Reconstruction method for an image from an image, called input image, produced by a portable device designed to generate a main magnetic field.

Abstract

A reconstruction method for determining an image, called the reconstructed image, said method comprising the following steps: a learning step for distortion correction reconstruction from training data, and an inference step (Ei) comprising determining said reconstructed image by the conjugate phase method; the learning step comprising training a variational network exhibiting: Figure to be published: Figure 1

Description

Title of the invention: Method for reconstructing an image from an image, called input, produced by a portable device designed to generate a main magnetic field. technical field

[0001] The present invention relates to the field of magnetic resonance imaging. More particularly, the present invention relates to a magnetic resonance imaging device, and in particular to a magnetic resonance imaging device having a radio frequency assembly provided with a transmit / receive radio frequency coil.

[0002] The present invention is particularly relevant when considering a portable magnetic resonance imaging device. Prior art

[0003] Magnetic resonance imaging (MRI) is now widely used to image, non-invasively, the interior of bodies, particularly human bodies. In particular, magnetic resonance imaging makes it possible to probe the hydrogen nuclei, and especially their nuclear spin, of water molecules that make up part of the body under examination.

[0004] In this regard, an MRI device is equipped with a magnet intended to impose a static magnetic field (called "main magnetic field") on the body, under the effect of which the nuclear spins associated with the hydrogen nuclei contained in the water molecules forming part of this body become polarized.

[0005] In particular, the magnetic moments associated with these spins align preferentially along an axis, called the z-axis, determined by the orientation of the main magnetic field so as to create a magnetization of the body.

[0006] An MRI device also includes gradient coils configured to produce small-amplitude, spatially varying magnetic fields when a current is applied to them. More specifically, the gradient coils are designed to produce a magnetic field component that is aligned parallel to the main magnetic field and that varies linearly in amplitude with position along one of the x, y, or z axes (the x, y, and z axes being pairwise perpendicular).

[0007] Thus, the combined effects of the magnetic fields imposed by the gradient coils make it possible to spatially encode each of the positions of the body intended to be probed.

[0008] An MRI device also includes at least one radio frequency (RF) coil intended to act as an RF transceiver. In particular, at least one radio frequency coil is configured to emit RF energy pulses of a frequency equal to or close to the resonance frequency of the spins of hydrogen nuclei and which is at least partially absorbed by these nuclei.

[0009] As soon as the RF emission is interrupted, the nuclear spins relax to return to their initial energy state and in turn emit an RF signal that can be collected by at least one RF coil. This RF signal is then processed using a computer and reconstruction algorithms to obtain an image of the body.

[0010] The main magnetic field, generally between 1.5 Tesla and 3 Tesla, makes it possible to achieve relatively reasonable signal-to-noise ratios (SNR) and consequently to form images of the human body of sufficient quality and for durations on the order of a minute or more.

[0011] However, there are circumstances in which it is not possible to implement a primary magnetic field of such intensity. Portable MRI devices are an example. These generally include a permanent magnet or electromagnets of limited capacity, and cannot impose a primary magnetic field with an intensity greater than 60 mT, or even greater than 200 mT, without negatively impacting the mass or size of the MRI device in question.

[0012] This limitation in terms of the main magnetic field strength directly affects the performance of the MRI device. In particular, images obtained with such an MRI device are likely to exhibit significantly degraded quality due to an unfavorable signal-to-noise ratio. This unfavorable signal-to-noise ratio partly reflects a significant decrease in the magnetization present in the tissues.

[0013] In the ideal case, the precession of the core is driven by a static magnetic field (named field B0) which is homogeneous. Spatial coding process model

[0014] Consider the example of a 2D Spin-Echo sequence. Suppose the z-direction is defined as the slice selection direction. The x and y directions can then be defined as the frequency (read) and phase encoding directions, respectively. Any 3D object is first truncated into a predefined number of slices along the z-direction. On each 2D slice, the process of encoding the object's tomographic information for a perfect MRI system could be modeled as a discrete Fourier transform process.

[0015] Without loss of generality, the image can be represented by a scalar-valued function x(r), the spatial coding process then being formulated as follows:

[0016] y(k(t) ) = fx(r)e~ j ^ r Dr. # (1) £2

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[0032] where k(t) is a position vector in space K, while this is the time-varying signal read by the receiver coil during the read step. The integral domain D is equal to the entire field of view (FOV) of the scanner. In a real MRI system, it is not possible to obtain a perfectly homogeneous BQ field and ideally linear gradient fields. While these inhomogeneities can sometimes be neglected when the main magnetic field has a relatively high intensity, this is not feasible in the context of low- or ultra-low-field MRI scanners. Thus, an additional phase-shift term must be added to the previous coding model to cover the inhomogeneity of the BQ field and the nonlinearity of the gradient fields. The corrected spatial coding process can then be formulated as follows: y(k(t) ) = Lx(r)ej^re-j2n^tdr # (2) £2 where ^B(r) is the magnetic field deflection in Hz units, quantifying both the level of inhomogeneity of the BQ field and the non-linearity of the gradient fields. Discretization Current computing units have limited hardware resources that do not allow for infinitesimal resolution of MRI images. Mathematically, this means that the continuous function xfr) mentioned earlier must be transformed into its discrete counterpart. This discretization is usually performed by a pixelation process. Thus, the integrals of equations (1) and (2) are converted into summations: y(kj) = (4) Discretization also applies to data in space K, where y[k(t]) become y^kj but their values ​​always vary over time. By writing these discrete equations (3) and (4) in matrix form with a coding matrix E, y a vector in space K and x the image vector, the equation can be written: y = Ex # (5) where the coding matrix E is defined differently with and without a phase-shift term: E^e^# (6) E^ = e-jkjr^nAB^ryj # ( 7 )

[0033] The presence of the phase-shift term makes the encoding matrix in equation (7) "ill-conditioned". Thus, finding a reconstructed image becomes a "ill-posed" discrete linear inverse problem.

[0034] Classical reconstruction method for correcting distortions

[0035] When the magnetic field deflection is significant, direct reconstruction based on the discrete Fourier transform (DFT) exhibits crucial geometric distortions and a decrease in the signal-to-noise ratio (SNR). These problems are partially resolved by classical distortion correction reconstruction methods.

[0036] The phase shift term in equation (2) is essential for performing a reconstruction with corrected or attenuated distortion. Therefore, the magnetic field deflection AB(r) must always be a known value. This deflection term can be obtained by measuring the BQ field and the gradient fields. When a measurement is not available, BQ field mapping is another option for controlling and quantifying the deflection.

[0037] Reconstruction by the conjugate phase method

[0038] Once the magnetic field AB(r) is known, it is possible to implement a conjugated phase reconstruction (CPR) method by inverting the spatial coding model: [0 ° 39] = #(8)

[0040] where x(r) is an approximation of x(r) since the inverse of equation (8) is not exact. In matrix form after discretization, we observed that this inverse operator is the conjugate transpose of the encoding matrix E:

[0041] £ = gHy # (9)

[0042] in which the coding matrix E follows the definition of equation (7). Model-based reconstruction

[0043] Unlike the direct inversion method of the CPR method, the model-based method approaches the reconstruction as an optimization problem by minimizing the smallest squared error:

[0044] x = nnn^ # ( 10)

[0045] In practice, data measured in K-space are always tainted with noise. To avoid overfitting to the noisy data composed within y when solving equation (10) with an iterative algorithm, it is necessary to stop the iteration early. This has been shown to be equivalent to a truncated or selective singular value decomposition (SVD).

[0046] Instead of early stopping, we more frequently extend the optimization by an additional regularization term R(x) in order to avoid overfitting and stabilize the iterative solution. This regularized problem is formulated as follows: [00471 x=min{^||£'xy|||+j^x)} #(11)

[0048] where A represents the weighting coefficient of the regularization term. The first term 1|| y ||2 quantifies the fidelity of the measured data from space K. The The second term measures the regularity of the solution. The minimum of equation (11) depends on the trade-off between fidelity to the data and regularization controlled by the weighting coefficient A.

[0049] Classically, the regularization term is constructed empirically "by hand". The most common solution is regularization by total variation, which applies a first-order difference matrix T to the solution x to calculate the jump values ​​between each pair of neighboring pixels.

[0050] = ||T>X||P

[0051] where the operator || ||p is the norm Ip of a vector. When p is different from 2, the problem must be solved by Bregman's method or iteratively reweighted least squares (IRLS).

[0052] The reader may advantageously refer to the article Goldstein T, Osher S (2009) The split Bregman method for Ll-regularized problems. SIAM J Imaging Sci 2(2):323-343 for the Bregman method.

[0053] Although the model-based method mentioned above gives relatively good reconstruction results, there are several drawbacks to overcome. The computational complexity is high: to solve the optimization problem defined in equations (11) and (12) with the fourth norm via the IRLS method, two iteration layers are required, with the inner layer solving a least-squares problem with a wide and complete linear operator, and the outer layer solving the weighted linear least-squares problem. These two loop layers make the solution exceptionally expensive.

[0054] In traditional methods, the regularization term and its weighting coefficient are developed and selected manually. They are therefore not always optimal. Furthermore, when the content of an image obtained by an MRI device changes, for example from the brain to the knee, or when the noise level and characteristics change due to varying circumstances, the regularization terms and their relative weighting must be adjusted.

[0055] Finally, the solution by these methods does not allow parallelization of calculations.

[0056] One object of the invention is to overcome all or part of the aforementioned disadvantages. Description of the invention

[0057] One idea that is at the basis of the invention is to address these problems by implementing machine learning models linked to artificial neural networks.

[0058] To this end, according to a first aspect of the invention, a reconstruction method is proposed to determine an image, called the reconstructed image, from an image, denoted y, called the input image.

[0059] The input image is in Fourier space, said input image being produced by a portable device designed to generate a main magnetic field, preferably less than 1 Te sla.

[0060] The process being implemented by a computing unit.

[0061] The process comprises the following steps: • a learning step to reconstruct distortion correction from training data, • an inference step (Ei) comprising a determination of said reconstructed image reconstruction by the conjugate phase method,

[0062] The training data present a plurality of pairs of images xj, yj, the image xj being a reference image and yj being the Fourier transform of the image xj.

[0063] When the device is perfect, yj = FFT(xj).

[0064] The learning step involves training a residual network exhibiting: • a predetermined number of iterations n, • each iteration featuring: • a branch with direct forward propagation, • a branch for checking the consistency of the data with the encoding model, • a regularization branch. • a recurrence equation.

[0065] The recurrence equation can be written as:

[0066] x n+1 =x n -HAS n E T -(Ex n-y^ - K^K D -u n ] • where E is a coding matrix satisfying y=Ex where j is a regularization term presented under the form of expert field models that are based on a predefined number of 2D convolution kernels and activation functions to determine the parameters 2, Kn,

[0067] The determination of said reconstructed image is carried out by the conjugate phase method: [0 ° 68] = j^y ( £(f) ) e jkWr e j2nAB(r)t d £ # ( g )

[0069] where £ = EHy

[0070] Learning can be self-supervised, supervised, or unsupervised.

[0071] According to a second aspect of the invention, a module is proposed comprising a computing unit configured to implement a process according to the first aspect of the invention.

[0072] According to a third aspect of the invention, a portable resonance imaging device is proposed according to the second aspect of the invention. Brief description of the figures

[0073] Other features and advantages of the invention will become apparent upon reading the detailed description that follows, for an understanding of which reference should be made to the accompanying drawings, in which: • [Fig. 1] illustrates a variational network implemented in a process according to the invention, • [Fig.2] illustrates steps in the implementation of the process according to the invention, • [Fig. 3] illustrates an embodiment of a device according to the invention. Description of embodiments

[0074] The embodiments described below are not in any way limiting; variants of the invention may, in particular, be considered comprising only a selection of the features described, hereinafter isolated from the other features described, if this selection of features is sufficient to confer a technical advantage or to differentiate the invention from the prior art. This selection includes at least one feature, preferably a functional one without structural details, or with only a portion of the structural details if this portion alone is sufficient to confer a technical advantage or to differentiate the invention from the prior art.

[0075] In the figures, an element appearing in several figures retains the same reference.

[0076] Fig. 3 is a representation of an MRI device 1 adapted for implementing the imaging method according to the present invention.

[0077] The MRI device 1 includes, in particular, a magnet 2 configured to impose a principal magnetic field Bo. The magnet 2 may, for example, include a permanent magnet. The magnet 2 may, in particular, extend along an elongation axis z.

[0078] More particularly, the magnet 2 defines a housing 3 opening through a first opening 4 and a second opening 5 opposite each other along the elongation axis z.

[0079] In this regard, the magnet 2 is arranged to allow the insertion of a body, and more particularly a human body, into the housing 3 through the first opening 4 along the elongation axis z.

[0080] The magnet 2 can be configured to impose a main magnetic field Bo oriented along an axis perpendicular to the elongation axis z, in an area, called the analysis area, of the housing 3.

[0081] In this respect, the magnet 2 may comprise an assembly of elementary magnets, particularly arranged in a series of Halbach rings. Patent EP3368914B1 provides an example. However, the invention is not limited to the configuration described in that patent.

[0082] By way of example, the magnet 2 is configured to impose a main magnetic field of an amplitude less than 0.1 Tesla, advantageously, less than 0.065 Tesla, even more advantageously less than or equal to 0.05 Tesla.

[0083] The MRI device 1 also includes a set of gradient coils 6. The gradient coils 6 are specifically configured to produce small amplitude and spatially varying magnetic fields when a current is applied to them.

[0084] More particularly, the gradient coils 6 are designed to produce a magnetic field component that is aligned parallel to the main magnetic field, and that varies linearly in amplitude with the position along one of the x, y or z axes (the x, y and z axes forming an orthogonal frame).

[0085] Thus, the combined effects of the magnetic fields imposed by the gradient coils 6 make it possible to spatially encode the signals originating from a body present in the housing 3 and intended to be probed. This spatial encoding is manifested in particular by a variation in the resonance energy of the nuclear spins of the hydrogen nuclei contained within the body intended to be probed and present in the analysis zone. In other words, the nuclear spins of the hydrogen nuclei are subjected to a magnetic field that differs from one position to another.

[0086] The MRI device 1 further comprises a radiofrequency coil 8 (hereinafter "RF coil"). The RF coil 8 is notably disposed in the housing 3 and delimits an examination volume of the MRI device 1, in which a body is intended to be housed.

[0087] Finally, the MRI device 1 also includes means for controlling said MRI device 1. These control means may in particular include a computer 13 interfaced, via interface means 11, with the various elements forming the MRI device 1.

[0088] The MRI device 1 thus described can be implemented for the execution of the process of forming an MRI image of a body disposed in the examination volume.

[0089] According to the terms of the present invention, a body image can be two-dimensional or three-dimensional.

[0090] A reconstruction method for determining a reconstructed image from an input image y in Fourier space is now described. The input image is produced by a portable device, such as the MRI device 1, designed to generate a primary magnetic field. The method is implemented by a computing unit. A module M comprising such a computing unit and a portable magnetic resonance imaging device 1 are also described.

[0091] The method includes a learning step, preferably of the supervised type, for distortion correction reconstruction. According to one variant, the learning can be self-supervised. According to another variant, the learning can be unsupervised. Data collection

[0092] The learning process requires a sufficiently large dataset.

[0093] Furthermore, each data point must contain a pair of correct MRI images and its data in K-space. The image pair comprises one image in physical space, for example, a tomographic image of a brain or a knee, and another image that is in K-space. A correct image is one free from artifacts or distortions, and almost noise-free.

[0094] However, the K-space data must have characteristics similar to those of the raw data acquired in practice with a portable magnetic resonance imaging device.

[0095] No MRI image database meets the conditions mentioned above. The entire training dataset is actually generated by passing high-field MRI images (1.5T or 3.0T) through a numerical simulation tool comprising primarily 3 steps: • a reduction in sampling: reducing the resolution of the original high-resolution MRI image to a resolution corresponding to a scanning protocol of a portable magnetic resonance imaging device; a simulation of the signal: calculate the K space with the magnetic field deviations from the results of the B0 mapping of the portable imaging device; noise addition: joining additive Gaussian noise to an SNR level in accordance with the results of our scanner. Variational network

[0096] A variational network (VN) is a deep learning approach built by iterating the method that solves the regularized inverse problem in an artificial neural network with an architecture similar to a recurrent neural network (RNN) and a residual neural network (ResNet). It allows the integration of prior knowledge about MRI images by learning the kernel of the regularization filter, the weight and size of the gradient descent step, as well as other parameters, from the data.

[0097] As shown in [Fig.1], a variational network is composed of a predefined number of cells / steps representing the iteration steps, and within each cell, the image data from step n flows into the next step n + 1 via 3 branches, as indicated by these 3 arrows: a direct feed-forward branch; a branch for checking data consistency with the model encoding; and a regularization branch.

[0098] The regularization term takes the form of expert field models based on a predefined number of 2D convolution kernels and activation functions. Following these two sets of variables, the step sizes of each cell / step complete the parameters of the variational network model.

[0099] The recurrence equation reads:

[0100] x n+l~ x n~ ^nE '(E'X n -y^ " '^b)

[0101] where Kn and An represent the convolution kernel of the variational network and the step size for step n, respectively. Kn and Aa are variables of the variational network that are determined during the training phases. Thus, the variational network will determine the optimal regularization value by eliminating any empirical regularization for each step n. Each step is represented by a cell with its own convolution kernel and step size.

[0102] The process of forming a variational network aims to find the values ​​of the groups of parameters mentioned above by minimizing a loss function. Three groups of parameters mentioned previously minimize a loss function. Different loss functions can be defined, as in other machine learning models in computer vision, such as the mean squared error (MSE) between images and data, and the mean squared error (MSE) between the model output and the reference. However, since MRI images have complex values, it is possible to use either the MSE of complex images or their magnitude, depending on whether the MRI model is used for machine learning or not.

[0103] Finally, popular deep learning optimization algorithms were used to accomplish the learning process, such as stochastic gradient descent or Adam.

[0104] The learning rate must be carefully tuned to ensure convergence. The learning rate is a hyperparameter that must be set during training and also depends on the optimization method used. In general, a smaller rate is more stable, but convergence is slower, meaning that a larger number of training epochs are required. For example, it is possible to set the rate to le-5.

[0105] The module M according to the invention can be implemented in the form of an electronic module comprising a memory in which is stored a computer program product comprising instructions intended to be executed by the computing unit UC or by the engine control unit ECU which then replaces the computing unit UC.

[0106] Finally, the method according to the invention and the corresponding module can be implemented with sensors other than magnetic, provided that the sensor is sensitive to the passage of reference elements of the target.

[0107] More generally, the variational network (VN) can be replaced by any unrolled deep learning-based iterative reconstruction process.

[0108] Within the general framework of such a process, • the number of iterations n is always predefined; • each iteration comprising >= 2 branches: • a control branch (bc) for data consistency with the encoding model; • a regularization branch but can be in another form for example U-net instead of expert fields including 2D convolution kernels and activation functions; • a direct branch (bd) may be present, but not necessarily.

[0109] Furthermore, the different features, forms, variants and embodiments of the invention can be associated with each other in various combinations insofar as they are not incompatible or mutually exclusive.

Claims

Demands

1. A reconstruction method (P) for determining an image, called the reconstructed image, from an image, called the input image, y in Fourier space, said input image being produced by a portable device designed to generate a principal magnetic field, the method being implemented by a computing unit, said method comprising the following steps: • a training step (Ea) for distortion correction reconstruction from training data by a variational network, and • an inference step (Ei) comprising determining said reconstructed image by the variational network, the training data presenting a plurality of image pairs x^, yj, the image x^ being a reference image and yj being the associated data in K space, the training step comprising training the variational network (VN) having: • a predetermined number n of iterations (il, i2 ...in), • each iteration presenting: • a forward-propagating branch (bd), • a consistency control branch (bc) for the data with the encoding model, • a regularization branch (br). • a recurrence equation that can be written: ■^n+i—^E'Xn-yn)- Knfp(KD• xn) where E is a coding matrix satisfying y=Ex with a phase shift term, Ka and 2n represent respectively the convolution kernel of the variational network and the step size for step n, where ( Kn'Xn ) is a regularization term taking the form of expert field models based on 2D convolution kernels and activation functions.

2. Module (M) comprising a computing unit configured to implement a method according to the preceding claim.

3. Portable magnetic resonance imaging device (1) comprising a module according to the preceding claim.

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