Rapid magnetic resonance parameter quantitative imaging method based on implicit neural representation learning

Abstract

The invention discloses a rapid magnetic resonance parameter quantitative imaging method based on implicit neural representation learning. The method comprises the following steps: constructing an implicit neural network for learning the representation of a T1 rho weighted image sequence; taking a set total loss function as an optimization target, and training the implicit neural network in a self-supervised learning mode; and for undersampled magnetic resonance imaging k-space data, reconstructing a T1 rho weighted image and a T1 rho quantitative map by using the trained implicit neural network. According to the method, high-quality image reconstruction can be realized at a high under-sampling rate, the method does not depend on complete sampling data, the scanning time is remarkably shortened, and the imaging efficiency is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of magnetic resonance imaging, and more specifically, to a rapid magnetic resonance parameter quantitative imaging method based on implicit neural representation learning. Background Art

[0002] T1ρ quantitative imaging is an important magnetic resonance imaging technique used to quantitatively evaluate the spin-lattice relaxation time (T1ρ) of tissues in a rotating frame. Although this technology has important applications in the early diagnosis of cardiovascular, nervous system and bone and joint diseases, its long scanning time limits its widespread clinical application.

[0003] Among the existing T1ρ quantitative imaging methods, fast imaging techniques usually rely on two main strategies. One is based on traditional image reconstruction algorithms, such as low-rank modeling methods based on compressed sensing. These methods reconstruct images by exploiting the sparsity and low-rank characteristics of the signal, but these methods perform poorly for large-scale datasets and high undersampling conditions. The other is based on deep learning methods. These methods recover high-quality images and quantitative maps from undersampled data through end-to-end learning, but they usually rely on a large amount of fully sampled data for training and have limited generalization capabilities when imaging parameters or sampling patterns change. Recently, self-supervised learning methods have begun to attract attention. They can train networks without fully sampled data and improve reconstruction performance by using physical models or data consistency constraints. However, the existing self-supervised learning methods significantly reduce the reconstruction quality when undersampling is high, making it difficult to achieve a balance between imaging quality and acceleration ratio.

[0004] In summary, the existing technology mainly has the following defects:

[0005] 1) Traditional image reconstruction methods rely on manually designed prior models and have limited speedup.

[0006] 2) Deep learning-based methods require a large amount of fully sampled data for training and have poor generalization capabilities when the sampling mode and imaging parameters change.

[0007] 3) Self-supervised learning methods cannot effectively maintain the reconstruction quality under high-fold undersampling conditions, resulting in a decrease in the quality of the reconstruction results. Summary of the invention

[0008] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and provide a method for rapid magnetic resonance parameter quantitative imaging based on implicit neural representation learning. The method comprises the following steps:

[0009] Construct an implicit neural network to learn the representation of T1ρ-weighted image sequences;

[0010] Taking the set total loss function as the optimization target, the implicit neural network is trained by using a self-supervised learning method;

[0011] For under-sampled magnetic resonance imaging k-space data, the trained implicit neural network is used to reconstruct T1ρ weighted images and T1ρ quantitative maps.

[0012] Compared with the prior art, the present invention has the advantages of proposing a self-supervised learning rapid quantitative T1ρ imaging method based on implicit neural representation (INR), which can achieve high-quality image reconstruction under high undersampling rates and does not rely on fully sampled data, significantly shortening the scanning time and improving imaging efficiency. The present invention solves the problem that the quality of reconstructed images decreases in the case of data undersampling in the existing T1ρ quantitative imaging method.

[0013] Further features and advantages of the present invention will become apparent from the following detailed description of exemplary embodiments of the present invention with reference to the attached drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] The accompanying drawings, which are incorporated in and constitute a part of the specification, illustrate embodiments of the invention and, together with the description, serve to explain the principles of the invention.

[0015] Figure 1 is a flow chart of a method for rapid magnetic resonance parameter quantitative imaging based on implicit neural representation learning according to an embodiment of the present invention;

[0016] Figure 2 It is a schematic diagram of the overall process of the rapid magnetic resonance parameter quantitative imaging method based on implicit neural representation learning;

[0017] Figure 3 is a comparison diagram of the effects of a reconstructed T1ρ-weighted image according to an embodiment of the present invention and the prior art;

[0018] Figure 4 It is a comparison diagram of the effect of the estimated T1ρ quantitative image in the reconstructed T1ρ weighted image according to an embodiment of the present invention and the prior art;

[0019] In the accompanying drawings, Coordinate Grid-coordinate grid; Fourier Feature mapping-Fourier feature mapping; Relaxation Model-relaxation model; Encoding Matrix-encoding matrix; convolution operator-convolution operator; Initialized Parameter-initialization parameter; Predicted Images-predicted images; Hankelmatrix construction operator-Hankel matrix construction operator. DETAILED DESCRIPTION

[0020] Various exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be noted that the relative arrangement of components and steps, numerical expressions and numerical values ​​set forth in these embodiments do not limit the scope of the present invention unless otherwise specifically stated.

[0021] The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses.

[0022] Technologies, methods, and equipment known to ordinary technicians in the relevant art may not be discussed in detail, but where appropriate, the technologies, methods, and equipment should be considered as part of the specification.

[0023] In all examples shown and discussed herein, any specific values ​​should be interpreted as merely exemplary and not limiting. Therefore, other examples of the exemplary embodiments may have different values.

[0024] It should be noted that like reference numerals and letters refer to similar items in the following figures, and therefore, once an item is defined in one figure, it need not be further discussed in subsequent figures.

[0025] In general, the present invention provides a fast magnetic resonance T1ρ quantitative imaging method based on self-supervised learning of implicit neural representation (INR, or based on), which uses implicit neural network to learn the implicit representation of T1ρ weighted image, avoiding the explicit discretization representation of image by traditional methods. In addition, a physically guided self-supervised learning framework is proposed, which takes the physical model of T1ρ imaging as a priori, optimizes the neural network through self-supervised learning, and directly reconstructs T1ρ weighted images and T1ρ quantitative maps from high-multiple undersampled k-space data. Moreover, in the process of self-supervised learning, the reconstruction performance is further improved by introducing signal relaxation prior and kt space self-consistency constraints.

[0026] See also Figure 1 As shown, the provided method for rapid magnetic resonance parameter quantitative imaging based on implicit neural representation learning includes: step S1, constructing an implicit neural network for learning the representation of T1ρ weighted image sequences; step S2, training the implicit neural network using a self-supervised learning method with a set total loss function as the optimization target; step S3, for undersampled magnetic resonance imaging k-space data, reconstructing T1ρ weighted images and T1ρ quantitative maps using the trained implicit neural network.

[0027] Combined with the following Figure 2 The specific embodiments of the present invention are described in detail, wherein Figure 2(a) Schematic diagram of the overall process of the rapid magnetic resonance parameter quantitative imaging method based on implicit neural representation learning. Figure 2 (b) is a schematic diagram of the self-consistency of multi-channel k-space data at all TSLs (spin lock times). Figure 2 (c) is a schematic diagram of the process of constructing the Hankel matrix. Figure 2 (d) is a schematic diagram of the structure of a multi-layer perceptron (MLP). Figure 2 (e) is a schematic diagram of undersampled k-space data at different TSLs.

[0028] 1. MRI image reconstruction forward model

[0029] For example, the general formula for reconstructing a T1ρ-weighted image x can be expressed as:

[0030]

[0031] Among them, y is the corresponding kt space measurement data, E represents the encoding operator, ||*|| F represents the Frobenius norm, R(x) represents the combination of regularization terms, and λ is the regularization parameter.

[0032] 2. Self-consistent priors of kt space

[0033] In one embodiment, based on parallel imaging (PI), the image is reconstructed by enforcing the self-consistency of k-space multi-channel coil data. The linear relationship between the k-space data inside and outside the coil is estimated from a small part of the center of a fully sampled k-space (i.e., the self-calibration signal line, ACS), and this relationship is applied to fill the unsampled lines in the undersampled k-space data. This process can be expressed in operator form:

[0034]

[0035] Among them, ε represents a small constant, which can be set as needed. represents the kt-space data of all coils, M represents the undersampling operator. G is the operator used to convolve the kt-space data with the calibration kernel estimated from ACS, including the temporal neighborhood of k-space sampling, see Figure 2 (b) I is the unit operator, (GI) is often referred to as the null space kernel, which can further regularize the optimization reconstruction problem.

[0036] 3. Signal relaxation prior

[0037] In parametric quantitative imaging, due to the exponential decay of the signal relaxation characteristics, the temporal evolution of the image signal is affected by chemical shift, field inhomogeneity, and multiple relaxation mechanisms, and can be modeled as a linear combination of exponentials. h=1,2,…,N x ,w=1,2,…,N y represents the spatial coordinate, t l For the lth TSL, the signal of each voxel along the time direction can form a Hankel matrix:

[0038]

[0039] Among them, v s represents the spatial coordinates, represents the grid in the x direction, Represents the grid in the y direction, N TSL Indicates N TSLs, N x Indicates the number of frequency encoding lines, N y Indicates the number of phase encoding lines.

[0040] The Hankel matrix has a low rank property, and k is chosen to be the nearest integer greater than or equal to half the number of time relaxation positions. The Hankel matrix construction process can be found in Figure 2 (c), can be expressed as i=[1,2,…,N v ],in is an operator that transforms a time signal at a fixed spatial position into a Hankel matrix.

[0041] 4. Overall framework of self-supervised learning

[0042] Still combined Figure 2 As shown, the T1ρ weighted image x is modeled as a continuous function parameterized by a neural network f(θ). For example, the network is implemented as a coordinate-based MLP (multilayer perceptron) parameterized by weights θ. The forward model can be transformed into optimizing the weights in f(θ), expressed as:

[0043]

[0044] Among them, θ * represents the optimized neural network parameters, v represents the coordinate space, γ(v) represents the encoded coordinate input, and f θ (γ(v)) represents the neural network using the encoded coordinates as input.

[0045] In one embodiment, reconstruction and parameter estimation are combined by integrating reconstruction and signal relaxation models. For example, the signal relaxation model M uses two learnable parameters M 0And T1ρ to synthesize T1ρ weighted image, expressed as:

[0046]

[0047] Among them, M 0 represents the proton density, N TSL Indicates the number of spin lock times, TSL l Indicates the lth TSL time point.

[0048] By comparing the reconstructed image and the synthesized image, an additional loss L is calculated MSE , to enforce consistency between the reconstruction and signal relaxation model blocks. In addition, to characterize the signal relaxation prior, two constraints are used to train the network f(θ), which are the self-consistency of the kt space prior and the low-rank prior of the hankel matrix. The final total loss function jointly optimizes θ, M 0 and T 1ρ Parameters, expressed as:

[0049]

[0050] in, Represents the optimized M 0 , Represents the optimized T 1ρ , L DC is the data consistency term, L HK is the low-rank term of the Hankel matrix, L SC is the self-consistency term in kt space, L MSE is the mean square error term, λ 1 ,λ 2 ,λ 3 is the coefficient of the corresponding term. Specifically expressed as:

[0051]

[0052] Among them, N v represents the total number of pixels, and N represents all the points in k-space.

[0053] Multilayer perceptrons can use special initialization schemes, such as the scheme "Sitzmann V, Martel J, Bergman A, et al. Implicit neural representations with periodic activation functions [J]. Advances in neural information processing systems, 2020, 33: 7462-7473".

[0054] After the network training is completed, the representation of the T1ρ-weighted image sequence is learned, so that the corresponding T1ρ map can be directly generated by applying the trained network to traverse all coordinates in the space and time fields. The entire training process can be seen in Figure 2 (a) shown.

[0055] To further verify the effect of the present invention, the present invention (or PEPPER) is compared with the prior art. The prior art is marked as:

[0056] MORASA (Peng

[0057] Joint MAPLE (Heydari A, Ahmadi A, Kim TH, et al. Joint MAPLE: Accelerated joint T1 and T 2*mapping with scan-specific self-supervised networks [J]. Magnetic Resonance in Medicine, 2024, 91(6): 2294-2309);

[0058] ZS-SSL (Yaman B, Hosseini SAH, Akcakaya M. Zero-ShotSelf-SupervisedLearning for MRI Reconstruction[C] / / International Conference on LearningRepresentations);

[0059] ConvDecoder (Darestani MZ, Heckel R. Accelerated MRI with un-trained neural networks [J]. IEEE Transactions on Computational Imaging, 2021,7:724-733);

[0060] IMJENSE (Zhang C, Moeller S, Demirel OB, et al. Residual RAKI: Ahybridlinear and non-linear approach for scan-specific k-space deep learning [J]. NeuroImage, 2022, 256: 119248);

[0061] L1-ESPIRiT (Uecker M, Lai P, Murphy MJ, et al. ESPIRiT—aneigen value approach to autocalibrating parallel MRI: where SENSE meets GRAPPA[J]. Magn. Reson. Med., 2014, 71(3):990-1001).

[0062] Figure 3 T1ρ-weighted images reconstructed on a retrospective dataset with TSL=80ms, with acceleration factors R=6, 10, and 14. A zoomed-in view of the region of interest (marked by a red box) is shown below each reconstructed image. Error maps relative to a fully sampled reference are also shown and magnified eight times for visualization. Quantitative metrics including PSNR, SSIM, and NRMSE are given at the bottom of each reconstructed image. Figure 3 It can be seen that the image reconstructed by the present invention shows high-quality reconstruction results in high-acceleration reconstruction, while other existing technologies have artifacts or noise to a certain extent.

[0063] Figure 4 The T1ρ maps reconstructed by the present invention (PEPPER) and the Joint MAPLE method are compared with the T1ρ maps estimated from the T1ρ weighted images reconstructed by the ZS-SSL, ConvDecoder, IMJENSE, MORASA and L1-ESPIRiT methods at acceleration factors R = 6, 10 and 14. The error maps calculated relative to the fully sampled reference are also shown, and the corresponding NRMSE values ​​are given at the bottom of the error maps. Figure 4 It can be seen that the T1ρ map directly generated by the present invention is comparable to the reference result and shows the smallest NRMSE value (less than 7.7%) compared with the other six existing methods.

[0064] In summary, compared with the prior art, the present invention has the following advantages:

[0065] 1) Compared with the existing reconstruction methods based on deep learning, the quantitative T1ρ imaging reconstruction method based on implicit neural representation of the present invention does not require fully sampled data for training, reducing the complexity and cost of data acquisition.

[0066] 2) The present invention combines the self-supervised learning framework of the physical model and introduces implicit neural representation, which can restore high-quality images under high-multiple undersampling conditions and significantly improve the acceleration ratio, for example, the acceleration ratio can reach 14 times.

[0067] 3) The present invention can effectively suppress artifacts and maintain image details, and has better image quality, especially has better generalization ability when imaging parameters and sampling modes change.

[0068] It should be noted that, without violating the spirit and scope of the present invention, those skilled in the art may make appropriate changes or modifications to the above embodiments. For example, the total loss function may be a linear weighted sum or an exponential weighted sum, and the weighting coefficient may be determined according to actual needs or simulation. For another example, in addition to the multilayer perceptron, the implicit neural network may adopt other types, such as a convolutional neural network, a recurrent neural network, etc.

[0069] The present invention may be a system, a method and / or a computer program product. The computer program product may include a computer-readable storage medium carrying computer-readable program instructions for causing a processor to implement various aspects of the present invention.

[0070] Computer readable storage medium can be a tangible device that can hold and store instructions used by an instruction execution device. Computer readable storage medium can be, for example, but not limited to, an electrical storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination thereof. More specific examples (non-exhaustive list) of computer readable storage medium include: a portable computer disk, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), a static random access memory (SRAM), a portable compact disk read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanical encoding device, for example, a punch card or a convex structure in a groove on which instructions are stored, and any suitable combination thereof. The computer readable storage medium used here is not interpreted as a transient signal itself, such as a radio wave or other freely propagating electromagnetic wave, an electromagnetic wave propagated by a waveguide or other transmission medium (for example, a light pulse by an optical fiber cable), or an electrical signal transmitted by a wire.

[0071] The computer-readable program instructions described herein can be downloaded from a computer-readable storage medium to each computing / processing device, or downloaded to an external computer or external storage device via a network, such as the Internet, a local area network, a wide area network, and / or a wireless network. The network can include copper transmission cables, optical fiber transmissions, wireless transmissions, routers, firewalls, switches, gateway computers, and / or edge servers. The network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards the computer-readable program instructions for storage in the computer-readable storage medium in each computing / processing device.

[0072] The computer program instructions for performing the operation of the present invention may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, state setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages, such as Smalltalk, C++, Python, etc., and conventional procedural programming languages, such as "C" language or similar programming languages. Computer-readable program instructions may be executed entirely on a user's computer, partially on a user's computer, as an independent software package, partially on a user's computer, partially on a remote computer, or entirely on a remote computer or server. In the case of a remote computer, the remote computer may be connected to the user's computer via any type of network, including a local area network (LAN) or a wide area network (WAN), or may be connected to an external computer (e.g., using an Internet service provider to connect via the Internet). In some embodiments, an electronic circuit, such as a programmable logic circuit, a field programmable gate array (FPGA), or a programmable logic array (PLA), may be personalized by utilizing the state information of the computer-readable program instructions, and the electronic circuit may execute the computer-readable program instructions, thereby realizing various aspects of the present invention.

[0073] Various aspects of the present invention are described herein with reference to the flow charts and / or block diagrams of the methods, devices (systems) and computer program products according to embodiments of the present invention. It should be understood that each box of the flow chart and / or block diagram and the combination of each box in the flow chart and / or block diagram can be implemented by computer-readable program instructions.

[0074] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, thereby producing a machine, so that when these instructions are executed by the processor of the computer or other programmable data processing device, a device that implements the functions / actions specified in one or more boxes in the flowchart and / or block diagram is generated. These computer-readable program instructions can also be stored in a computer-readable storage medium, and these instructions cause the computer, programmable data processing device, and / or other equipment to work in a specific manner, so that the computer-readable medium storing the instructions includes a manufactured product, which includes instructions for implementing various aspects of the functions / actions specified in one or more boxes in the flowchart and / or block diagram.

[0075] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device so that a series of operating steps are performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to implement the functions / actions specified in one or more boxes in the flowchart and / or block diagram.

[0076] The flow charts and block diagrams in the accompanying drawings show the possible architecture, functions and operations of the systems, methods and computer program products according to multiple embodiments of the present invention. In this regard, each box in the flow chart or block diagram can represent a part of a module, a program segment or an instruction, and a part of the module, a program segment or an instruction contains one or more executable instructions for realizing the specified logical function. In some alternative implementations, the functions marked in the box can also occur in a different order from the order marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flow chart, and the combination of the boxes in the block diagram and / or flow chart can be implemented by a dedicated hardware-based system that performs the specified function or action, or can be implemented by a combination of dedicated hardware and computer instructions. It is well known to those skilled in the art that it is equivalent to implement it by hardware, implement it by software, and implement it by combining software and hardware.

[0077] Embodiments of the present invention have been described above, and the above description is exemplary, not exhaustive, and is not limited to the disclosed embodiments. Many modifications and variations will be apparent to those of ordinary skill in the art without departing from the scope and spirit of the described embodiments. The selection of terms used herein is intended to best explain the principles of the embodiments, practical applications, or technical improvements in the marketplace, or to enable other persons of ordinary skill in the art to understand the embodiments disclosed herein. The scope of the present invention is defined by the appended claims.

Claims

1. A method for rapid magnetic resonance parameter quantitative imaging based on implicit neural representation learning, comprising the following steps: Construct an implicit neural network to learn the representation of T1ρ-weighted image sequences; Taking the set total loss function as the optimization target, the implicit neural network is trained by using a self-supervised learning method; For under-sampled magnetic resonance imaging k-space data, the trained implicit neural network is used to reconstruct T1ρ weighted images and T1ρ quantitative maps.

2. The method according to claim 1, characterized in that The total loss function is a weighted sum of data consistency loss, Hankel matrix low-rank term loss, kt space self-consistency loss and mean square error loss.

3. The method according to claim 2, characterized in that The total loss function is expressed as: in: Among them, L DC is the data consistency term, L HK is the low-rank term of the Hankel matrix, L SC is the self-consistency term in kt space, L MSE is the mean square error term, λ1, λ2 and λ3 are the coefficients of the corresponding terms, and Represents two optimized parameters of the signal relaxation model, θ * represents the optimized implicit neural network parameters, v represents the coordinate space, γ(v) represents the encoded coordinate input, and f θ (γ(v)) represents the implicit neural network that uses the encoded coordinates as input, E represents the encoding operator, and N y represents the number of phase encoding lines, in is an operator used to convert the time signal at a fixed spatial position into a Hankel matrix, where M0 represents the proton density and N TSL Indicates the number of spin lock times TSL, TSL l represents the lth TSL time point, G is the convolution operator, I is the unit operator, GI is the null space kernel, N TSL represents N TSLs, and y is the corresponding kt space measurement data.

4. The method according to claim 1, characterized in that: The implicit neural network is constructed using a multi-layer perceptron.

5. The method according to claim 3, characterized in that: The signal relaxation model is expressed using two learnable parameters M0 and T1ρ: Where M0 represents the proton density, N TSL Indicates the number of spin lock times TSL, TSL l Indicates the lth TSL time point.

6. The method according to claim 2, characterized in that The optimized implicit neural network parameters are expressed as: Among them, y is the kt space measurement data, E represents the encoding operator, ||*|| F represents the Frobenius norm, R(x) represents the combination of regularization terms, and λ is the regularization parameter.

7. The method according to claim 4, characterized in that The multi-layer perceptron comprises an input layer, a multi-layer hidden layer and an output layer, and the node connections of the multi-layer hidden layer adopt full connection.

8. The method according to claim 3, characterized in that The process of self-consistency in kt space is in operator form: Among them, ε is a set constant, represents the kt-space data of the coil, M represents the undersampling operator, G is the convolution operator, I is the unit operator, and GI is the null-space kernel.

9. A computer-readable storage medium having a computer program stored thereon, wherein: When the computer program is executed by a processor, the steps of the method according to any one of claims 1 to 8 are implemented.

10. A computer device comprising a memory and a processor, wherein a computer program capable of running on the processor is stored in the memory, characterized in that: When the processor executes the computer program, the steps of the method according to any one of claims 1 to 8 are implemented.

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