A non-cartesian magnetic resonance adaptive reconstruction method based on robust noise variance calibration

Abstract

This invention discloses a non-Cartesian adaptive reconstruction method for magnetic resonance imaging (MRI) based on robust noise variance calibration, belonging to the field of MRI data processing. This method addresses the problem of inaccurate SURE risk estimation caused by noise statistical characteristic mismatch under non-Cartesian undersampling conditions. It acquires multi-coil undersampling k-space data and performs adjoint reconstruction; employs a quantile truncation strategy to lock the background subset and adaptively estimates the effective noise variance based on median statistics; substitutes the effective noise variance into the Monte Carlo SURE expression to construct a risk estimation function; searches for the optimal regularization parameter corresponding to the minimum risk value within a preset parameter space, and performs final image reconstruction accordingly. This invention achieves robust and automatic optimization of regularization parameters without requiring a real reference image, effectively suppressing undersampling artifacts while preserving image details, significantly improving the quantitative indicators and visual quality of the reconstructed image, and has promising clinical application prospects.

Description

Technical Field

[0001] This invention belongs to the field of magnetic resonance imaging technology, specifically relating to a non-Cartesian magnetic resonance adaptive reconstruction method based on robust noise variance calibration. It is particularly suitable for non-Cartesian sampling trajectories such as helical or radial, and can automatically select regularization parameters for high-quality image reconstruction without the need for a real reference image. Background Technology

[0002] Magnetic resonance imaging (MRI) is widely used in clinical diagnosis due to its non-ionizing radiation and excellent soft tissue contrast capabilities, but its long scan time remains a bottleneck. To shorten scan time, undersampling techniques have been introduced, but this has turned image reconstruction into an ill-conditioned inverse problem. Therefore, reconstruction methods based on regularization constraints such as total variation (TV) are widely adopted. The selection of regularization parameters is crucial to image quality: too small a parameter results in artifacts, while too large a parameter leads to excessive smoothing of details. Therefore, achieving automatic and robust parameter selection in the absence of a true reference image has become one of the key issues in MRI reconstruction.

[0003] In automatic parameter selection methods, Stein's Unbiased Risk Estimation (SURE) provides a theoretical basis for unsupervised parameter tuning. This method, assuming the noise follows an independent and identically distributed Gaussian model, can achieve an unbiased estimate of reconstruction errors. However, existing studies are mostly based on idealized simulation environments, where the noise variance can be accurately obtained according to a preset signal-to-noise ratio. In actual MRI imaging, real images are unavailable, and the statistical characteristics of noise are difficult to accurately obtain, especially under undersampling conditions. The uncertainty of the noise prior directly affects the stability of SURE parameter tuning.

[0004] The aforementioned problems are more pronounced under non-Cartesian sampling conditions (such as spiral and radial trajectories). The introduction of non-uniform fast Fourier transform (NUFFT) and density compensation disrupts the orthogonality of the operators. Furthermore, the superposition of multi-coil sensitivity encoding and undersampling artifacts leads to significant changes in the statistical characteristics of image domain noise. After mapping by the reconstruction operator, the energy distribution of uniform noise in the original k-space is affected by the sampling trajectory, density compensation, and artifacts, forming a spatially mixed effective perturbation energy. If the original noise variance is used for SURE estimation at this point, it will lead to systematic bias in risk estimation and failure in parameter tuning. Existing research is mostly limited to Cartesian sampling or idealized assumptions, with insufficient attention paid to the mechanism of effective noise variance distortion under non-Cartesian undersampling conditions, and lacks a method that can adaptively calibrate the noise variance and achieve stable parameter selection. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of the prior art by providing a non-Cartesian magnetic resonance adaptive reconstruction method based on robust noise variance calibration. This method aims to solve the problems of inaccurate SURE risk estimation and the inability to automatically select regularization parameters under non-Cartesian undersampling conditions due to the mismatch of noise statistical characteristics.

[0006] To achieve the above objectives, the technical solution adopted by this invention is as follows: a non-Cartesian magnetic resonance adaptive reconstruction method based on robust noise variance calibration, comprising the following steps: Step 1: Acquire multi-coil undersampled k-space data using non-Cartesian sampling trajectories. Simultaneously, obtain the predicted value of the inherent noise floor of the system hardware. Density compensation matrix and the set of regularization parameters to be searched ,in The total number of regularization parameters to be searched; Step 2: Utilize the adjoint reconstruction operator of non-uniform fast Fourier transform k-space data Perform adjoint reconstruction to obtain the adjoint reconstructed image. ; Step 3: Based on the reconstructed image, an adaptive estimation of the effective noise variance is performed using a quantile truncation strategy. , Step 4: Construct the Monte Carlo SURE risk estimation function, and use the effective noise variance obtained in Step 3. Substitute the SURE formula to construct a risk estimation function that matches the current undersampling conditions; Step 5: Within the preset parameter space, search for the optimal regularization parameter that minimizes the risk estimate. ,in, For the first in the preset parameter set One candidate regularization parameter; Step 6: Based on the optimal regularization parameters The k-space data is reconstructed using a preset reconstruction algorithm. Perform final image reconstruction.

[0007] Specifically, step 3 includes: Calculate the empirical cumulative distribution function of the amplitude of the reconstructed image. ; According to the preset quantile Define the cutoff region ,in For pixel spatial location index, For the accompanying reconstructed image in the first The value at the position of each pixel. for -Quantities; In the truncated region Within this framework, robust variance estimation is performed based on median statistics, and artifact calibration factors are calculated. ,in As a consistency correction factor, This is the median operator; Based on the artifact calibration factor, the effective noise variance is obtained. .

[0008] Specifically, the SURE formula in step 4 is:

[0009] in, For the system sampling encoding operator, To use regularization parameters The nonlinear reconstruction results For the perturbated data Use regularization parameters The reconstruction results It is a tiny complex Gaussian random perturbation. For the perturbation step size, The trace of the matrix, This indicates the operation of taking the real part.

[0010] Specifically, the preset reconstruction algorithm in step 6 is the Fast Iterative Shrinkage Threshold Algorithm (FISTA) based on total variational TV regularization, which achieves the final reconstruction by iteratively solving the following optimization problem:

[0011] in, For the final reconstructed image, For the image variables to be optimized, For the total variation regularization term of the image.

[0012] Preferably, the preset quantile in step 3 The value is 0.05, which is the consistency correction factor. The value is 1.6.

[0013] Preferably, the perturbation step size in step 4 is... Values .

[0014] Compared with the prior art, the beneficial effects of the present invention are: 1. Strong robustness: This invention adopts a quantile truncation strategy to actively select pixel areas with less damage and contamination for noise statistics. This avoids the problem of overestimation of noise variance caused by artifact mixing in traditional background area calibration methods under high acceleration factors, and significantly improves the robustness of noise estimation.

[0015] 2. Good adaptability: By introducing an artifact calibration factor This invention can adaptively estimate the effective noise variance under non-Cartesian undersampling conditions, making the SURE risk estimation function match the actual image domain perturbation energy, thereby solving the noise statistical mismatch problem.

[0016] 3. No reference image required: This invention achieves automatic selection of regularization parameters without the need for a real reference image, which is more in line with actual clinical imaging scenarios and has good prospects for clinical application.

[0017] 4. High reconstruction quality: By accurately estimating the effective noise variance and optimizing the regularization parameters, this invention can effectively suppress undersampling artifacts while preserving image detail information to the greatest extent, thus obtaining high-quality reconstructed images.

[0018] Results on helical and radial datasets show that, compared to uncalibrated and conventionally calibrated SURE datasets, the method employed in this invention improves the peak signal-to-noise ratio (PSNR) by an average of 4.04 dB (approximately 11.83%) and 1.42 dB (approximately 3.86%), and reduces the high-frequency error norm (HFEN) by an average of 0.133 (approximately 43.25%) and 0.046 (approximately 20.78%). The method employed in this invention exhibits excellent robustness under different acceleration factors and fluctuating noise levels, providing a feasible solution for unsupervised automated reconstruction in clinical settings. The automatically selected regularization parameters closely approximate the optimal parameters achieved through manual fine-tuning, with virtually no difference in reconstruction performance. Attached Figure Description

[0019] Figure 1 The flowchart illustrates a non-Cartesian magnetic resonance adaptive reconstruction method based on robust noise variance calibration, as provided in this embodiment of the invention.

[0020] Figure 2 In this embodiment of the invention, non-Cartesian spiral sampling data is analyzed using an acceleration factor. A comparison of the reconstructed image and the error heatmap below. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to specific embodiments. However, it should be understood that the specific embodiments of this invention are only for explaining the invention and are not intended to limit the scope of protection of this invention.

[0022] Example 1: This example provides a non-Cartesian magnetic resonance adaptive reconstruction method based on robust noise variance calibration. The specific steps are as follows: Step S1: Using a non-Cartesian spiral sampling trajectory, a multi-channel receiving coil is used to perform an MRI scan on the subject to acquire undersampled k-space data. Simultaneously, the predicted value of the inherent noise floor of the system hardware was obtained through prior measurement. In this embodiment, the system refers to a magnetic resonance imaging system. The sensitivity distribution of each coil is obtained through calibration scanning or self-calibration methods. Calculate the density compensation vector based on the sampling trajectory. And construct the density compensation matrix. ,in The number of coils For Kronecker product, Represented by vector The elements are a diagonal matrix with the main diagonal elements.

[0023] Step S2: Utilize the adjoint operator of Non-Uniform Fast Fourier Transform (NUFFT) and coil sensitivity Constructing the adjoint reconstruction operator For k-space data Perform adjoint reconstruction to obtain the adjoint reconstructed image. The image contains anatomical information, but also contains undersampling artifacts and noise.

[0024] Step S3: Robust noise variance calibration. Based on the reconstructed image, an effective noise variance is adaptively estimated using a quantile truncation strategy. Specifically, this includes: First, calculate the accompanying reconstructed image. amplitude values ​​of each pixel And statistically analyze its empirical cumulative distribution function. In this embodiment, quantiles are selected. Find the corresponding quantiles Then, define the cutoff region. This region consists of all amplitude values ​​less than or equal to The composition of pixels, i.e. ,in For pixel spatial location index, For the accompanying reconstructed image in the first The value at the position of each pixel. for - Quantiles. Pixels in this region are considered to be least affected by artifacts, and their statistical characteristics are mainly dominated by system noise.

[0025] Next, in the truncated region Within, calculate the median of the squared amplitudes of all pixels. Robust variance estimation is performed based on median statistics, and the artifact calibration factor is calculated. Introducing a consistency correction factor This is used to transform the median estimate into a statistic that matches the variance. According to robust statistics theory, for Gaussian distributed data, when the cutoff region is sufficiently pure, It can be approximated as 1.6. Therefore, the variance of the robust estimate is... This estimate incorporates the energy of system hardware noise and some low-amplitude artifacts, and is taken as the effective perturbation energy in the image domain under the current imaging conditions, denoted as . Simultaneously, the artifact calibration factor can be calculated. This is used to quantitatively describe the amplification factor of effective noise relative to the physical noise floor, and then the effective noise variance can be obtained. .

[0026] Step S4: Calculate the effective noise variance obtained in step S3. Substitute the Monte Carlo SURE formula. First, generate a k-space data... Small complex Gaussian random perturbation vectors of the same dimension And set the perturbation step size. Pick For any given regularization parameter Perform two reconstructions: one using the original data. To obtain the reconstructed image ; Data after perturbation used once To obtain the reconstructed image Then, calculate the risk estimate using the following formula:

[0027] in, For the system sampling encoding operator, To use regularization parameters The nonlinear reconstruction results For the perturbated data Use regularization parameters The reconstruction results It is a tiny complex Gaussian random perturbation. For the perturbation step size, The trace of the matrix, This indicates the operation of taking the real part; Step S5: Define a candidate set of regularization parameters ,in The total number of regularization parameters to be searched. For each parameter in the set... Calculate its corresponding value according to step S4. Value. Selection makes smallest As the optimal regularization parameter ,Right now ,in, For the first in the preset parameter set There are 10 candidate regularization parameters.

[0028] Step S6: Use the FISTA-TV algorithm and the optimal regularization parameters obtained in step S5. For the original k-space data The final reconstruction is then performed. The FISTA-TV algorithm solves the following optimization problem iteratively:

[0029] in, For the final reconstructed image, For the image variables to be optimized, This is the total variational regularization term for the image. Through iterative updates, the algorithm eventually converges to a high-quality reconstructed image. This image effectively suppresses undersampling artifacts while preserving edge and detail information.

[0030] Through the above steps, this embodiment achieves fully automatic and robust image reconstruction of non-Cartesian undersampled MRI data in the absence of a real reference image. Experimental verification shows that this method can stably select near-optimal reconstruction parameters and obtain high-quality reconstruction results under helical and radial sampling trajectories, different acceleration factors, and different noise levels.

[0031] The uncalibrated method, the conventional calibration method, the robust calibration method proposed in this invention, and the manual parameter tuning method were tested on a non-Cartesian spiral sampling brain dataset, using an acceleration factor of [missing information]. and The peak signal-to-noise ratio (PSNR), structural similarity index (SSIM), and high-frequency error norm (HFEN) of the reconstructed images are shown in Table 1. Overall, compared to the comparative methods (uncalibrated and conventionally calibrated), the method of this invention significantly improves the quantization metrics PSNR and SSIM, and substantially reduces the error HFEN. This invention offers a significant improvement in undersampled image reconstruction performance and closely approximates the optimal performance of manually tuned parameters.

[0032]

[0033] In the comparison between the "invention" and the "uncalibrated method": setting an acceleration factor At that time, the PSNR of the method of the present invention was approximately 3.25 dB higher, the SSIM was approximately 0.0217 higher, and the HFEN was approximately 0.0373 lower; an acceleration factor was set. At that time, the PSNR of the method of the present invention was significantly higher by approximately 7.66 dB, the SSIM was approximately 0.1260 higher, and the HFEN was approximately 0.1094 lower. In the comparison between the "present invention" and the "conventional calibration method": an acceleration factor was set. At that time, the PSNR of the method of the present invention was approximately 1.23 dB higher, the SSIM was approximately 0.0019 higher, and the HFEN was approximately 0.0096 lower; an acceleration factor was set. At that time, the PSNR of the method of this invention was approximately 1.96 dB higher and the HFEN was approximately 0.0473 lower. Compared with the manually tuned benchmark, all the indicators of this invention are very close, demonstrating the high accuracy of this method in automatic optimization.

[0034] The four methods described above were cross-validated on a non-Cartesian radial sampling brain dataset, using the same acceleration factor. and The quantization metrics of the reconstructed images are shown in Table 2.

[0035]

[0036] In the comparison between the "invention" and the "conventional calibration method": setting an acceleration factor At that time, the PSNR of the method of the present invention was approximately 0.79 dB higher, the SSIM was approximately 0.0145 higher, and the HFEN was approximately 0.0076 lower; an acceleration factor was set. At that time, the PSNR of the method of this invention was about 1.33 dB higher, the SSIM was about 0.0368 higher, and the HFEN was about 0.0040 lower. Under radial sampling with more complex data structures, conventional calibration methods are prone to interference from structured artifacts, leading to inaccurate parameter estimation. However, the method of this invention still maintains extremely high robustness and effectively improves the imaging quality under complex sampling trajectories.

[0037] Depend on Figure 2 We can obtain: the reconstruction plot and error plot of the uncalibrated method ( Figure 2 (b) and Figure 2 (g) contains a large number of aliasing artifacts and noise residue, and the highlighted areas in the error heatmap are concentrated; conventional calibration methods ( Figure 2 (c) and Figure 2 (h) While suppressing some background artifacts, it leads to over-smoothing, resulting in severe loss of high-frequency edge details such as folds in the cerebral cortex; in contrast, the robust calibration method proposed in this invention ( Figure 2 (d) and Figure 2(i) Effectively removes artifact interference, resulting in high image sharpness and clear structural boundaries. As can be seen from the error heatmap, this invention has the lowest error energy, and its overall visual effect is closest to the "gold standard" of manually tuned parameters (i) for its internal geometry. Figure 2 (e) and Figure 2 (j) further confirms from a subjective visual perspective that the present invention effectively improves the smoothing phenomenon and detail loss problem in undersampled MRI reconstruction.

[0038] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A non-Cartesian magnetic resonance adaptive reconstruction method based on robust noise variance calibration, characterized in that, Includes the following steps: Step 1: Acquire multi-coil undersampled k-space data using non-Cartesian sampling trajectories. Simultaneously, obtain the predicted value of the inherent noise floor of the system hardware. Density compensation matrix and the set of regularization parameters to be searched ,in The total number of regularization parameters to be searched; Step 2: Utilize the adjoint reconstruction operator of non-uniform fast Fourier transform k-space data Perform adjoint reconstruction to obtain the adjoint reconstructed image. ; Step 3: Based on the reconstructed image, an adaptive estimation of the effective noise variance is performed using a quantile truncation strategy. , Step 4: Construct the Monte Carlo SURE risk estimation function, and use the effective noise variance obtained in Step 3. Substitute the SURE formula to construct a risk estimation function that matches the current undersampling conditions; Step 5: Within the preset parameter space, search for the optimal regularization parameter that minimizes the risk estimate. ,in, For the first in the preset parameter set One candidate regularization parameter; Step 6: Based on the optimal regularization parameters The k-space data is reconstructed using a preset reconstruction algorithm. Perform final image reconstruction.

2. The non-Cartesian magnetic resonance adaptive reconstruction method based on robust noise variance calibration according to claim 1, characterized in that: Step 3 specifically includes: Calculate the empirical cumulative distribution function of the amplitude of the reconstructed image. ; According to the preset quantile Define the cutoff region ,in For pixel spatial location index, For the accompanying reconstructed image in the first The value at the position of each pixel. for -Quantities; In the truncated region Within this framework, robust variance estimation is performed based on median statistics, and artifact calibration factors are calculated. ,in As a consistency correction factor, This is the median operator; Based on the artifact calibration factor, the effective noise variance is obtained. .

3. The non-Cartesian magnetic resonance adaptive reconstruction method based on robust noise variance calibration according to claim 1, characterized in that: The SURE formula in step 4 is: ； in, For the system sampling encoding operator, To use regularization parameters The nonlinear reconstruction results For the perturbated data Use regularization parameters The reconstruction results It is a tiny complex Gaussian random perturbation. For the perturbation step size, The trace of the matrix, This indicates the operation of taking the real part.

4. The non-Cartesian magnetic resonance adaptive reconstruction method based on robust noise variance calibration according to claim 1, characterized in that: The reconstruction algorithm preset in step 6 is the Fast Iterative Shrinking Threshold Algorithm (FISTA) based on total variational TV regularization, which achieves the final reconstruction by iteratively solving the following optimization problem: ； in, For the final reconstructed image, For the image variables to be optimized, For the total variation regularization term of the image.

5. The non-Cartesian magnetic resonance adaptive reconstruction method based on robust noise variance calibration according to claim 2, characterized in that: The preset quantile in step 3 The value is 0.05, which is the consistency correction factor. The value is 1.

6.

6. The non-Cartesian magnetic resonance adaptive reconstruction method based on robust noise variance calibration according to claim 3, characterized in that: The perturbation step size in step 4 Values .

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