching given here applies to any optimizer, comprising parameters 0 capable of receiving a degraded set of data and of developing, in response, an improved set of data encoding the reconstructed image Irec. For this, the values ​​of the parameters 0j are determined during a machine learning phase like that described previously. In particular, during this machine learning phase, the value of the cost function is calculated from the indices Icob of the reconstructed images Irec.

[0139]

[0097] The teaching given here is not limited to the case where the optimizer develops the improved data set by supplementing the degraded data set with data interpolated from the data present in this degraded data set. For example, what has been described here applies to the denoising of images to reduce structured artifacts, because an image in which these are reduced has an Icob index lower than the Icob index of the initial noisy image. In this case, the degraded data set encodes the noisy image and the improved data set encodes a reconstructed image in which the structured noise has been reduced.

[0140]

[0098] The Icob index can also be used in the field of image registration. Indeed, a well-registered image has a lower Icob index than a poorly registered image. In this case, the degraded data set codes the non-registered image(s) and the improved data set codes a registered image in which the registration has been improved. The construction of the registered image generally requires the use of a transformation model. The parameters 0j whose values ​​are determined during the learning phase then correspond to the different parameters of this transformation model. As an illustration, the optimizer can implement one of the transformation models briefly presented in Table 1 of the following article: Avants BB et Al: “A reproducible evaluation of ANTs similarity metric performance in brain image registration”. Neuroimage, 2011 Feb 1; 54(3): 2033-44. doi:

[0141] 10.1016 / day. neuroimage.2010.09.025.

[0142]

[0099] Furthermore, what has been described here in the particular case of the imaging field applies to any field where a device for reconstructing an Irec image from a degraded data set is implemented. For example, what has been described here applies to the fields of lossy image or video compression and also to the reconstruction of images or video from damaged files (also known as "Inpainting").

[0143]

[0100] In the case of lossy image or video compression, the degraded data set encodes the compressed image and the enhanced data set encodes the decompressed image. In the field of lossy image or video compression, the step 100 of providing and recording the database 34 comprises:

[0144] - the acquisition of original data sets, i.e. uncompressed images, then

[0145] - lossy compression of each original acquired data set to obtain the degraded data set corresponding to each of these original acquired data sets, then

[0146] - recording, in the database 34, each degraded set of data obtained associated with the corresponding original set of data acquired.

[0147]

[0101] In the case of image or video reconstruction, the degraded data set is the damaged file. The database 34 then includes damaged files and, for each of these damaged files, the original data set, i.e. the undamaged file.

[0148]

[0102] It is emphasized that, outside the field of imaging, the reconstruction device is not necessarily associated with a measuring device. In this case, the reconstruction device is capable of acquiring a digital file containing the degraded set of data. This acquired degraded set of data has previously been generated, for example, by a remote measuring device or created electronically by a computer in response to instructions transmitted by an operator.

[0149]

[0103] Variants of machine learning:

[0150]

[0104] Other cost functions are possible. For example, the value of the Fc function is equal to the Lp norm of the vector formed by all the measured Icob indices, with p greater than one. The value of the Fc function can also vary as a function of other criteria such as, for example, other quality indices than the Icob index. For example, the value of the Fc function can also vary, in addition, as a function of the PSNR or SSIM index.

[0151]

[0105] Other criteria for stopping the learning phase are possible.

[0152]

[0106] Alternatively, the learning module 30 is unable to control the apparatus 4 to generate the data sets useful for populating the database 34. In this case, complete k-spaces are provided to it. For example, these may be the complete k-spaces contained in a public database such as that known as fastMRI. If the sub-sampled k-spaces corresponding to the provided complete k-spaces are not also provided, the module 34 is configured to generate these sub-sampled k-spaces from the provided complete k-spaces. For this, the module 34 sub-samples the provided complete k-spaces to populate the database 34 with both the complete k-spaces and the sub-sampled k-spaces. In another alternative, the sub-sampled k-spaces are also provided to the module 34 which can then directly record them in the database 34.

[0153]

[0107] Alternatively, the system 2 does not include a learning device. The module 30 and the database 34 are omitted. The system 2 cannot self-calibrate. In this case, the module 30 is implemented in a computer different from the computer 20 to form a learning device independent of the system 2. This independent learning device is then, for example, only used during the manufacture of the system 2 to determine the values ​​of the parameters 0j to be implemented in the system 2. Then, the values ​​of the parameters 0j of the optimizer 28 can no longer be modified or only modified by replacing the file 32 with a new file.

[0154]

[0108] Other variants:

[0109] In a simplified variant, the apparatus 4 is only a low-resolution measuring apparatus which is not capable of generating the original data set. In this case, at least during the training phase, an additional high-resolution measuring apparatus is used to generate each original data set of the database 34. Then, during the exploitation phase 150, the high-resolution measuring apparatus is omitted.

[0155]

[0110] Other embodiments of the apparatus 4 are possible. For example, it may be a radiography apparatus using ionizing radiation such as X-rays or gamma rays. It may also be a camera or a video camera capable of capturing visible light reflected by an object. In these last two examples, the data sets encoding the images are not k spaces.

[0156]

[0111] System 2 is not necessarily an imaging system used in the medical field. For example, system 2 can also be adapted to be used in different industrial fields to, for example, detect a defect in a manufactured or repaired part.

[0157]

[0112] Several of the variants described above can be combined in the same embodiment.

[0158]

[0113] Chapter IV: Advantages of the described embodiments:

[0159]

[0114] Measuring the quality of a reconstructed image relative to the original image by constructing a residual image and then calculating the coefficients C(P k ) allows to better highlight the presence of artifacts in the reconstructed image than is currently possible using other known methods of measuring image quality such as those using only PSNR and SSIM indices.

[0160]

[0115] Because of this, when this measurement of the quality of an image is used to determine the values ​​of the parameters 0j of the optimizer 28, the image reconstructed by the image reconstruction device exhibits fewer artifacts than when the values ​​of the parameters 0j are determined using other known methods.

Claims

Claims 1. Method for measuring the quality of a reconstructed image in relation to an original image, this method comprising the execution of the following step by an electronic computer: 1) the construction (52) of a residual image, during which the value of each pixel k of the residual image is calculated using the following relation: lres(P k ) =lorg(P k ) - lrec(P k ), Or : - P k is the position of pixel k in the reconstructed, original and residual images, - lres(P k ) is the value of the pixel of the residual image located at position P k , - lorg(P k ) is the value of the pixel of the original image located at position P k , - lrec(P k ) is the value of the pixel of the reconstructed image located at position P k, and characterized in that the method also comprises the execution of the following steps by the electronic computer: 2) for several pixels of the residual image, the calculation (54) of a coefficient C(P k ) representative of the correlation between the pixels of a region of the residual image centered on the pixel located at position P k and pixels of the same region in the original image, the size and shape of each region being the same for all calculated correlation coefficients, the predetermined size of each region being greater than nine pixels and each coefficient C(P k ) being calculated from the covariance between the pixels of the residual image region and the pixels of the same region in the original image, 3) the construction (56) of a measure of the quality of the reconstructed image from the coefficients calculated during step 2).

2. The method of claim 1, wherein constructing a measure of image quality comprises: - the calculation of an Lp norm using the following relation: Or : - Icob is the value of the Lp norm, - p is a predetermined integer greater than or equal to one, - Ti is the size of the original and reconstructed images, - C(P k ) are the coefficients calculated during step 2), and - the construction of the measurement of the quality of the reconstructed image from the Icob value of this Lp standard.

3. A method according to any one of the preceding claims, wherein the method comprises: - the construction of an image in which the value of each pixel k is constructed from the value of the coefficient C(P k) calculated, to obtain an image representing the locations where artifacts are located in the reconstructed image, then - displaying this image on a screen.

4. Automatic learning process of optimal values 0j, op t for parameters 0j of an image quality optimizer capable of receiving a degraded set of data encoding a degraded image and of developing, from this degraded set of data and the values of the parameters 0j, an improved set of data encoding a reconstructed image whose quality, when measured using a method according to any one of the preceding claims, is better than the quality of the degraded image, this machine learning method comprising: - the supply (100) and the recording in a memory of an electronic computer, of a database containing degraded sets of data representative of the degraded sets of data likely to be supplied to the optimizer and, for each of these degraded sets of data, an original set of data coding an original image whose quality is maximum, then the execution of the following steps by the electronic computer: 1) an initialization step (102) during which initial values are chosen for each parameter 0j of the optimizer, then 2) an optimization step (104) which determines new values for the parameters 0j of the optimizer, which decrease the value of a predetermined cost function, during this optimization step, the value of the cost function corresponding to current values of the parameters 0j of the optimizer is calculated by executing the following operations: 2a) the development (106), by the optimizer parameterized with these current values of the parameters 0j and for each degraded set of data contained in the database, of an improved set of data, then 2b) for each improved data set produced during operation 2a), the measurement (108) of the quality of the reconstructed image, coded by this improved data set, compared to the original image, the original image being that coded by the original data set associated, by the database, with the degraded data set from which the optimizer produced this improved data set, then 2c) the calculation (110) of the value of the cost function from the measurements of the quality of the reconstructed images, carried out during operation 2b), then 3) a step (114) of verifying that the current values of the parameters 0j determined during step 2) correspond to a value of the cost function close to its minimum, 4) if the cost function is not close to its minimum, the process returns to step 2) and, on the contrary, if the cost function is sufficiently close to its minimum, the optimal values 0j, op t for each parameter 0j are taken equal (116) to the corresponding current values of the parameters 0j, characterized in that during operation 2b), the measurement of the quality of each reconstructed image is carried out by implementing a method according to any one of the preceding claims.

5. Method according to claim 4, in which the step (100) of providing and recording the database comprises: - the generation, using measuring equipment, of each of the original data sets contained in the database, and Tl - the automatic generation, for each of the original sets contained in the database, of the degraded set of data associated with this original set of data in the database.

6. The method of claim 5, wherein the automatic generation of each of the degraded data sets comprises generating these degraded data sets by the same measuring apparatus as that used to generate the original data sets.

7. Method according to claim 5 or 6, in which the measuring apparatus is a magnetic resonance imaging apparatus and the degraded data sets are sub-sampled k spaces.

8. Method according to any one of claims 4 to 7, wherein the image optimizer comprises a neural network.

9. Information recording medium (26), readable by a microprocessor, comprising instructions executable by this microprocessor, characterized in that this medium comprises non-transitory instructions for the execution of a method according to any one of claims 4 to 8, when these instructions are executed by the microprocessor.

10. Method for manufacturing a device for reconstructing an image from a degraded data set, this degraded data set encoding only a degraded image whose quality, when measured using a method according to any one of claims 1 to 3, is lower than the quality of the reconstructed image, this method comprising: - the implementation (134), in an electronic computer, of an image quality optimizer, this optimizer being capable of receiving the degraded set of data and of developing, from this degraded set of data, an improved set of data coding the reconstructed image, this image quality optimizer comprising parameters 0j from which each improved set of data is also developed, - automatic learning (136) of optimal values 0j, op t for the 0j parameters of the image quality optimizer, - the implementation (138), in the electronic calculator, of a value for each of the parameters 0j between 0.95*0j, op t and l,O5*0j, op t, to obtain the image reconstruction device, characterized in that the automatic learning (136) is carried out in accordance with any one of claims 4 to 9.

11. Imaging system comprising: - measuring equipment (4) capable of generating: - original data sets each encoding an original image whose quality, when measured using a method according to any one of claims 1 to 3, is maximum, and - degraded data sets each encoding a degraded image whose quality, when measured using a method according to any one of claims 1 to 3, is lower than the quality of the corresponding original image, - a device for reconstructing a so-called "reconstructed" image capable of constructing, from a degraded set of data generated by the measuring apparatus (4), an improved set of data encoding a reconstructed image whose quality, when measured using a method according to any one of claims 1 to 3, is better than the quality of the degraded image, this reconstruction device comprising an electronic computer (20) in which is implemented an image quality optimizer (28) capable of receiving the degraded set of data and of developing, from this degraded set of data, the improved set of data encoding the reconstructed image, this image quality optimizer (28) comprising parameters 0j from which each improved set of data is also developed, and - an automatic learning device for optimal values 0j, opt for the parameters 0j of the image quality optimizer, characterized in that the machine learning device is configured to implement a method of machine learning the optimal values 0j, op t in accordance with claim 5.

Images