WO2025119519A1 - Method for reconstructing an image from an input image produced by a portable device provided for generating a main magnetic field - Google Patents

Abstract

The invention relates to a reconstruction method for determining an image, referred to as a reconstructed image, the method including the following steps: a training step for reconstructing distortion correction using training data, and an inference step (Ei) which includes determining the reconstructed image, reconstructing by means of the phase conjugation method; the training step including training a variational network.

Description

Method of reconstructing an image from an image, called an input image, produced by a portable device designed to generate a main magnetic field.

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 radiofrequency assembly provided with a transmitting/receiving radiofrequency coil.

The present invention is particularly of interest when it comes to considering a portable magnetic resonance imaging device.

State of the prior art

Magnetic resonance imaging (MRI) is now widely used to non-invasively image the interior of bodies, particularly human bodies. In particular, magnetic resonance imaging can probe the hydrogen nuclei, and in particular their nuclear spin, of water molecules that form part of the body under examination.

In this regard, an MRI device is equipped with a magnet intended to impose a static magnetic field on the body (called the "main magnetic field"), 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.

In particular, the magnetic moments associated with these spins preferentially align 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.

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 configured to produce a magnetic field component that is aligned parallel to the main magnetic field, and that varies linearly in magnitude with position along one of the x, y, or z axes (the x, y, and z axes being pairwise perpendicular).

Thus, the combined effects of the magnetic fields imposed by the gradient coils make it possible to spatially code each of the positions of the body to be probed.

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

Once 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.

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 over durations of the order of a minute or more.

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

This limitation in terms of main magnetic field intensity directly affects the performance of the MRI device. In particular, the images obtained with such an MRI device are likely to have a quality significantly degraded by an unfavorable signal-to-noise ratio. This unfavorable signal-to-noise ratio reflects, in part, a significant reduction in the magnetization present in the tissues.

In the ideal case, the precession of the nucleus is driven by a static magnetic field (called the B 0 field) which is homogeneous.

Spatial coding process model

Considering a 2D Spin-Echo sequence as an example, suppose the z-direction is defined as the slice selection direction. The x- and y-directions can then be defined as the frequency (readout) and phase encoding directions respectively. Any 3D object under 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.

Without loss of generality, the image can be represented by a function scalar-valued, the spatial coding process then being formulated as follows:

Or is a position vector in K-space, while it is the time-varying signal read by the receiver coil during the readout step. The integral domain 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 B 0 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 possible 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 B 0 field and the nonlinearity of the gradient fields. The corrected spatial coding process can then be formulated as follows:

Or is the deviation of the magnetic field in units of Hz quantifying both the level of inhomogeneity of the B 0 field and the non-linearity of the gradient fields.

Discretization

Current computing units have limited hardware resources that do not allow infinitesimal resolution for images obtained by MRI. Mathematically, this means that the continuous function mentioned above must be transformed into its discreet counterpart .

This discretization is usually done by a pixelation process.

Thus, the integrals of equations (1) and (2) are converted into summations:

Discretization also applies to K-space data, where become but always vary over time.

By writing these discrete equations (3) and (4) in matrix form with a coding matrix , y a vector of the space K and x the image vector, the equation can be written:

where the coding matrix E is defined differently with and without the phase shift term:

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

Classical reconstruction method for correcting distortions

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

The phase shift term in equation (2) is essential to perform a reconstruction with corrected or attenuated distortion. Therefore, the magnetic field deflection must always be a known datum. It is possible to obtain this deviation term by measuring the B 0 field and the gradient fields. When a measurement is not accessible, the B 0 field mapping technique is another choice to control and quantify the deviation.

Reconstruction by the conjugate phase method

Once the magnetic field is known , it is possible to carry out a conjugated phase reconstruction (CPR) method by inverting the spatial coding model:

Or is an approach to 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:

in which the coding matrix E follows the definition of equation (7).

Model-based reconstruction

Unlike the direct inversion method of the CPR method, the model-based method approaches by formulating the reconstruction as an optimization problem by minimizing the least squared error:

In practice, measured data 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 proven to be equivalent to a truncated or selective singular value decomposition (SVD).

Instead of early stopping, we more often extend the optimization with an additional regularization term R(x) to avoid overfitting and stabilize the iterative solution. This regularized problem is formulated as follows:

Or represents the weighting coefficient of the regularization term. The first term quantifies the fidelity of the measured data from K space. The second term measures the regularity of the solution. The minimum of equation (11) depends on the trade-off between data fidelity and regularization controlled by the weighting coefficient .

Conventionally, the regularization term is constructed empirically "by hand". The most common solution is total variation regularization which applies a first-order difference matrix on the solution x to calculate the values of the jumps between each pair of neighboring pixels.

where the operator is the lp norm of a vector. When p is different from 2, the problem must be solved by the Bregman method or iteratively reweighted least squares (IRLS).

The reader may wish to refer to the article Goldstein T, Osher S (2009) The split Bregman method for   L1-regularized problems . SIAM J Imaging Sci 2(2):323–343 for the Bregman method.

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 norm via the IRLS method, 2 iteration layers 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.

In traditional methods, the regularization term and its weighting coefficient are developed and selected manually. Therefore, they are not always optimal. In addition, 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 features change due to varying circumstances, the regularization terms and their relative weighting must be adapted.

Finally, the resolution by these methods does not allow parallelization of calculations.

One aim of the invention is to overcome all or part of the aforementioned drawbacks.

One idea behind the invention is to address these problems by implementing machine learning models linked to artificial neural networks.

To this end, according to a first aspect of the invention, a reconstruction method is proposed for determining an image, called a reconstructed image, from an image, noted y, called an input image.

The input image y is in Fourier space, said input image being produced by a portable device intended to generate a main magnetic field, preferably less than 1 Tesla.

The process being implemented by a computing unit.

• une étape d’apprentissage de reconstruction de correction de distorsion à partir de données d’apprentissages,
• une étape d’inférence (Ei) comportant une détermination de ladite image reconstruite par une formule de récurrence,

The process involves the following steps:

• a distortion correction reconstruction learning step from training data,
• an inference step (Ei) comprising a determination of said reconstructed image by a recurrence formula,

The training data presents a plurality of image pairs , , the image being a reference image and being its data in K space using equation (7).

When the device is perfect, = FFT( ) (equation (6)).

• un nombre prédéterminé d’itération n,
• chaque itération présentant :
  • une branche à propagation avant directe,
  • une branche de contrôle de cohérence des données avec le modèle d’encodage,
  • une banche de régularisation.
• une équation de récurrence.

The learning step involves training a residual network exhibiting:

• a predetermined number of iterations n,
• each iteration presenting:
  • a direct forward propagating branch,
  • a data consistency check branch with the encoding model,
  • a regularization bench.
• a recurrence equation.

The recurrence equation can be written:

• where E is a coding matrix verifying y=E.x of equation (7)
• Or is a regularization term comes in the form of expert field models that are based on a predefined number of 2D convolution kernels and activation functions to determine the parameters , ,

The determination of said initial image reconstructed is carried out by the conjugate phase method:

Or

Learning can be self - supervised , supervised, or unsupervised .

According to a second aspect of the invention, a module is proposed comprising a calculation unit configured to implement a method according to the first aspect of the invention.

According to a third aspect of the invention, there is provided a portable resonance imaging device according to the second aspect of the invention.

Brief description of the figures

• illustre un réseau variationnel mis en œuvre dans un procédé selon l’invention,
• illustre des étapes du mode de réalisation du procédé selon l’invention,
• illustre un mode de réalisation d’un dispositif selon l’invention.

Other characteristics and advantages of the invention will appear during the reading of the detailed description which follows for the understanding of which one will refer to the appended drawings in which:

• illustrates a variational network implemented in a method according to the invention,
• illustrates steps of the embodiment of the method according to the invention,
• illustrates an embodiment of a device according to the invention.

Description of embodiments

The embodiments described below being in no way limiting, it will be possible in particular to consider variants of the invention comprising only a selection of the characteristics described, subsequently isolated from the other characteristics described, if this selection of characteristics is sufficient to confer a technical advantage or to differentiate the invention compared to the state of the prior art. This selection comprises at least one characteristic, preferably functional without structural details, or with only a part of the structural details if this part only is sufficient to confer a technical advantage or to differentiate the invention compared to the state of the prior art.

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

There is a representation of an MRI device 1 suitable for implementing the imaging method according to the present invention.

The MRI device 1 notably comprises a magnet 2 configured to impose a main magnetic field B ₀ . The magnet 2 may for example comprise a permanent magnet. The magnet 2 may notably extend along an elongation axis z.

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.

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.

The magnet 2 can be configured to impose a main magnetic field B ₀ oriented along an axis perpendicular to the elongation axis z, in an area, called the analysis area, of the housing 3.

In this regard, magnet 2 may comprise an assembly of elementary magnets, and in particular arranged in a series of Halbach rings. Patent EP3368914B1 gives an example of this. However, the invention is not limited to the configuration described in this patent.

For example, magnet 2 is configured to impose a main magnetic field with an amplitude of less than 0.1 Tesla, advantageously less than 0.065 Tesla, even more advantageously less than or equal to 0.05 Tesla.

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

Specifically, 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 magnitude with position along one of the x, y, or z axes (the x, y, and z axes forming an orthogonal coordinate system).

Thus, the combined effects of the magnetic fields imposed by the gradient coils 6 make it possible to spatially code the signals coming from a body present in the housing 3 and intended to be probed. Spatial encoding is manifested in particular by a variation in the resonance energy of the nuclear spins of the hydrogen nuclei included in 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 which differs from one position to another.

The MRI device 1 further comprises a radiofrequency coil 8 (hereinafter “RF coil”). The RF coil 8 is in particular arranged in the housing 3 and delimits an examination volume of the MRI device 1 and in which a body is intended to be housed.

Finally, the MRI device 1 also comprises means for controlling said MRI device 1. These control means may in particular comprise a computer 13 interfaced, via interfacing means 11, with the various elements forming the MRI device 1.

The MRI device 1 thus described can be implemented for carrying out the method of forming an MRI image of a body placed in the examination volume.

According to the present invention, a body image may be two-dimensional or three-dimensional.

A reconstruction method is now described for determining an image called a reconstructed image, from an image, called an input image, y in Fourier space, said input image being produced by a portable device, such as the MRI device 1, designed to generate a main magnetic field, the method being implemented by a computing unit. A module M comprising such a computing unit and a portable MRI imaging device 1 by magnetic resonance are described at the same time.

The method comprises a learning step, preferably of the supervised type, of distortion correction reconstruction. According to one variant, the learning can be self-supervised. According to another variant, the learning can be unsupervised.

Data collection

The learning process requires having a set of sufficient size.

Furthermore, each data point must contain a correct MRI image pair and its data in K-space. The image pair consists of one image in physical space, for example, a CT image of a brain or a knee, and another image that is in K-space. A correct image is one that is free of artifacts or distortions, and almost without noise.

However, K-space data should exhibit similar characteristics to raw data acquired in practice with a portable magnetic resonance imaging device.

• une réduction de l’échantillonnage : réduction de la résolution de l’image IRM originale à haute résolution à une résolution correspondant à un protocole de balayage de dispositif d’imagerie portable par résonance magnétique ;
• une simulation du signal : calculer l’espace K avec les écarts de champ magnétique à partir des résultats de la cartographie B0 du dispositif d’imagerie portable ;
• un ajout de bruit : joindre un bruit gaussien additif à un niveau SNR en accord avec les résultats de notre scanner.

No MRI image database meets the above-mentioned conditions. The training dataset is actually generated by passing high-field MRI images (1.5T or 3.0T) through a numerical simulation tool that mainly involves 3 steps:

• downsampling: reducing the resolution of the original high-resolution MRI image to a resolution corresponding to a portable magnetic resonance imaging device scanning protocol;
• a signal simulation: calculate the K space with the magnetic field deviations from the results of the B0 mapping of the portable imaging device;
• a noise addition: joining additive Gaussian noise at an SNR level consistent with our scanner results.

Variational network

A variational network (VN) is a deep learning approach built by rolling out the iterative 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 incorporating prior knowledge about MRI images by learning the regularization filter kernel, gradient descent weight and step size, and other parameters from the data.

• une branche à propagation avant directe, pour l’anglais direct feed-forward ;
• une branche de contrôle de cohérence des données avec le modèle d’encodage ; et
• une banche de régularisation.

As shown on , a variational network is composed of a predefined number of cells/stages representing the iteration steps, and within each cell, the image data from stage n flows into the next stage n+1 via 3 branches, as indicated by these 3 arrows:

• a direct feed-forward branch;
• a data consistency check branch with the encoding model; and
• a regularization bench.

The regularization term comes in the form of expert field models that are based on a predefined number of 2D convolution kernels and activation functions. After these two groups of variables, the step sizes of each cell/stage complete the parameters of the variational network model.

The recurrence equation reads:

Or represents the data in the K space of the image to be reconstructed, And represent the convolution kernel of the variational network and the step size for step n, respectively. And are variables of the variational network that are determined during the training phases. Thus, the variational network will determine the optimal regularization value by removing any empirical regularization for each step n. Each step is represented by a cell with its own convolution kernel and step size.

The process of training a variational network aims to find the values of the above-mentioned parameter groups by minimizing a loss function. 3 groups of parameters mentioned previously that minimize a loss function. We can define different loss functions like other machine learning models in computer vision, such as the mean square error (MSE) between images and data. mean square error (MSE) between the model output and the reference. However, since MRI images are complex-valued, it is possible to use the mean square error of complex images or their magnitude, depending on whether MRI is a machine learning model or not.

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

The learning rate must be carefully tuned to ensure convergence. The learning rate is a hyperparameter to be tuned during training, which also depends on the optimization method used. In general, when it is small, it is more stable but convergence is slower, which means that a larger number of training epochs are required. For example, it is possible to set the rate to 1e-5.

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 calculation unit UC or by the engine control unit ECU which then replaces the calculation unit UC.

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 target reference elements.

More generally, the variational network (VN) can be replaced by any unrolled iteration type process for reconstruction based on deep learning (for the English unrolled deep learning based iterative reconstruction ).

• le nombre d’itération n est toujours prédéfini ;
• chaque itération comprenant >= 2 branches :
  • une branche de contrôle (bc) de cohérence des données avec le modèle d’encodage ;
  • une branche de régularisation mais peut être sous une autre forme par example U-net à la place de champs d’experts comportant des noyaux de convolution 2D et de fonctions d’activation ;
  • une branche (bd) directe peut être présente, mais non nécessairement.

In the general framework of such a process,

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

Furthermore, the various features, forms, variations and embodiments of the invention may be combined with each other in various combinations to the extent that they are not incompatible or mutually exclusive.

Claims (3)

Reconstruction method (P) for determining an image, called reconstructed image,
from an image, called input, y in Fourier space, said input image being produced by a portable device intended to generate a main magnetic field,
the method being implemented by a computing unit,
said method comprising the following steps:

• a learning step (Ea) of distortion correction reconstruction from learning data by a variational network, and
• an inference step (Ei) comprising a determination of said image reconstructed by the variational network,

training data presenting a plurality of image pairs , , the image being a reference image and being the associated data in the K space,
the learning step involving the training of the variational network (VN) presenting:

• a predetermined number n of iterations (i1, i2 … in),
• each iteration presenting:
  • a direct forward propagation branch (bd),
  • a control branch (bc) of data consistency with the encoding model,
  • a regularization branch (br).
• a recurrence equation that can be written:

where E is a coding matrix verifying y=Ex with a phase shift term,
Or This regularization term comes in the form of expert field models which are based on a predefined number of 2D convolution kernels and activation functions. Module (M) comprising a calculation unit configured to implement a method according to the preceding claim. Portable magnetic resonance imaging device (1) comprising a module according to the preceding claim.