Magnetic resonance CEST image reconstruction method and device, storage medium and electronic equipment

Abstract

The invention discloses a magnetic resonance CEST image reconstruction method and device, a storage medium and electronic equipment, and relates to the technical field of magnetic resonance imaging. The method comprises the following steps: acquiring a magnetic resonance CEST image to be reconstructed; respectively performing low-rank sparse decomposition on the magnetic resonance CEST image to be reconstructed in an image domain and a K space; constructing an objective function based on a low-rank sparse decomposition result; and solving the objective function, and obtaining a reconstruction result of the magnetic resonance CEST image to be reconstructed based on a solving result. Thus, accurate and robust reconstruction of the magnetic resonance CEST image can be achieved by simultaneously utilizing the low-rank features in the K-space and the image domain for accelerated acquisition and data de-noising.

Description

Technical Field

[0001] This invention relates to the field of magnetic resonance imaging technology, and in particular to a method, apparatus, storage medium, and electronic device for reconstructing magnetic resonance CEST images. Background Technology

[0002] Chemical Exchange Saturation Transfer (CEST) magnetic resonance imaging (MRI) is a promising molecular imaging technique that enables in vivo metabolic contrast by detecting proton exchange effects between water molecules and solute pools. It has shown potential in various clinical applications, including brain tumor grading, treatment response assessment, and the diagnosis of other diseases such as mental illness and cancer. For example, amide proton transfer (APT) imaging has been used for histopathological grading of brain tumors and for detecting tumor response to radiotherapy; glutamate CEST has been used in the diagnosis of mental illness patients; other applications include the diagnosis of lung cancer, breast cancer, and prostate cancer. However, traditional CEST MRI methods suffer from long scan times, low signal-to-noise ratio (SNR), and asymmetric signal changes, posing challenges to rapid and robust image acquisition and reconstruction. It is important to note that CEST MRI exhibits asymmetric signal changes at a certain percentage level, a characteristic that challenges the rapid acquisition and high-quality reconstruction of undersampled and low-SNR CEST data.

[0003] Therefore, efficient K-space undersampling techniques and corresponding reconstruction strategies are employed to accelerate acquisition, including Parallel Imaging (PI), Compressed Sensing (CS), and Deep Learning (DL). These techniques aim to recover CEST images from undersampled K-space data by utilizing redundant information in spatial, spectral, or multi-channel dimensions. PI is the most commonly used acceleration technique for reconstruction, offering advantages such as fast acquisition speed and robustness. However, the acceleration factors (AF) of PI are difficult to exceed 4. CS-based methods can be combined with traditional PI to achieve higher AF by utilizing the K-space sparsity of the image at a single saturation frequency, but the K-space characteristics in the Z-spectral direction are not included.

[0004] Furthermore, these methods require constructing objective functions based on sparse constraints derived from prior information, which typically relies on manual design. In contrast, deep learning (DL) methods can automatically learn optimized sparse constraints on a specific dataset using millions of network parameters, enabling direct projection from undersampled to fully sampled images. Despite offering higher auto-assembly (AF) and faster reconstruction speeds compared to traditional methods, DL-based techniques are heavily dependent on the size and distribution of the training dataset. Obtaining large-scale datasets can be challenging in practice, and DL methods are prone to overfitting, resulting in high performance but instability, which limits their clinical application. Summary of the Invention

[0005] The purpose of this invention is to provide a method, apparatus, storage medium, and electronic device for reconstructing magnetic resonance CEST images, so as to achieve accurate and robust reconstruction of magnetic resonance CEST images.

[0006] In a first aspect, embodiments of the present invention propose a method for reconstructing a magnetic resonance CEST image, the method comprising: acquiring a magnetic resonance CEST image to be reconstructed; performing low-rank sparse decomposition on the magnetic resonance CEST image to be reconstructed in the image domain and K-space respectively; constructing an objective function based on the low-rank sparse decomposition result; solving the objective function, and obtaining the reconstruction result of the magnetic resonance CEST image to be reconstructed based on the solution result.

[0007] In some embodiments, the low-rank sparse decomposition result includes the low-rank component and sparse component of the magnetic resonance CEST image to be reconstructed in the image domain, and the low-rank component and sparse component in the K-space; the objective function is expressed as follows:

[0008]

[0009]

[0010] in, , These represent the low-rank component and sparse component of the magnetic resonance CEST image to be reconstructed in the image domain, respectively. , Let T and E represent the low-rank and sparse components of the CEST image to be reconstructed in K-space, respectively; T represents the sparse transform operator; E represents the sensitivity encoding operator; U represents the K-space undersampling mask; and d represents the K-space data corresponding to the CEST image to be reconstructed. Denotes the square of the L2 norm. Represents the nuclear norm. Represents the L1 norm; , , , This represents hyperparameters.

[0011] In some embodiments, E is obtained by performing a fast Fourier transform on a preset sensitivity map, and the hyperparameters are determined by grid search.

[0012] In some embodiments, the objective function is solved using the proximal gradient method.

[0013] In some embodiments, the solution results include , , , The result of the nth iteration , The reconstruction result of the CEST magnetic resonance image to be reconstructed is... get, , , , They are represented as follows:

[0014]

[0015]

[0016]

[0017] in, This represents the singular value threshold operator. , These represent the constant step size used by the algorithm in the image domain and K-space, respectively; Indicates the inverse of T. This represents the soft threshold operator.

[0018] Secondly, embodiments of the present invention provide a reconstruction apparatus for magnetic resonance CEST images. The apparatus includes: an acquisition module for acquiring a magnetic resonance CEST image to be reconstructed; a decomposition module for performing low-rank sparse decomposition on the magnetic resonance CEST image to be reconstructed in the image domain and K-space, respectively; a construction module for constructing an objective function based on the low-rank sparse decomposition result; and a solution module for solving the objective function and obtaining the reconstruction result of the magnetic resonance CEST image to be reconstructed based on the solution result.

[0019] In some embodiments, the low-rank sparse decomposition result includes the low-rank component and sparse component of the magnetic resonance CEST image to be reconstructed in the image domain, and the low-rank component and sparse component in the K-space; the objective function is expressed as follows:

[0020]

[0021]

[0022] in, , These represent the low-rank component and sparse component of the magnetic resonance CEST image to be reconstructed in the image domain, respectively. , Let T and E represent the low-rank and sparse components of the CEST image to be reconstructed in K-space, respectively; T represents the sparse transform operator; E represents the sensitivity encoding operator; U represents the K-space undersampling mask; and d represents the K-space data corresponding to the CEST image to be reconstructed. Denotes the square of the L2 norm. Represents the nuclear norm. Represents the L1 norm; , , , This represents hyperparameters.

[0023] In some embodiments, the solution results include , , , The result of the nth iteration , , , The reconstruction result of the CEST magnetic resonance image to be reconstructed is... get, , , , They are represented as follows:

[0024]

[0025]

[0026]

[0027] in, This represents the singular value threshold operator. , These represent the constant step size used by the algorithm in the image domain and K-space, respectively; Indicates the inverse of T. This represents the soft threshold operator.

[0028] Thirdly, embodiments of the present invention provide a computer-readable storage medium having a computer program stored thereon, wherein when the computer program is executed by a processor, it implements the magnetic resonance CEST image reconstruction method described in the first aspect.

[0029] Fourthly, embodiments of the present invention provide an electronic device, including a memory, a processor, and a computer program stored in the memory, wherein when the computer program is executed by the processor, it implements the magnetic resonance CEST image reconstruction method described in the first aspect.

[0030] The present invention provides a method, apparatus, storage medium, and electronic device for reconstructing magnetic resonance CEST images. This method involves performing low-rank sparse decomposition on the magnetic resonance CEST image to be reconstructed in both the image domain and K-space, then constructing an objective function based on the low-rank sparse decomposition results; solving the objective function; and obtaining the reconstruction result of the magnetic resonance CEST image based on the solution. Therefore, by simultaneously utilizing low-rank features in both the K-space and image domain to accelerate acquisition and data denoising, accurate and robust reconstruction of magnetic resonance CEST images can be achieved. Attached Figure Description

[0031] Figure 1 This is a flowchart of a magnetic resonance CEST image reconstruction method according to an embodiment of the present invention; Figure 2 This is a schematic diagram of the reconstruction process of a CEST magnetic resonance image to be reconstructed according to an embodiment of the present invention; Figure 3 This is a schematic diagram of the experimental results of the first example of the present invention; Figure 4 This is a schematic diagram of the experimental results of the first example of the present invention; Figure 5 This is a schematic diagram of the experimental results of the first example of the present invention; Figure 6 This is a schematic diagram of the experimental results of the first example of the present invention; Figure 7 This is a schematic diagram of the experimental results of the first example of the present invention; Figure 8 This is a schematic diagram of the experimental results of the first example of the present invention; Figure 9 This is a schematic diagram of the experimental results of the first example of the present invention; Figure 10 This is a structural block diagram of an electronic device according to an embodiment of the present invention. Detailed Implementation

[0032] Recently, the spatiotemporal correlation properties of the CEST dataset have been used for image and Z-spectrum denoising by incorporating low-rank or sparse constraints during reconstruction. Given that signal variations observed in CEST MRI are at the percentage level and highly sensitive to reconstruction errors, such denoising techniques can provide robust contrast maps and have significant clinical translational potential. However, these techniques have not directly benefited the acceleration of CEST imaging. Furthermore, although some studies have explored the low-rank properties of the Z-spectrum, the K-space characteristics of the Z-spectral direction for the CEST dataset have not been investigated. Since small-saturation B1 CESTs typically acquire a large number of saturation frequencies, resulting in a significant increase in scan time and relatively low contrast, this invention also investigates the distribution characteristics of CEST datasets with relatively small-saturation B1 along the spectral direction in the central and peripheral regions of the K-space domain.

[0033] Because K-space sequences contain sparsity and redundancy features complementary to the image domain, this invention proposes a magnetic resonance imaging (MRI) CEST image reconstruction technique based on a low-rank plus sparse model (KILS) across the KI domain, to accelerate CEST acquisition and accurately preserve contrast. To demonstrate the effectiveness of this invention, retrospective and prospective results from phantoms, healthy adults, and brains of patients with brain tumors were evaluated in detail. Furthermore, experiments were conducted on 3T human livers and 9.4T rat brains to demonstrate the general applicability of KILS.

[0034] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0035] The following description, with reference to the accompanying drawings, describes a method, apparatus, storage medium, and electronic device for reconstructing magnetic resonance CEST images according to embodiments of the present invention.

[0036] Figure 1 This is a flowchart of a magnetic resonance CEST image reconstruction method according to an embodiment of the present invention.

[0037] like Figure 1 As shown, the reconstruction methods for CEST magnetic resonance images include: S11, acquire the CEST image of the magnetic resonance imaging to be reconstructed.

[0038] S12 performs low-rank sparse decomposition on the CEST magnetic resonance image to be reconstructed in the image domain and K space, respectively.

[0039] Specifically, when the saturation frequency (ω) is close to the water peak, the magnetic resonance CEST image appears darker, while when ω is far from the water peak, the image becomes brighter. The variation of image intensity along ω is called the Z-spectrum, which can be decomposed into a low-rank component and a sparse component (e.g., ...). Figure 2 (As shown in (A) and (B)). Therefore, the reconstructed low-rank and sparse images allow for the separation of primary contrast from sparse noise or artifacts (see [reference]). Figure 1 The image (from the image above) is used for imaging acceleration and denoising. According to Passevar's theorem, the total energy of the CEST image at each ω is equal to its corresponding K-space portion. Figure 2 As shown in (C) and (D), the K-space signal exhibits a valley shape along the ω direction similar to the Z-spectrum in the image domain, and can also be decomposed into low-rank and sparse components. Since each point in K-space represents a specific spatial frequency component extracted from the entire image domain, its corresponding spectrum along ω has a unique shape and low-rank characteristics.

[0040] S13, construct the objective function based on the low-rank sparse decomposition results.

[0041] In some embodiments of the present invention, the low-rank sparse decomposition result includes the low-rank component and sparse component of the CEST magnetic resonance image to be reconstructed in the image domain, and the low-rank component and sparse component in the K-space; the objective function is expressed as follows:

[0042]

[0043]

[0044] in, , These represent the low-rank and sparse components of the CEST magnetic resonance image to be reconstructed in the image domain, respectively. , denoted as the low-rank component and sparse component of the CEST image to be reconstructed in K-space, respectively; T represents the sparse transform operator; E represents the sensitivity encoding operator; U represents the K-space undersampling mask; d represents the K-space data corresponding to the CEST image to be reconstructed. Denotes the square of the L2 norm. Represents the nuclear norm. Represents the L1 norm; , , , This represents hyperparameters.

[0045] For example, E is obtained by performing a fast Fourier transform on a preset sensitivity map, and the hyperparameters are determined by grid search.

[0046] Specifically, for reconstruction of undersampled dynamic MRI, the L+S method is achieved by solving the following formula:

[0047]

[0048] like Figure 2 As shown in (A)-(D), the K-space sequence of the CEST magnetic resonance images also exhibits low-rank property in the ω dimension, containing complementary information needed to recover missing data and reduce multi-coil artifacts. Therefore, a similar decomposition is further performed on the CEST magnetic resonance images in K-space, i.e., low-rank + sparse decomposition is performed simultaneously in K-space and the image domain. The objective function then becomes:

[0049]

[0050]

[0051] To maintain consistency between the image domain and the K-space, an additional regularization term is introduced into this optimization problem. Therefore, the objective function can be rewritten as:

[0052] S14, solve the objective function, and obtain the reconstruction result of the CEST magnetic resonance image to be reconstructed based on the solution result.

[0053] For example, the objective function is solved using the proximal gradient method.

[0054] In this example, the solution result may include , , , The result of the nth iteration , , , The reconstruction results of the CEST magnetic resonance images to be reconstructed are derived from... get, , , , They are represented as follows:

[0055]

[0056]

[0057]

[0058] in, This represents the singular value threshold operator. , These represent the constant step size used by the algorithm in the image domain and K-space, respectively; Indicates the inverse of T. This represents the soft threshold operator.

[0059] Specifically, in the above objective function, , Both are convex and smooth functions. , , , All are convex but non-smooth functions, which can be solved using the proximal gradient method. For example... Figure 2 As shown in Figure (E), in the nth iteration (when the objective function is minimized), the four components... , , , The final update expression is as shown above.

[0060] Figure 2 The middle (E) shows It includes four components of the output of the nth iteration, where 2D-FT represents the two-dimensional Fourier transform and DC represents the data consistency constraint.

[0061] Ultimately, the reconstructed image was generated by Calculated.

[0062] To demonstrate the effectiveness of the method of the present invention, an experiment was conducted, the process of which is as follows: (I) Acquisition of CEST images to be reconstructed 1) 3T BSA phantom experiment BSA phantoms were prepared by placing seven tubes (six BSA tubes and one PBS tube) in a water-filled flask. The BSA tubes were divided into two groups: one containing gadolinium and the other without. The concentrations in each group were 0.075 g / mL, 0.1 g / mL, and 0.15 g / mL, respectively. Experiments were performed on a Philips Ingenia 3T scanner using 3D multiple-excitation Turbo Field Echo (TFE) CEST sequences. The sequences contained 25 frequency offsets: ±10 ppm, ±8 ppm, ±6 ppm, ±5 ppm, ±4 ppm, ±3.5 ppm, ±3 ppm, ±2.5 ppm, ±2 ppm, ±1.5 ppm, ±1 ppm, ±0.5 ppm, and -1560 ppm. The scanning parameters were: voxel size 2×2×6. Field of View (FOV): 230×201×30 Flip Angle (FA) 10°; Repetition Time (TR) 6.2ms; Echo Time (TE) 3.3ms; TFE factor 25. CEST saturation B1 is set to 1μT, and saturation duration is 2 seconds.

[0063] 2) 3T Human Brain Experiment A retrospective experiment was conducted using a Philips Ingenia 3T scanner with 3D multiple-excitation TSE CEST sequences, setting 31 frequency offsets: -10ppm, -8ppm, -6ppm, -5ppm, -4ppm, -3.5ppm, -3ppm, -2.1ppm, -1ppm, -0.5ppm, 0.5ppm, 0.8ppm, 1ppm, 1.2ppm, 1.7ppm, 1.9ppm, 2.1ppm, 2.3ppm, 2.5ppm, 3ppm, 3.4ppm, 3.5ppm, 3.6ppm, 3.7ppm, 4ppm, 4.5ppm, 5ppm, 6ppm, 8ppm, 10ppm, and -1560ppm. Data was collected from 11 healthy volunteers and 15 patients with brain tumors. Data from healthy volunteers was acquired using a 32-channel phased array head coil with the following scan parameters: voxel size 1.8 × 1.8 × 3.3. FOV 220×200×60 FA 90°; TR 3155ms; TE 7.8ms; echo train length 174; CEST saturation B1=1μT, saturation time 2 seconds. A 16-channel phased array head coil was used for brain tumor patients. Scanning parameters: voxel size 2×2×6. FOV 230×201×30 FA 90°; TR 5500ms; TE 7.8ms; echo train length 174; CEST saturation B1=0.7μT, saturation time 2 seconds Furthermore, KILS was also validated in a prospective study of healthy volunteers. The 3D multiple-emission TFE CEST sequence parameters were: voxel size 2×2×2. TR 6.7ms; TE 3.5ms; FA 8°; echo train length 330 (total readout time 1.2s, similar to the retrospective experiment). Undersampled data used only 990 lines (3 excitations), while full sampling requires 7575 lines, a scan time of approximately 45 minutes, and a total of 23 excitations; therefore, full sampling was not performed. Other parameters were consistent with the retrospective experiment.

[0064] 3) 4T rat brain experiment A stroke-affected rat was scanned using a 2D CEST RARE sequence on a 9.4T Bruker scanner, with the same frequency offset settings as in the human brain experiment. Scanning parameters were: voxel size 0.27 × 0.33 × 1.2. Field of view (FOV): 35×32×1.2 Flip angle (FA) 90°; repetition time (TR) 5000ms; echo time (TE) 3.7ms; RARE factor 32. CEST saturation B1 is set to 1μT, and saturation duration is 2 seconds.

[0065] 4) 3T human liver experiment The study used a 3T scanner (Philips Ingenia, Philips Healthcare) with a free-breathing abdominal CEST sequence, combined with water presaturation and respiratory gating, and a 16-channel phased array coil. The subject was a healthy volunteer.

[0066] The CEST sequence contained 43 frequency offsets: ±10ppm, ±8ppm, ±6.5ppm, ±5.5ppm, ±5ppm, ±4.75ppm, ±4.5ppm, ±4.25ppm, ±4ppm, ±3.75ppm, ±3.5ppm, ±3.25ppm, ±3ppm, ±2.75ppm, ±2.5ppm, ±2.25ppm, ±2ppm, ±1.75ppm, ±1.5ppm, ±1ppm, ±0.5ppm, and 0ppm, as well as a frequency offset of -1560ppm far from the water peak. Scan parameters were: 2D single-shot TSE readout; voxel size 1.7 × 1.7 Layer thickness 4mm; FOV 230×350 FA 90°. CEST saturation B1 was set to 1 μT, and the saturation duration was 1.8 seconds. The scan plane was taken in the coronal position, located in the middle of the liver.

[0067] (II) Image Reconstruction Based on the images acquired in the above experiments, image reconstruction was performed using computer software such as MATLAB 2021b. To verify the feasibility of the proposed method, the experiment focused on a two-dimensional reconstruction scene to simplify implementation. The central region of the K-space undersampling mask U was completely filled, while the peripheral sampling positions followed a Gaussian distribution. The acceleration factors (AF, Ncenter|Ny) used are as follows: phantom experiments: 2 (28|56), 4 (12|28), 6 (8|18), 8 (6|14); human brain experiments: 2 (28|56), 3 (18|38), 4 (12|28), 5 (10|22), 6 (8|18), 8 (6|14); human liver experiments: 6 (20|42); rat brain experiments: 6 (8|18). The sparse transform operator T was selected as the Fast Fourier Transform (FFT) operator in the time direction. In retrospective experiments, sensitivity maps were estimated using an improved iterative self-consistent parallel imaging reconstruction method (ESPIRiT, based on eigenvector maps). It is important to note that for brain tumor patients, human liver, and rat brain data, only single-channel DICOM data were available, rather than fully sampled multi-channel K-space data. Therefore, sensitivity maps from randomly selected healthy subjects were multiplied by the single-channel DICOM data to simulate multi-channel images. The multi-channel sensitivity encoding operator E was implemented using FFT.

[0068] Reconstruction hyperparameters , , , , and The hyperparameters were determined through grid search. The hyperparameter with the smallest nMSE on the retrospective dataset was selected for reconstruction. To reduce the search space, the optimal hyperparameter was first searched in the L+S reconstruction. , and fix = =1. Then fix it. , ,search and Finally, search again. , The final optimized parameters are: =0.9, =1, =0.005, =0.0012, =0.002, =0.0005.

[0069] In contrast, kt sparse and L+S reconstruction methods were also implemented, with the hyperparameters of the L+S reconstruction determined through grid search. The kt sparse method performs 1D FFT thresholding in the frequency offset direction and total variation (TV) constraints in the spatial direction. The image is obtained by solving the following optimization problem:

[0070] in, represents the Fast Fourier Transform; TV represents the Total Variation; X is the image to be solved. Parameters and Set them to 0.003 and 0.0001 respectively.

[0071] (III) Data Analysis In phantom experiments, the contrast-to-noise ratio (CNR) was obtained by calculating the signal intensity difference between the CEST tube and the reference tube. To evaluate the image quality of different methods, the peak signal-to-noise ratio (PSNR) and normalized mean squared error (nMSE) were calculated between the reconstructed image and the gold standard. These metrics were used to quantitatively compare image quality.

[0072] In CEST quantification, B0 inhomogeneity correction was performed voxel-by-voxel: the acquired spectra were fitted to B-spline functions with 0.1 ppm intervals, and the lowest point was selected as the water peak position. Subsequently, post-processing was performed using MTR asymmetry (MTRasym) and Lorentzian difference (LD), as follows:

[0073]

[0074] in, Indicates frequency offset. Indicates a reference image. Represents a saturated image. This represents the Lorentz function for simulating direct saturation of water. The acquired Z-spectrum is represented. For statistical analysis, paired t-tests were used to compare the CNR and image quality of different reconstruction methods. The Bland-Altman method was used to evaluate the signal consistency between the reconstructed images and the gold standard. Quantitative indices and comparison plots were calculated using computer software, and statistical analysis was performed using the R language.

[0075] (iv) Experimental Results 1) Results of phantom experiments Figure 3 The contrast maps and quantitative indicators of CEST images obtained by different reconstruction methods are presented, including kt sparsity, L+S, and KILS, with results under acceleration factors (AF) of 2–8. Figure 3 A) shows the Lorentz difference plot of amide protons (approximately 3.5 ppm, LDamide). Figure 3 Figure B) shows the Lorentz difference plot of the proton NOE of the macromolecular aliphatic molecules (approximately -3.5 ppm, LDNOE). Overall, both the L+S and KILS methods produced relatively uniform and smooth signals within a single tube, while the contrast plot generated by the kt sparse method was more noisy. Quantitatively, KILS achieved the highest peak signal-to-noise ratio (PSNR) and structural similarity index (SSIM), as well as the lowest normalized mean square error (nMSE). Compared to L+S reconstruction, KILS showed more significant differences between tubes with different BSA concentrations, indicating that KILS better captured the similarities and differences in the Z-spectrum.

[0076] 2) Results of human brain experiments Figure 4 – Figure 7 It presents retrospective results from human brain experiments. Figure 4 The main focus is on quantitative image quality assessment. Figure 4 Image A) shows the original 3.5 ppm CEST image of a healthy volunteer. Figure 4 Figure B) shows the error plot and normalized mean square error (nMSE, ×) corresponding to A). Using fully sampled images as the gold standard, it can be seen that KILS outperforms other methods in reconstructing saturated images, exhibiting the smallest error (see [link to relevant documentation]). Figure 4 As shown in Figures A and B). Statistical analysis further confirms the advantages of KILS reconstruction accuracy, with higher PSNR and lower nMSE (see Figure A). Figure 4 As shown in C) and D), p < 0.01). Since the B0 image generated by the Z spectrum obtained by direct fitting is similar to that obtained by the WASSR method, this invention uses the former's self-calibration method to calculate the quantitative image. Figure 5 and Figure 6 CEST contrast plots are shown for healthy volunteers and brain tumor patients under different acceleration factors (AF=2–8). For healthy volunteers, the contrast plot obtained by KILS is closest to the expected results and is significantly better than L+S and kt sparse methods (see [link to CEST analysis]). Figure 5 In patients with brain tumors, (A)-(C)). Figure 6 Figure A) shows the T1w, T2w, MTLRasym plot (3.5 ppm, 2T), and the original saturation plot (3.5 ppm, 0.7T). Figure 6(B) shows the original 3.5ppm CEST image, with nMSE (×) labeled in the upper left corner. Full sampling is the gold standard; Figure 6 The LDamide diagram is shown in C). Figure 6 D) shows the LDNOE plot; Figure 6 Tables E and F show the quantitative statistical indicators, PSNR and nMSE, respectively. Five slides were taken from each patient, for a total of 15 patients (n=75). See also Figure 6 In images A-F), the lesion area exhibited higher intensity amide proton signals and lower intensity NOE signals, consistent with previous studies compared to normal brain tissue. Therefore, KILS improved the visualization of contrast enhancement in the lesion area. At AF=8, all methods showed blurred anatomical details in their contrast maps, but KILS maintained contrast between different tissue types (e.g., white matter vs. gray matter, lesion vs. healthy tissue), demonstrating its robustness in CEST contrast enhancement. Furthermore, KILS effectively reduced some noise caused by low signal-to-noise ratios, which may be present even in fully sampled CEST images. Since clinical CESTMRI applications focus more on contrast enhancement in the lesion area than on rich anatomical texture, KILS's advantages in both high acceleration factor and robust contrast further illustrate its clinical application potential.

[0077] To study L after matrix decomposition I S I L K and S K The role of the components (four components that complement each other). Figure 7 Images of healthy volunteers and patients with brain tumors are presented in various components. In L+S reconstruction, adding sparse components to the image can improve anatomical details but does not significantly alter tissue contrast (see [link]). Figure 7 Figures A-C) show that the low-rank components represent the baseline of the CEST image, while the sparse components represent part of the image texture. The same conclusion can be drawn from... Figure 7 (D) It is concluded that the sparse component of the L+S method failed to capture the differences in Z-spectrum between different voxels. Conversely, in KILS, the LK contrast plot shows the baseline intensity and rich anatomical texture of the CEST contrast; when S... K Join L K Subsequently, voxels of different tissue types can be distinguished. Specifically, brain tumor areas show enhanced signal on MTRAsym and LDamide maps, while the signal weakens on LDNOE maps. The ablation experiment results further support the interpretation of the KILS model, namely that the low-rank and sparse components in K-space correspond to the similarity and difference of the Z-spectrum, respectively.

[0078] Figure 8This study presents prospective results from a healthy volunteer, including three orthogonal views, yielding 2mm isotropic whole-brain Z-spectrums at 31 frequency offsets, with a scan time of 5 minutes and 51 seconds. Full sampling would have required 41 minutes and yielded 7575 lines (Ky×Kz), and quantitative maps are inevitably affected by motion and misalignment between multiple acquisitions; therefore, full sampling was not performed. The proposed reconstruction method generates high-quality saturated images with excellent spatial-spectral resolution. Contrast maps can be calculated from the reconstructed Z-spectrums, reflecting the spatial distribution of various metabolites, including amide protons (3.5 ppm), creatine phosphate (2.5 ppm), and NOE (-3.5 ppm). These prospective results demonstrate the potential of a rapid and reliable clinical CEST protocol.

[0079] 3) Other applications To explore robustness under undersampled MRI CEST images, KILS was also applied to human liver and rat brain MRI CEST. Figure 9 Image A) shows a rat brain image and MTLRasym plot; Figure 9 Figure B) shows the Z-spectrum of the lesion and healthy areas. In the MTRasy plots obtained by all methods, the signal in the lesion area is lower than that in the healthy area, consistent with previous studies. Figure 9 Figure C) shows saturated images and MTLARsym maps of a human liver under a 3T scanner, reconstructed using L+S, KILS, kt sparse, and full sampling methods, respectively. Notably, KILS exhibits the smallest reconstruction error in both the saturated image and the MTLARsym map.

[0080] As described above, this invention proposes an iterative low-rank + sparse matrix factorization method across the KI domain for magnetic resonance CEST image reconstruction, termed KILS. This method enables simultaneous L+S decomposition in both the K-space and image domains, achieving robust CEST contrast reconstruction even with undersampled K-space data (up to 8x speedup). Furthermore, experimental results from phantoms, human brains, human livers, and rat brains demonstrate that KILS generates faithful image reconstructions across various evaluation metrics and yields robust contrast maps after post-processing. Additionally, ablation experiments investigated the low-rank and sparse components in the KI domain, confirming that KILS effectively captures the similarities and differences in the Z-spectrum within the K-space. Notably, KILS is compatible with various MRI CEST sequences, including fast readout sequences and techniques that shorten TR and saturation time.

[0081] According to Parseval's theorem, the valley-like distribution of the K-space signal along ω is similar to the Z-spectrum in the image domain (see...). Figure 1 Therefore, KILS achieves higher fidelity in Z-spectral quantification compared to methods that use L+S constraints only in the image domain (see [link]). Figure 3Furthermore, traditional image-domain L+S reconstruction often introduces a smoothing effect, leading to oversimplification of both the image and the spectral lines. For example, small peaks in the spectral lines are removed along with noise due to dimensionality reduction (see [link to relevant documentation]). Figure 5 –6). In KILS, since each point in the K space contains information about the entire image domain, adding L+S constraints to the K space can better preserve image details and small peaks.

[0082] Some reconstruction methods have utilized the low-rank property of CEST to recover dealiased images from undersampled data. However, these methods typically treat Z-spectral differences and aliasing artifacts as small singular values ​​in Singular Value Decomposition (SVD) and remove them with soft thresholding in L+S reconstruction in the image domain. This results in sparse components simultaneously containing multiple effects such as B0 inhomogeneity, aliasing artifacts, and Z-spectral differences. Therefore, the sparsity constraints in the image domain struggle to distinguish between artifacts and CEST signals, often mistakenly eliminating Z-spectral differences and artifacts together. In the experiments of this invention, KILS extends the L+S framework to the KI domain, enabling the differentiation of Z-spectral differences and aliasing artifacts. Retrospective results show that the K-space sparse components (S K This effectively represents the differences in the Z-spectrum, which is consistent with the original design intent.

[0083] KILS utilizes the low-rank and sparse characteristics of K-space to further improve reconstruction performance. This characteristic can be explained in two ways: (1) The center and edge of K-space reflect the low spatial frequency contrast and high spatial frequency structural details in the image domain, respectively. The K-space spectral morphology and low-rank properties are different in the center and edge regions; (2) The performance improvement of KILS may also benefit from the SENSE parallel reconstruction mechanism. Compared with single-channel reconstruction, the K-space signals acquired by multi-channel coils have subtle differences in sensitivity maps and noise. Adding L+S decomposition to K-space can compensate for the neglect of these cross-channel differences, thereby improving the reconstruction quality.

[0084] It is important to note that the original L+S theory suggests that the ratio of low-rank to sparse regularization parameters is related to the undersampling rate during matrix reconstruction. While this invention selects the optimal parameter combination within the possible range and does not strictly adhere to this ratio, the goal of this invention is to obtain high-quality images, therefore this restriction is not necessary. The L+S theory also assumes that the low-rank and sparse components are completely separable and incoherent. However, in MRI CEST, although the Z-spectrums of different voxels differ, their line shapes are identical because they all originate from the same endogenous molecules. Therefore, there is a correlation between the similarity and difference in the Z-spectrums, and the L and S components of the image domain and K-space are also correlated to some extent. Since this invention focuses on the final reconstruction result (i.e., L...),... K +S K (sum of), therefore strict separation of L is not required. K With S K.

[0085] In summary, the feasibility of the method of this invention has been verified in various clinical applications. Experimental results show that the method of this invention can reconstruct robust CEST contrast maps from K-space data with up to 8x undersampling, thereby helping to accelerate clinical CEST protocols, obtain robust contrast maps, and expand the clinical application of CESTMRI.

[0086] The present invention also proposes a device for reconstructing magnetic resonance CEST images.

[0087] In this embodiment, the magnetic resonance CEST image reconstruction device includes: an acquisition module, a decomposition module, a construction module, and a solution module.

[0088] The acquisition module is used to acquire the CEST image to be reconstructed; the decomposition module is used to perform low-rank sparse decomposition on the CEST image to be reconstructed in the image domain and K space respectively; the construction module is used to construct the objective function based on the low-rank sparse decomposition result; and the solution module is used to solve the objective function and obtain the reconstruction result of the CEST image to be reconstructed based on the solution result.

[0089] In some embodiments of the present invention, the low-rank sparse decomposition result includes the low-rank component and sparse component of the CEST magnetic resonance image to be reconstructed in the image domain, and the low-rank component and sparse component in the K-space; the objective function is expressed as follows:

[0090]

[0091]

[0092] in, , These represent the low-rank and sparse components of the CEST magnetic resonance image to be reconstructed in the image domain, respectively. , denoted as the low-rank component and sparse component of the CEST image to be reconstructed in K-space, respectively; T represents the sparse transform operator; E represents the sensitivity encoding operator; U represents the K-space undersampling mask; d represents the K-space data corresponding to the CEST image to be reconstructed. Denotes the square of the L2 norm. Represents the nuclear norm. Represents the L1 norm; , , , This represents hyperparameters.

[0093] For example, the solution results include , , , The result of the nth iteration , , , The reconstruction results of the CEST magnetic resonance images to be reconstructed are derived from... get, , , , They are represented as follows:

[0094]

[0095]

[0096]

[0097] in, This represents the singular value threshold operator. , These represent the constant step size used by the algorithm in the image domain and K-space, respectively; Indicates the inverse of T. This represents the soft threshold operator.

[0098] It should be noted that for other specific embodiments of the magnetic resonance CEST image reconstruction apparatus of the present invention, please refer to the specific embodiments of the magnetic resonance CEST image reconstruction method of the above embodiments.

[0099] Based on the magnetic resonance CEST image reconstruction method of the above embodiments, the present invention proposes a computer-readable storage medium.

[0100] In an embodiment of the present invention, a computer program is stored on a computer-readable storage medium, and when the computer program is executed by a processor, it implements the magnetic resonance CEST image reconstruction method of the above embodiment.

[0101] The present invention also proposes an electronic device.

[0102] like Figure 10 As shown, the electronic device 500 includes a processor 501 and a memory 503. The processor 501 and the memory 503 are connected, for example, via a bus 502. Optionally, the electronic device 500 may also include a transceiver 504. It should be noted that in practical applications, the transceiver 504 is not limited to one type, and the structure of this electronic device 500 does not constitute a limitation on the embodiments of the present invention.

[0103] Processor 501 may be a CPU (Central Processing Unit), a general-purpose processor, a DSP (Digital Signal Processor), an ASIC (Application Specific Integrated Circuit), an FPGA (Field Programmable Gate Array), or other programmable logic devices, transistor logic devices, hardware components, or any combination thereof. It can implement or execute the various exemplary logic blocks, modules, and circuits described in conjunction with the disclosure of this invention. Processor 501 may also be a combination that implements computational functions, such as including one or more microprocessor combinations, a combination of a DSP and a microprocessor, etc.

[0104] Bus 502 may include a pathway for transmitting information between the aforementioned components. Bus 502 may be a PCI (Peripheral Component Interconnect) bus or an EISA (Extended Industry Standard Architecture) bus, etc. Bus 502 can be divided into address bus, data bus, control bus, etc. For ease of representation, Figure 10 The bus is represented by a single thick line, but this does not mean that there is only one bus or one type of bus.

[0105] The memory 503 stores a computer program corresponding to the magnetic resonance CEST image reconstruction method of the above embodiments of the present invention. This computer program is controlled and executed by the processor 501. The processor 501 executes the computer program stored in the memory 503 to implement the content shown in the foregoing method embodiments.

[0106] Among them, electronic devices 500 include, but are not limited to: laptops, desktop computers, etc. Figure 10 The electronic device 500 shown is merely an example and should not be construed as limiting the functionality and scope of use of the embodiments of the present invention.

[0107] It should be noted that the logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be specifically implemented in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable media include: an electrical connection having one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Alternatively, the computer-readable medium may be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in a computer memory.

[0108] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0109] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0110] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this invention, "a plurality of" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0111] In this invention, unless otherwise explicitly specified and limited, "above" or "below" the second feature can mean that the first feature is in direct contact with the second feature, or that the first feature is in indirect contact with the second feature through an intermediate medium. Furthermore, "above," "over," and "on top" of the second feature can mean that the first feature is directly above or diagonally above the second feature, or simply that the first feature is at a higher horizontal level than the second feature. "Below," "below," and "under" the second feature can mean that the first feature is directly below or diagonally below the second feature, or simply that the first feature is at a lower horizontal level than the second feature.

[0112] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for reconstructing CEST magnetic resonance images, characterized in that, The method includes: Acquire the CEST image of the magnetic resonance imaging to be reconstructed; The CEST magnetic resonance image to be reconstructed is subjected to low-rank sparse decomposition in the image domain and K-space, respectively. Construct the objective function based on the results of low-rank sparse decomposition; Solve the objective function, and obtain the reconstruction result of the magnetic resonance CEST image to be reconstructed based on the solution result.

2. The method for reconstructing CEST images according to claim 1, characterized in that, The low-rank sparse decomposition result includes the low-rank and sparse components of the CEST magnetic resonance image to be reconstructed in the image domain and in the K-space; the objective function is expressed as follows: in, , These represent the low-rank component and sparse component of the magnetic resonance CEST image to be reconstructed in the image domain, respectively. , Let T and E represent the low-rank and sparse components of the CEST image to be reconstructed in K-space, respectively; T represents the sparse transform operator; E represents the sensitivity encoding operator; U represents the K-space undersampling mask; and d represents the K-space data corresponding to the CEST image to be reconstructed. Denotes the square of the L2 norm. Represents the nuclear norm. Represents the L1 norm; , , , This represents hyperparameters.

3. The method for reconstructing magnetic resonance CEST images according to claim 2, characterized in that, E is obtained by performing a fast Fourier transform on a preset sensitivity map, and the hyperparameters are determined by grid search.

4. The method for reconstructing magnetic resonance CEST images according to claim 2 or 3, characterized in that, The objective function is solved using the proximal gradient method.

5. The method for reconstructing magnetic resonance CEST images according to claim 4, characterized in that, The solution results include , , , The result of the nth iteration , , , The reconstruction result of the CEST magnetic resonance image to be reconstructed is... get, , , , They are represented as follows: in, This represents the singular value threshold operator. , These represent the constant step size used by the algorithm in the image domain and K-space, respectively; Indicates the inverse of T. This represents the soft threshold operator.

6. A device for reconstructing CEST magnetic resonance images, characterized in that, The device includes: The acquisition module is used to acquire the CEST image of the magnetic resonance imaging to be reconstructed. The decomposition module is used to perform low-rank sparse decomposition on the CEST magnetic resonance image to be reconstructed in the image domain and K-space, respectively; the construction module is used to construct an objective function based on the low-rank sparse decomposition results. The solution module is used to solve the objective function and obtain the reconstruction result of the magnetic resonance CEST image to be reconstructed based on the solution result.

7. The apparatus for reconstructing magnetic resonance CEST images according to claim 6, characterized in that, The low-rank sparse decomposition result includes the low-rank and sparse components of the CEST magnetic resonance image to be reconstructed in the image domain and in the K-space; the objective function is expressed as follows: in, , These represent the low-rank component and sparse component of the magnetic resonance CEST image to be reconstructed in the image domain, respectively. , Let T and E represent the low-rank and sparse components of the CEST image to be reconstructed in K-space, respectively; T represents the sparse transform operator; E represents the sensitivity encoding operator; U represents the K-space undersampling mask; and d represents the K-space data corresponding to the CEST image to be reconstructed. Denotes the square of the L2 norm. Represents the nuclear norm. Represents the L1 norm; , , , This represents hyperparameters.

8. The apparatus for reconstructing magnetic resonance CEST images according to claim 7, characterized in that, The solution results include , , , The result of the nth iteration , , , The reconstruction result of the CEST magnetic resonance image to be reconstructed is... get, , , , They are represented as follows: in, This represents the singular value threshold operator. , These represent the constant step size used by the algorithm in the image domain and K-space, respectively; Indicates the inverse of T. This represents the soft threshold operator.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the method for reconstructing magnetic resonance CEST images as described in any one of claims 1-5.

10. An electronic device, characterized in that, The system includes a memory, a processor, and a computer program stored in the memory, which, when executed by the processor, implements the method for reconstructing magnetic resonance CEST images as described in any one of claims 1-5.

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