Magnetic resonance fingerprint imaging technology based on dictionary sparse reconstruction

Abstract

The invention discloses a magnetic resonance fingerprint imaging technology based on dictionary sparse reconstruction in the technical field of magnetic resonance fingerprint imaging, and aims to solve the technical problems that in the prior art, aliasing artifact interference is caused by K-space high-power undersampling, and a traditional reconstruction method is difficult to accurately recover a tissue physiological parameter quantitative diagram. The method comprises the following steps: projecting an under-sampling K space signal and a magnetic resonance fingerprint dictionary to a low-dimensional subspace through singular value decomposition, and reducing the calculation complexity; constructing a reconstruction framework in a low-dimensional space by combining a forward model and an adaptive sparse representation model, and introducing dictionary constraints to suppress aliasing artifacts; and iteratively optimizing mode matching, dictionary learning and K space fidelity steps based on an alternating minimization strategy to realize high-precision reconstruction of magnetic resonance fingerprint image space data. And finally, obtaining a tissue physiological parameter quantitative diagram through fingerprint dictionary matching. According to the method, the accuracy and robustness of magnetic resonance fingerprint reconstruction under the under-sampling condition are remarkably improved.

Description

Technical Field

[0001] The present invention relates to the field of magnetic resonance fingerprinting (MRF) imaging, and particularly to a magnetic resonance fingerprint reconstruction algorithm and technique based on adaptive sparse dictionary representation. Background Art

[0002] Magnetic Resonance fingerprinting (MRF), as a new quantitative magnetic resonance imaging (qMRI) technique, was first proposed in 2013, breaking through the limitations of traditional qMRI techniques, such as long scanning time and difficulty in simultaneously obtaining multiple tissue physiological parameters, and promoting the clinical application process of qMRI techniques.

[0003] However, in order to achieve fast scanning, the K-space signal sampling frequency adopted by the MRF technique is much lower than the Nyquist frequency, which poses a challenge to the accurate reconstruction of MRF image space data. Conventional MRF techniques use the non-uniform Fourier transform algorithm to reconstruct MRF image space data from undersampled K-space signals. Although it has high computational efficiency, the reconstructed MRF image space data contains serious aliasing artifacts, which are reflected as severe folding noise in the time-domain fingerprint signal. If the template matching algorithm cannot overcome the interference of folding noise, the reconstruction result of tissue physiological parameters will contain a large error. Therefore, introducing the prior information of MRF image space data to improve the ill-posedness of reconstructing MRF image space data from highly undersampled K-space signals has become the mainstream solution idea. After years of development, the low-rank prior model and the sparse prior model have gradually taken the leading position.

[0004] Considering the protection of edge information while suppressing noise, the sparse prior constraint has a better noise reduction effect than the low-rank constraint. The MRI reconstruction framework based on compressed sensing theory (CSMRI) utilizes the sparsity of magnetic resonance images in a specific transform domain to achieve the accurate reconstruction of magnetic resonance images from undersampled k-space signals. Traditional CSMRI methods use global and fixed analytical sparse transforms (such as wavelets, curvelets, finite differences) to sparsely represent magnetic resonance images. The predefined and fixed analytical sparse transforms cannot adaptively and accurately sparsify specific image instances. Therefore, the CSMRI reconstruction framework is usually limited to a relatively low k-space undersampling rate (less than 5 times). To obtain a higher sparsity, Ravishankar et al. used an adaptive sparse representation model and dictionary learning algorithm to construct an adaptive and overcomplete local sparse basis for any specific image instance, and proposed a new MRI reconstruction framework (dictionary learning MRI, DLMRI) based on this. Empirical results show that DLMRI supports the accurate reconstruction of a single magnetic resonance image at a higher k-space undersampling rate (about 10 times, and the limit performance even exceeds 20 times).

[0005] To accelerate the scanning speed, the MRF technique uses an extremely high k-space undersampling rate (usually greater than 20 times) during signal acquisition, which will lead to a serious degradation of the reconstruction performance of existing CSMRI methods. Inspired by the DLMRI reconstruction framework, the present invention first proposes an MRF technique based on dictionary sparse reconstruction. This technique first eliminates the aliasing artifacts caused by the high-fold k-space undersampling rate by introducing the MRF dictionary prior, and maximally suppresses its adverse effects on the dictionary learning algorithm. Secondly, the SVD compression method is used to project the acquired k-space signal into the low-dimensional SVD space in advance to reduce the computational cost required for reconstructing the MRF image space data. Finally, an alternating minimization solution algorithm combining three steps of pattern matching, dictionary learning, and k-space signal fidelity is designed to solve the non-convex objective optimization function in the dictionary sparse reconstruction process. This method improves the fingerprint reconstruction effect while ensuring the interpretability of the algorithm, thereby ensuring the accuracy of quantitative parameter inversion and contributing to promoting the early clinical use of the MRF technique. Summary of the Invention

[0006] The present invention proposes a magnetic resonance fingerprint reconstruction method based on adaptive sparse representation to solve the problems of magnetic resonance fingerprint reconstruction and quantitative tissue physiological parameter map inversion accuracy under undersampling patterns.

[0007] The technical solution adopted by the present invention to solve the above problems is as follows:

[0008] A magnetic resonance fingerprint reconstruction method based on adaptive sparse representation, comprising the following steps:

[0009] Step 1: Obtain the undersampled K-space signal Y of the observation target.

[0010] Step 2: Based on the Bloch equation and the combination of quantitative parameters, construct a magnetic resonance fingerprint dictionary D through computer simulation.

[0011] Step 3: Project the K-space signal obtained in Step 1 and the fingerprint dictionary into the low-dimensional subspace defined by the first several left singular vectors of the fingerprint dictionary.

[0012] Step 4: In the low-dimensional subspace, combine the forward model of magnetic resonance fingerprint, the adaptive sparse representation model, and the fingerprint dictionary constraint conditions to establish a magnetic resonance fingerprint reconstruction model based on adaptive sparse representation.

[0013] Step 5: Based on the alternating minimization strategy, solve the reconstruction model established in Step 4 to obtain the reconstruction result of the magnetic resonance fingerprint image space data.

[0014] Step 6: Perform pattern matching on the reconstruction result obtained in Step 5 and the fingerprint dictionary in Step 2 to obtain the quantitative map of the tissue physiological parameters of the observation target.

[0015] Further, perform singular value decomposition on the fingerprint dictionary, i.e., D = U∑V * , to obtain the U and V matrices. Then select the first R column vectors of U to form the projection matrix U R = [u1,..., u R , and project the fingerprint dictionary into the low-dimensional subspace, i.e., Similarly, project the undersampled K-space signal into the low-dimensional subspace defined by U R , i.e.,

[0016] Further, Step 4 establishes a magnetic resonance fingerprint reconstruction model based on adaptive sparse representation:

[0017]

[0018] In the formula, represents the 2D Casorati matrix corresponding to the 3D magnetic resonance fingerprint image space data to be reconstructed, where represents 's r-th row vector, i.e., the r-th magnetic resonance image to be reconstructed; represents 's r-th row vector; F u (·) represents the non-uniform Fourier transform; (i, j) represents the spatial position coordinates of the upper-left pixel of the local image block in the observation target, used to index different local image blocks; E ij (·) represents taking from the image Extract a local image patch with spatial position index (i, j); Φ (r) Denote the adaptive sparse basis dictionary to be constructed; Denote the sparse representation coefficients; s0 denotes the sparsity threshold; H denotes the best matching matrix, and each column vector of it has and only has one non-zero element, indicating that each reconstructed fingerprint signal can only match one fingerprint entry in the fingerprint dictionary; v r Is a weight factor used to balance the fidelity of the K-space signal and the sparse coding quality of the magnetic resonance image.

[0019] Furthermore, step five solves the reconstruction model established in step three based on the alternating minimization strategy, specifically including three cyclic iterative solution steps of pattern matching, dictionary learning, and K-space signal fidelity.

[0020] Furthermore, the pattern matching step includes matching the reconstructed fingerprint with the fingerprint entries in the fingerprint dictionary in the form of calculating the vector inner product, and taking the entry with the largest inner product as the best matching fingerprint dictionary entry for updating the reconstructed fingerprint.

[0021] Furthermore, in the dictionary learning step, the spatial data of the magnetic resonance fingerprint image to be reconstructed is kept fixed, and the K-SVD algorithm and the OMP algorithm are used to adaptively update the sparse basis and the sparse representation coefficients.

[0022] Furthermore, in the K-space signal fidelity step, the adaptive sparse basis and the sparse representation coefficients are kept fixed, and the conjugate gradient algorithm is used to solve the solution of the least squares problem to update the spatial data of the magnetic resonance fingerprint image.

[0023] Furthermore, step six matches the final result of the reconstructed fingerprint obtained through step five with all the ideal fingerprint entries in the MRF dictionary, selects the best matching ideal fingerprint entry, and indexes the tissue physiological parameters of the best matching dictionary entry.

[0024] The present invention has the following beneficial effects:

[0025] Aiming at the high-fold undersampling rate adopted in the K-space signal acquisition process of magnetic resonance fingerprint imaging technology, an adaptive sparse representation model is first introduced to improve the MRF reconstruction framework: the collected K-space signal is pre-projected into a low-dimensional subspace by using the SVD compression method, and a reconstruction framework is constructed in the low-dimensional subspace by combining the forward model of the MRF image space data and the adaptive sparse representation model, reducing the computational cost required to construct the adaptive sparse basis dictionary; by introducing the MRF dictionary prior in the reconstruction framework, the aliasing artifacts caused by the high-fold K-space undersampling rate are suppressed, and the adverse interference of the aliasing artifacts on the dictionary learning process is minimized to the greatest extent. Description of the Drawings

[0026] Figure 1It is the overall flowchart of the present invention

[0027] Figure 2 It is the flip angle parameter of the pSSFP RF sequence used in the embodiment of the present invention

[0028] Figure 3 It is the schematic diagram of the variable density spiral sampling template used in the embodiment of the present invention

[0029] Figure 4 It shows the quantitative map of the physiological parameters of the human brain tissue reconstructed in the embodiment of the present invention

[0030] Figure 5 It shows the relative error map of the physiological parameters of the human brain tissue reconstructed in the embodiment of the present invention Detailed implementation manners

[0031] The objectives, technical solutions and advantages of the present invention will be described in detail below in conjunction with the accompanying drawings and examples

[0032] In view of the high-fold undersampling rate adopted by the MRF technology in the process of K-space signal acquisition, the present invention proposes a new MRF reconstruction model based on dictionary sparse reconstruction and establishes an effective solution algorithm, and finally realizes the purpose of accurately reconstructing the MRF image space data and tissue physiological parameters. Specifically, the singular value decomposition (SVD) compression method is used to project the K-space signal onto a low-dimensional subspace in advance, and a reconstruction model is established by combining the forward model of the MRF image space data and the adaptive sparse representation model in the low-dimensional subspace; the MRF dictionary prior is introduced into the reconstruction model to suppress the aliasing artifacts caused by the high-fold K-space undersampling rate. The overall process of the present invention specifically includes the following steps

[0033] Step 1: Obtain the undersampled K-space signal Y of the observation target

[0034] According to the embodiment of the present invention, the K-space signal is obtained by means of numerical simulation. The RF pulse sequence is set as a pSSFP sequence including 850 repetition time (TR) periods, wherein the TR period sequence is calculated based on the pSSFP mode, and the flip angle (FA) parameter is as Figure 2 shown. The variable density spiral sampling template with full sampling at the center of K-space and 1 / 48 undersampling at the edge of K-space is used to undersample the K-space signal, which includes 1960 sampling points, and the variable density spiral sampling template is as Figure 3 shown

[0035] Download a data with a size of 256×256 and a field of view of 256×256mm from the BminWeb database 2Digital brain cross-sectional model and its corresponding T1, T2, and proton density (PD) tissue physiological parameter maps; after selecting the radiofrequency pulse sequence and its scanning parameters, based on Bloch simulation, obtain the ideal MRF image spatial data of the digital brain model; convert the ideal MRF image spatial data to the K-space through fast Fourier transform, and use a variable density spiral sampling template to undersample the K-space; add complex Gaussian white noise to obtain the final undersampled K-space signal Y, whose size is 850×1960; the t-th row vector of Y can be expressed as Y t , representing the K-space signal collected at the t-th TR time point.

[0036] Step 2: Based on the Bolch equation and a preset combination of quantitative parameters, construct an MRF dictionary D through computer simulation:

[0037] According to the embodiments of the present invention, within the reasonable value range of the T1 and T2 parameters of the human brain, discretize the T1 and T2 parameters, set the value range of the T1 parameter and the step to be 20 ms within the parameter range of 100 ms to 2000 ms, 200 ms within the parameter range of 2000 ms to 5000 ms, the value range of the T2 parameter and the step to be 2 ms within the parameter range of 10 ms to 50 ms, 5 ms within the parameter range of 50 ms to 300 ms, and 20 ms within the parameter range of 300 ms to 500 ms. Use the extended phase graph method (EPG) to form an MRF dictionary D with a size of 850×8595, and each of its column vectors represents an ideal fingerprint entry.

[0038] Step 3: Project the undersampled K-space signal obtained in Step 1 and the MRF dictionary obtained in Step 2 into the low-dimensional subspace defined by the first several left singular vectors of the MRF dictionary:

[0039] According to the embodiments of the present invention, perform singular value decomposition (SVD) on the MRF dictionary D obtained in Step 2, as shown in the following formula:

[0040] D = U∑V * (1)

[0041] Furthermore, in this embodiment, select the first 5 left singular vectors of the MRF dictionary to define the low-dimensional SVD space, and project the undersampled K-space signal Y and the MRF dictionary D into the low-dimensional SVD space:

[0042]

[0043] In the formula, respectively represent the undersampled K-space signal and the MRF dictionary after subspace projection; U5 is composed of the first 5 column vectors of the matrix U.

[0044] Step 4: In the low-dimensional subspace, combine the forward model of magnetic resonance fingerprinting, the adaptive sparse representation model, and the fingerprint dictionary constraint condition to establish a magnetic resonance fingerprint reconstruction model based on adaptive sparse representation:

[0045] According to an embodiment of the present invention, let the 2D Castrati matrix corresponding to the original 3D MRF image space data to be reconstructed be X, with a size of 850×65536. Each row vector represents the magnetic resonance image to be reconstructed at a TR time point; each column vector represents the fingerprint signal corresponding to a pixel point in the observation target.

[0046] Project the matrix X into the low-dimensional SVD space:

[0047]

[0048] In the formula, represents the MRF image space data after subspace projection, with a size of 5×65536. Further, the relationship between it and can be shown as the following formula:

[0049]

[0050] In the formula, F u (·) represents the non-uniform fast Fourier transform (NUFFT).

[0051] The magnetic resonance fingerprint reconstruction method based on adaptive sparse representation according to the present invention selects to reconstruct in the low-dimensional SVD space to reduce the computational cost. First, establish the adaptive sparse representation model of

[0052]

[0053] In the formula, is the r-th row vector of ij and represents the r-th magnetic resonance image to be reconstructed; (i, j) represents the spatial position coordinates of the upper left pixel point of the local image block in the observation target and is used to index different local tissue blocks; the function E extracts the local image block with the spatial position index (i, j) from the image (r) and repacks it in the form of a column vector. In this embodiment, the size of the local image block is set to 5×5; Φ represents the adaptive sparse basis dictionary to be constructed, and each column vector represents an adaptive sparse basis. In this embodiment, the number of atoms in the adaptive sparse basis dictionary is set to 128;

[0054] Furthermore, using the undersampled K-space signal obtained in Step 3 construct a data fidelity term and additionally introduce the MRF dictionary constraint condition, and the following reconstruction model objective optimization function can be obtained:

[0055]

[0056] In the formula, in order to eliminate the redundant solution results caused by scale inconsistency, the L2 norms of all adaptive sparse bases are normalized; H represents the best matching matrix, with a size of 8595×65536, and each column vector of it has and only has one non-zero element, indicating that each reconstructed fingerprint signal can only match one fingerprint entry in the fingerprint dictionary; v r is a weight factor used to balance the fidelity of the K-space signal and the sparse coding quality of the magnetic resonance image. In this embodiment, v r = 5×10 3 .

[0057] Step 5. Based on the alternating minimization strategy, solve the reconstruction model established in Step 4 to obtain the reconstruction result of the magnetic resonance fingerprint image space data:

[0058] According to the embodiment of the present invention, using the alternating minimization strategy to solve the reconstruction model objective optimization function established in Step 4 specifically includes three cyclic iterative solution steps of pattern matching, dictionary learning, and K-space signal fidelity.

[0059] First, the pattern matching step can be modeled as the following sub-problem:

[0060]

[0061] Use the matching pursuit algorithm to solve the objective optimization function in the above formula, and combine the final solution result to use to update the MRF image space data to suppress aliasing artifacts.

[0062] Furthermore, in the dictionary learning step, fix to solve the following sub-problem to update the adaptive sparse basis dictionary {Φ (r) |r = 1, 2,..., 5} and the sparse representation coefficient

[0063]

[0064] Use the K-SVD algorithm to solve the objective optimization function in the above formula. The detailed solution steps are as follows:

[0065]

[0066]

[0067] Further, in the dictionary learning step, the adaptive sparse basis dictionary {Φ (r) | r = 1, 2,... 5} and the sparse representation sparsity Solve the following least squares problem:

[0068]

[0069] Take the derivative of the objective optimization function in the above formula, and its solution result satisfies the following formula:

[0070]

[0071] In the formula, respectively represent the adjoint operators of E ij (·) and F u (·). Use the conjugate gradient algorithm to solve the above formula and update

[0072] Finally, when the maximum number of iterations is reached or the error between two adjacent iterations is lower than the set threshold, the above iteration terminates; otherwise, repeat step five.

[0073] Step six: Perform pattern matching on the reconstruction result obtained through step four and the fingerprint dictionary obtained through step one to obtain a quantitative map of the tissue physiological parameters of the observed target:

[0074] According to the embodiments of the present invention, use the MRF dictionary obtained in step three to establish a tissue physiological parameter look-up table LUT, and fill the tissue physiological parameter combinations corresponding to the ideal fingerprint entries sequentially on the k-th entry of the LUT table, and finally form a look-up table LUT with a size of 8595×2.

[0075] For the reconstructed fingerprint signal of the n-th pixel point in the observed target Its corresponding tissue physiological parameters can be obtained through the following formula:

[0076]

[0077] In the formula, are the T1 and T2 parameters corresponding to the n-th pixel point in the observed target, and PD n is the proton density parameter corresponding to the n-th pixel point in the observed target. Traverse all pixel points in the observed target to obtain the T1, T2, and PD physiological parameter maps of the observed target.

[0078] Figure 4The figure shows the quantitative tissue physiological parameter map reconstructed according to the embodiments of the present invention. From the intuitive comparison of the reconstructed images, it can be seen that the quantitative tissue physiological parameter map reconstructed by the present invention is closer to the true value due to the conventional NUFFT reconstruction algorithm.

[0079] Figure 5 The figure shows the relative error map between the reconstructed quantitative tissue physiological parameter map and the true value. From the comparison of the relative error maps, it can be seen that the quantitative tissue physiological parameter map reconstructed by the present invention has a lower relative error due to the NUFFT reconstruction algorithm.

Claims

1. A magnetic resonance fingerprint reconstruction method based on adaptive sparse representation, characterized in that: The following steps are involved: Step 1: Obtain an undersampled K-space signal Y of the observed target; Step 2: Based on the Bolch equation and quantitative parameter combination, a magnetic resonance fingerprint dictionary D is constructed by computer simulation; Step 3: Project the K-space signal and the fingerprint dictionary obtained in step 1 into a low-dimensional subspace defined by the first several left singular vectors of the fingerprint dictionary; Step 4: In the low-dimensional subspace, the forward model of the magnetic resonance fingerprint, the adaptive sparse representation model and the fingerprint dictionary constraint conditions are combined to establish a magnetic resonance fingerprint reconstruction model based on adaptive sparse representation; Step 5: Based on the alternating minimization strategy, solve the reconstruction model established in step 4 to obtain the reconstruction result of the magnetic resonance fingerprint image spatial data; Step 6: Perform pattern matching on the reconstruction result of step 5 and the fingerprint dictionary of step 2 to obtain a quantitative map of the tissue physiological parameters of the observed target.

2. The magnetic resonance fingerprint reconstruction method based on adaptive sparse representation according to claim 1, characterized in that: The specific method of step three is as follows: Perform singular value decomposition on the fingerprint dictionary, that is, D = U∑V * , get the U, V matrix. Then select the first R column vectors of U to form the projection matrix U R =[u1,...,u R ], project the fingerprint dictionary into a low-dimensional subspace, that is, Similarly, the undersampled K-space signal is projected onto U R In the low-dimensional subspace defined, 3. The magnetic resonance fingerprint reconstruction method based on adaptive sparse representation according to claim 1, characterized in that: The specific description of the magnetic resonance fingerprint reconstruction model based on adaptive sparse representation established in step 4 is: In the formula, Represents the 2D Casorati matrix corresponding to the spatial data of the 3D magnetic resonance fingerprint image to be reconstructed, where express The r-th row vector of , i.e., the r-th magnetic resonance image to be reconstructed; express The rth row vector of u (·) represents non-uniform Fourier transform; (i, j) represents the spatial position coordinates of the upper left corner pixel of the local image block in the observed object, which is used to index different local image blocks; E i , (·) indicates that from the image Extract the local image block with spatial position index (i, j) from Φ (r) represents the adaptive sparse basis dictionary to be constructed; represents the sparse representation coefficient; s0 represents the sparsity threshold; H represents the best matching matrix, each column vector of which has only one non-zero element, indicating that each reconstructed fingerprint signal can only match one fingerprint entry in the fingerprint dictionary; v r is a weighting factor used to balance the fidelity of the K-space signal and the sparse coding quality of the magnetic resonance image.

4. The magnetic resonance fingerprint reconstruction method based on adaptive sparse representation according to claim 1, characterized in that: Step 5 solves the reconstruction model established in step 3 based on the alternating minimization strategy, which specifically includes three cyclic iterative solution steps: pattern matching, dictionary learning, and K-space signal fidelity.

5. The magnetic resonance fingerprint reconstruction method based on adaptive sparse representation according to claim 4, characterized in that: The pattern matching step includes matching the reconstructed fingerprint with the fingerprint entries in the fingerprint dictionary by calculating the vector inner product, and taking the entry with the largest inner product as the best matching fingerprint dictionary entry for updating the reconstructed fingerprint.

6. The magnetic resonance fingerprint reconstruction method based on adaptive sparse representation according to claim 4, characterized in that: The dictionary learning step keeps the spatial data of the magnetic resonance fingerprint image to be reconstructed fixed, and uses the K-SVD algorithm and the OMP algorithm to adaptively update the sparse basis and sparse representation coefficients.

7. The magnetic resonance fingerprint reconstruction method based on adaptive sparse representation according to claim 4, characterized in that: The K-space signal fidelity step keeps the adaptive sparse basis and the sparse representation coefficients fixed, uses the conjugate gradient algorithm to solve the least squares problem, and updates the magnetic resonance fingerprint image space data.

8. The magnetic resonance fingerprint reconstruction method based on adaptive sparse representation according to claim 1, characterized in that: Step 6 matches the final result of the reconstructed fingerprint obtained in step 5 with all entries in the fingerprint dictionary, selects the best matching fingerprint dictionary entry, and indexes the tissue physiological parameters of the best matching fingerprint dictionary entry.

Images