Method and system for removing nyquist artifacts in ultra-low field MRI EPI

Abstract

This invention discloses a method and system for eliminating Nyquist artifacts in ultra-low field MRI EPI. The method involves preprocessing two-dimensional complex EPI k-space data with center protection to remove anomalous noise and electromagnetic interference. Based on the preprocessed two-dimensional complex EPI k-space data, a high-order odd-even phase / amplitude joint error model for ultra-low field EPI is established. For the high-order odd-even phase / amplitude joint correction model, an odd-even k-space complex consistency evaluation index is constructed. Based on the odd-even k-space complex consistency evaluation index, a multi-objective safety optimization model is constructed, and the compromise-optimal high-order odd-even phase / amplitude correction parameters are solved. Finally, Hankel structure low-rank joint iteration is performed on the high-order odd-even phase / amplitude joint error model for ultra-low field EPI corresponding to the compromise-optimal high-order odd-even phase / amplitude correction parameters to suppress residual structured artifacts.

Description

Technical Field

[0001] This invention relates to the fields of magnetic resonance imaging, nuclear magnetic resonance engineering, and medical image reconstruction technology, specifically to a method and system for eliminating Nyquist artifacts in ultra-low field MRI EPI based on parity-k spatial consistency and multi-objective safety optimization. Background Technology

[0002] Magnetic resonance imaging (MRI) is widely used in medical diagnosis, brain function research, and non-destructive testing of materials due to its advantages such as no ionizing radiation, high soft tissue contrast, and multi-parameter imaging. With the development of portable, low-cost, and open-system MRI, low-field and ultra-low-field MRI are gradually becoming important technologies for bedside testing, mobile healthcare, emergency screening, and primary care due to their simple structure, low cost, high safety, and flexible deployment. Especially in emergency scenarios such as stroke, rapid and accessible imaging is crucial, and echo-planar imaging (EPI) can complete k-space acquisition in a short time, making it one of the important sequences for achieving rapid brain imaging with ultra-low-field MRI. However, in EPI, odd and even echoes are usually acquired using alternating readout polarities. Affected by gradient delay, eddy current effects, sampling timing errors, and receiver link differences, phase and amplitude inconsistencies are easily generated, resulting in a Nyquist artifact (N / 2 artifact) that shifts half the field of view in the image domain. This artifact reduces image contrast and structural clarity, affecting the application of ultra-low-field MRI in bedside brain imaging and emergency auxiliary assessment.

[0003] Existing EPI Nyquist artifact correction methods mainly include reference scan or navigation echo correction, zero-order / first-order parity phase correction, and reference-free optimization methods based on indicators such as image entropy, singular value decomposition, or artifact rate. However, under ultra-low field MRI conditions, the image signal-to-noise ratio is low, and the segmentation of the main body region, background region, and artifact region is unstable; external electromagnetic interference can easily form spikes, abnormal sampling rows and columns, or increased noise floor in k-space; at the same time, the stability of the main magnetic field, gradient system, and receiver link is weak, which may cause parity echo errors to manifest in complex forms such as slow drift, nonlinear phase bending, and amplitude inconsistency. Traditional methods that rely solely on simple phase models or single image domain evaluation indicators are prone to problems such as insufficient adaptability, weakening of the main body signal, amplification of background noise, destruction of central k-space information, or generation of false structures.

[0004] Therefore, it is necessary to propose a robust Nyquist artifact elimination method for ultra-low field MRI EPI data, which can simultaneously address issues such as low signal-to-noise ratio, external electromagnetic interference, complex parity echo errors, residual half-field artifacts, and overcorrection risks without relying on additional reference scans. Summary of the Invention

[0005] The purpose of this invention is to provide a method and system for eliminating Nyquist artifacts in ultra-low field MRI EPI, which can cope with complex working conditions such as low signal-to-noise ratio, electromagnetic interference, and odd-even echo error. It solves the defects of traditional phase correction and reference scanning methods, such as unstable parameter estimation, artifact residue, signal damage, and noise amplification, effectively improving image quality and helping ultra-low field MRI to be applied in bedside brain imaging, emergency and rapid detection scenarios at the grassroots level.

[0006] To achieve the above objectives, the present invention adopts the following technical solution: The method for eliminating Nyquist artifacts in ultra-low field MRI EPI includes the following steps: Step 1: Perform center protection preprocessing on the two-dimensional complex EPI k-space data to remove abnormal noise and electromagnetic interference; Step 2: Based on the two-dimensional complex EPI k-space data after preprocessing for abnormal noise and electromagnetic interference, establish a high-order odd-even phase / amplitude joint error model for ultra-low field EPI; Step 3: For the high-order parity phase / amplitude joint correction model, construct a parity k-space complex number consistency evaluation index; Step 4: Construct a multi-objective security optimization model based on the parity k-space complex number consistency evaluation index, and solve for the compromise optimal high-order parity phase / amplitude correction parameters; Step 5: Perform Hankel structure low-rank joint iteration on the high-order parity phase / amplitude joint error model for ultra-low field EPI corresponding to the optimal high-order parity phase / amplitude correction parameters in the compromise to suppress residual structured artifacts.

[0007] Furthermore, step one specifically includes: Acquire the two-dimensional complex EPI k-space data K(m,n) to be processed in ultra-low field MRI, where m represents the sampling line number of the phase encoding direction and n represents the sampling point number of the readout direction; Robust preprocessing is performed on the two-dimensional complex EPI k-space data K(m,n). Isolated spikes, abnormal sampling rows and columns are identified based on the robust statistics of k-space amplitude, and repair is performed by interpolation of the neighborhood complex median or adjacent normal sampling lines. Phase-preserving soft threshold suppression is applied to the peripheral noise outside the central k-space protection zone of the two-dimensional complex EPI k-space data.

[0008] Furthermore, step two specifically involves: Considering the effects of slow drift of the main magnetic field, non-ideal gradient response, eddy current residue and unstable receiving link under ultra-low field conditions, the zero-order phase, first-order linear phase, inter-line slow drift, second-order nonlinear phase bending and parity amplitude difference are incorporated into a unified parity phase / amplitude joint error model. Let the symbols for odd and even echoes be... Where odd-numbered sampling lines are taken as +1 and even-numbered sampling lines are taken as -1, the higher-order phase error between odd and even echoes is expressed as:

[0009] in, This represents the higher-order phase error between odd and even echoes. This indicates the zero-order phase difference between odd and even echoes. This indicates the first-order phase or equivalent subpixel displacement of the readout direction. This represents the slow drift coefficient along the sampling line direction. This represents the second-order nonlinear phase curvature coefficient of the readout direction. For normalized sampling line coordinates, To normalize the readout direction coordinates, It is a second-order Legendre polynomial; The second-order Legendre polynomial is expressed as:

[0010] Introducing logarithmic amplitude difference of odd and even echoes To compensate for potential amplitude inconsistencies during forward and reverse readout, the higher-order parity phase / amplitude joint error model for ultra-low field EPI is expressed as: .

[0011] Furthermore, step three specifically includes: In the complex domain of k-space, the consistency of even and odd sampling lines is evaluated. For even sampling lines, a prediction line is constructed using their two adjacent odd sampling lines:

[0012] And define the complex residual between the even-numbered line and the predicted line:

[0013] Define the parity term for complex residuals from the above formula:

[0014] in The reliability weight for complex consistency evaluation, with a value range of [value range missing]. ε is a preset positive number set to prevent the denominator from being zero or too small; Define the phase consistency term:

[0015] in,( ) Represents complex conjugation, Re( ) indicates taking the real part of a complex number; Define the amplitude consistency term:

[0016] Define image focusing evaluation terms:

[0017] in N I This represents the total number of image pixels involved in the calculation. To normalize the image energy distribution; set up This refers to the k-space after step one processing, before parity / even phase / amplitude correction is performed. To define the k-space conservation weights, we define the k-space energy preservation term:

[0018] Based on the consistency of complex numbers in the even-odd k-space, combined with the consistency of complex residuals in the even-odd k-space... Phase consistency Amplitude consistency Image focusing and k-space energy preservation term A comprehensive no-reference evaluation function suitable for ultra-low field EPI is constructed, and its expression is:

[0019] in, All are non-negative weighting coefficients, used to adjust the relative importance of each evaluation sub-item in the comprehensive no-reference evaluation function.

[0020] Furthermore, step four specifically involves: The parameter optimization objective of the multi-objective safety optimization model is set as simultaneously minimizing the parity consistency term, residual artifact term, main damage term, background noise term, and center k-space variation term, as expressed below:

[0021] A multidimensional parameter search space is constructed based on the preset value range of the higher-order odd-even phase / amplitude correction parameters, and several initial candidate parameters that can uniformly cover the search space are generated using Sobol sequences, Halton sequences or other low-difference sequences. Substitute each set of initial candidate parameters into the high-order odd-even phase / amplitude joint correction model to obtain the corresponding candidate correction results, and calculate the objective function values ​​of each item of the multi-objective security optimization model to form the initial sample set required for parameter optimization. Based on the initial sample, an approximate prediction model between the parameters and each objective function is fitted. New candidate parameters are selected through multi-objective Bayesian optimization iteration, and random weight scalarization is used to coordinate the relative importance between different optimization objectives. After iteration, all candidate parameters are sorted in a non-dominated manner to obtain the Pareto candidate solution set, and the compromise optimal higher-order parity phase / amplitude correction parameters are determined.

[0022] Furthermore, step five specifically includes: After obtaining the compromise-optimal high-order parity phase / amplitude correction parameters, the high-order parity phase / amplitude joint error model for ultra-low field EPI is divided into blocks to construct the Hankel matrix and complete low-rank joint iteration processing. This is then used to iteratively optimize the correction parameters, forming a joint iteration mechanism of the high-order parity phase / amplitude joint error model and low-rank constraints for ultra-low field EPI. This improves the suppression of residual Nyquist artifacts in low signal-to-noise ratio scenarios. The low-rank constraint is expressed as follows:

[0023] in, This represents the Hankel matrix construction operator. This represents the singular value contraction operator. This represents the unHankelization and overlapping block averaging operations; To avoid low-rank processing from disrupting the central k-space, a further mixing process using centrally protected weights is employed:

[0024] in, For the phase model correction results, For low-rank mixing intensity, As a central protection weight, This indicates point-by-point multiplication.

[0025] Furthermore, it also includes the following steps: Step 6: After the low-rank joint iteration of the Hankel structure, adaptive interpolation resampling is used to further correct the non-integer sampling misalignment; Step 7: After completing adaptive interpolation resampling, perform phase-preserving amplitude soft suppression on the residual N / 2 artifacts in the image domain; Step 8: Perform a safety evaluation on the higher-order parity phase / amplitude correction parameters obtained in Steps 5, 6, and 7, and select the optimal higher-order parity phase / amplitude correction parameters for image reconstruction.

[0026] Furthermore, steps six and seven specifically involve: Adaptive interpolation resampling is used to perform complex interpolation on the k-space along the readout direction or the phase encoding direction, and the local resampling offset is determined with the goal of minimizing the parity of complex numbers. The cost function of adaptive interpolation resampling is expressed as:

[0027] in, Indicates the candidate offset The sampling line after resampling This represents the prediction line constructed from adjacent odd and even lines. As weight, A preset positive number is set to prevent the denominator from being zero or the value from being too small; After adaptive interpolation resampling, a high-confidence artifact region is constructed outside the main protected area. Soft suppression of the amplitude of this high-confidence artifact region is applied only to the background level, while preserving the original complex phase. The soft suppression is expressed as:

[0028] in, The current complex image is, For amplitude, For phase, The background target threshold.

[0029] Furthermore, step eight specifically includes: For each of the higher-order odd-even phase / amplitude correction parameters obtained in steps five, six, and seven, the main energy preservation, background noise variation, residual ghost intensity, and relative change in the center k-space are calculated, and a security scoring function is constructed. The final result is selected from the candidate set that satisfies the safety constraints:

[0030] After determining the optimal higher-order parity phase / amplitude correction parameters for the safety scoring function, these parameters are substituted into the higher-order parity phase / amplitude joint correction model to obtain the final corrected two-dimensional complex k-space, denoted as... A two-dimensional discrete inverse Fourier transform is performed on the finally corrected two-dimensional complex k-space to obtain the final complex reconstructed image:

[0031] Where represents the two-dimensional discrete inverse Fourier transform, M and N represent the number of sampling points in the phase encoding direction and readout direction, respectively, x and y represent the spatial location index in the reconstructed image, and j represents the imaginary unit.

[0032] The ultra-low field MRI EPI Nyquist artifact elimination system includes: Module 1: Preprocessing for abnormal noise and electromagnetic interference to perform center protection on two-dimensional complex EPI k-space data; The second module is used to establish a high-order odd-even phase / amplitude joint error model for ultra-low field EPI based on the two-dimensional complex EPI k-space data preprocessed with abnormal noise and electromagnetic interference. The third module is used to construct a complex consistency evaluation index for the odd-even k-space for high-order odd-even phase / amplitude joint correction models. The fourth module is used to construct a multi-objective security optimization model based on the parity k-space complex number consistency evaluation index, and to solve for the compromise optimal high-order parity phase / amplitude correction parameters. The fifth module is used to perform Hankel structure low-rank joint iteration on the high-order parity phase / amplitude joint error model for ultra-low field EPI corresponding to the compromise optimal high-order parity phase / amplitude correction parameters in order to suppress residual structured artifacts.

[0033] Compared with the prior art, the present invention has the following beneficial technical effects: This invention addresses the challenges of low signal-to-noise ratio, strong electromagnetic interference, complex odd-even echo errors, and difficulty in effectively suppressing N / 2 artifacts in ultra-low field MRI EPI data. It employs robust k-space preprocessing, high-order odd-even phase amplitude joint error modeling, and multi-objective constraint parameter optimization. Combined with Hankel structure low-rank joint iteration, adaptive interpolation resampling, and artifact post-processing techniques, it comprehensively suppresses various Nyquist artifacts while effectively protecting the main image signal and central k-space information, avoiding noise amplification and signal distortion. Furthermore, multi-level safety evaluation, automatic backoff, and parameter adaptive mechanisms significantly reduce reliance on manual parameter tuning, eliminating image distortion and pseudo-structure problems caused by overcorrection. This invention significantly improves the structural recognition, reconstruction stability, and diagnostic reliability of ultra-low field MRI images, adapting to complex on-site imaging environments. It provides stable and high-quality imaging support for practical applications such as bedside brain imaging, stroke emergency screening, and rapid detection at the grassroots level, demonstrating excellent practical value and promising prospects for widespread adoption. Attached Figure Description

[0034] The accompanying drawings are provided to further understand the invention and constitute a part of this invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0035] Figure 1 This is a schematic diagram of the overall process of the present invention for robust elimination of Nyquist artifacts in ultra-low field MRI EPI.

[0036] Figure 2The images are comparisons of EPI images before and after processing according to the present invention. (a) to (f) represent the EPI image processing results of water models, fruits, and heads under different sample morphologies, subject positions, and artifact distribution conditions acquired on a 0.068T ultra-low field nuclear magnetic resonance system.

[0037] Figure 3 For Figure 2 The image shown in (f) is a comparison of the k-space diagrams and odd / even line residuals before and after correction, using the head EPI image as an example. (a) is the original k-space diagram, (b) is the corrected k-space diagram, (c) is the original odd / even line residual diagram, and (d) is the corrected odd / even line residual diagram. The odd / even line residual is defined as: signed residual = odd line The even line indicates positive residuals in red and negative residuals in blue.

[0038] Figure 4 The image shows the GSR ROI annotation map used to calculate the residual Nyquist artifact index, where (a) is the ROI annotation result of the original EPI image and (b) is the ROI annotation result of the EPI image after the final correction according to the present invention. Detailed Implementation

[0039] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0040] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0041] Example 1 This invention provides a method for eliminating Nyquist artifacts in ultra-low field MRI EPI, comprising the following steps: Step 1: Perform center protection preprocessing on the two-dimensional complex EPI k-space data to remove abnormal noise and electromagnetic interference; Step 2: Based on the two-dimensional complex EPI k-space data after preprocessing for abnormal noise and electromagnetic interference, establish a high-order odd-even phase / amplitude joint error model for ultra-low field EPI; Step 3: For the high-order parity phase / amplitude joint correction model, construct a parity k-space complex number consistency evaluation index; Step 4: Construct a multi-objective security optimization model based on the parity k-space complex number consistency evaluation index, and solve for the compromise optimal high-order parity phase / amplitude correction parameters; Step 5: Perform Hankel structure low-rank joint iteration on the high-order parity phase / amplitude joint error model for ultra-low field EPI corresponding to the optimal high-order parity phase / amplitude correction parameters in the compromise to suppress residual structured artifacts.

[0042] Example 2 This invention provides a method for eliminating Nyquist artifacts in ultra-low field MRI EPI, comprising the following steps: Step 1: Perform center protection preprocessing on the two-dimensional complex EPI k-space data to remove abnormal noise and electromagnetic interference; Step 2: Based on the two-dimensional complex EPI k-space data after preprocessing for abnormal noise and electromagnetic interference, establish a high-order odd-even phase / amplitude joint error model for ultra-low field EPI; Step 3: For the high-order parity phase / amplitude joint correction model, construct a parity k-space complex number consistency evaluation index; Step 4: Construct a multi-objective security optimization model based on the parity k-space complex number consistency evaluation index, and solve for the compromise optimal high-order parity phase / amplitude correction parameters; Step 5: Perform Hankel structure low-rank joint iteration on the high-order parity phase / amplitude joint error model for ultra-low field EPI corresponding to the optimal high-order parity phase / amplitude correction parameters in the compromise to suppress residual structured artifacts.

[0043] Step 6: After the low-rank joint iteration of the Hankel structure, adaptive interpolation resampling is used to further correct the non-integer sampling misalignment; Step 7: After completing adaptive interpolation resampling, perform phase-preserving amplitude soft suppression on the residual N / 2 artifacts in the image domain; Step 8: Perform a safety evaluation on the higher-order parity phase / amplitude correction parameters obtained in Steps 5, 6, and 7, and select the optimal higher-order parity phase / amplitude correction parameters for image reconstruction.

[0044] This invention eliminates Nyquist artifacts in ultra-low field MRI EPI based on high-order odd-even echo error modeling, odd-even k-space complex consistency evaluation, multi-objective safety optimization, Hankel structure low-rank joint iteration, adaptive interpolation resampling, and safety backoff mechanism, which can improve the stability, robustness, and engineering applicability of ultra-low field EPI image post-processing.

[0045] Example 3 Specifically, the present invention provides a method for eliminating Nyquist artifacts in ultra-low field MRI EPI, comprising the following steps: Step 1: Perform center protection preprocessing on the two-dimensional complex EPI k-space data to remove abnormal noise and electromagnetic interference; First, acquire the two-dimensional complex EPI k-space data K(m,n) to be processed from ultra-low field MRI, where m represents the sampling line number of the phase encoding direction and n represents the sampling point number of the readout direction. For multi-channel data, each channel can be processed separately, or processed after channel synthesis.

[0046] After determining the input data, this invention first performs robust preprocessing on the original k-space data to reduce the impact of weak signals and external electromagnetic interference in ultra-low field MRI on subsequent corrections. Specifically, isolated spikes, anomalous sampling rows, and anomalous sampling columns are identified based on robust k-space amplitude statistics, and repaired using neighborhood complex median or interpolation of adjacent normal sampling lines. Simultaneously, phase-preserving soft thresholding suppression is applied to peripheral noise outside the central k-space protection zone of the two-dimensional complex EPI k-space data. This processing only repairs extreme anomalies and peripheral noise, avoiding damage to central low-frequency information, thereby improving the stability of odd-even phase estimation and parameter optimization, and protecting the main image contour and low-frequency structure.

[0047] Step 2: Based on the two-dimensional complex EPI k-space data after preprocessing for abnormal noise and electromagnetic interference, establish a high-order odd-even phase / amplitude joint error model for ultra-low field EPI; After preprocessing for k-space anomalous noise and electromagnetic interference, this invention further establishes a high-order joint model for the systematic errors of odd and even echoes in ultra-low field EPI. This invention considers the effects of factors such as slow drift of the main magnetic field, non-ideal gradient response, eddy current residue, and receiver link instability under ultra-low field conditions, and incorporates zero-order phase, first-order linear phase, inter-line slow drift, second-order nonlinear phase bending, and odd / even amplitude difference into a unified odd / even phase / amplitude joint error model. Let the odd / even echo symbols be... Where odd-numbered sampling lines are taken as +1 and even-numbered sampling lines are taken as -1, the higher-order phase error between odd and even echoes can be expressed as:

[0048] in, This represents the higher-order phase error between odd and even echoes. This indicates the zero-order phase difference between odd and even echoes. This indicates the first-order phase or equivalent subpixel displacement of the readout direction. This represents the slow drift coefficient along the sampling line direction. This represents the second-order nonlinear phase curvature coefficient of the readout direction. For normalized sampling line coordinates, To normalize the readout direction coordinates, This is a second-order Legendre polynomial. The second-order Legendre polynomial can be expressed as:

[0049] Furthermore, this invention introduces the logarithmic amplitude difference between odd and even echoes. This is used to compensate for potential amplitude inconsistencies during forward and reverse readout. Therefore, the high-order parity phase / amplitude joint error model for ultra-low field EPI can be expressed as:

[0050] Step 3: For the high-order parity phase / amplitude joint correction model, construct a parity k-space complex number consistency evaluation index; After obtaining the high-order odd-even phase / amplitude joint correction model, this invention further constructs an odd-even k-space complex consistency index to evaluate the correction effect. This invention directly evaluates the consistency of odd-even sampling lines in the k-space complex domain. For even-numbered sampling lines, a prediction line is constructed using its two adjacent odd-numbered sampling lines:

[0051] And define the complex residual between the even-numbered line and the predicted line:

[0052] Define the parity term for complex residuals using formula (5):

[0053] in The reliability weight for complex consistency evaluation, with a value range of [value range missing]. ε is a preset positive number set to prevent the denominator from being zero or too small.

[0054] Define the phase consistency term:

[0055] in,( ) Represents complex conjugation, Re( ) indicates taking the real part of a complex number.

[0056] Define the amplitude consistency term:

[0057] Define image focusing evaluation terms:

[0058] in N I This represents the total number of image pixels involved in the calculation. This represents the normalized image energy distribution.

[0059] set up This refers to the k-space after step one processing, before parity / even phase / amplitude correction is performed. To define the k-space conservation weights, we define the k-space energy preservation term:

[0060] This invention focuses on the consistency of complex numbers in the even-odd k-space, combined with the consistency of complex residuals in the even-odd k-space. Phase consistency Amplitude consistency Image focusing and k-space energy preservation term A comprehensive no-reference evaluation function suitable for ultra-low field EPI is constructed, and its expression is:

[0061] in, All are non-negative weighting coefficients, used to adjust the relative importance of each evaluation sub-item in the comprehensive no-reference evaluation function.

[0062] Step 4: Construct a multi-objective security optimization model based on the parity k-space complex number consistency evaluation index, and solve for the correction parameters; After establishing the parity-k-space complex consistency evaluation index, this invention further optimizes the higher-order parity-k-space phase / amplitude correction parameters. To balance artifact suppression and image structure preservation, the parameter optimization objective is set to simultaneously minimize the parity-k-space consistency term, residual artifact term, subject damage term, background noise term, and center k-space variation term, i.e., a multi-objective safety optimization model.

[0063] In practice, a multidimensional parameter search space is first constructed based on the preset value range of the higher-order parity phase / amplitude correction parameters. Several initial candidate parameters that can uniformly cover this search space are generated using Sobol sequences, Halton sequences, or other low-difference sequences. Each set of initial candidate parameters is substituted into the higher-order parity phase / amplitude joint correction model to obtain the corresponding candidate correction results. The objective function values ​​in formula (12) are then calculated to form the initial sample set required for parameter optimization. Subsequently, an approximate prediction model between the parameters and the objective functions is fitted based on the initial samples. New candidate parameters are selected through multi-objective Bayesian optimization iteration, and the relative importance of different optimization objectives is coordinated using random weight scalarization. After iteration, all candidate parameters are non-dominated and sorted to obtain the Pareto candidate solution set, ultimately determining the optimal higher-order parity phase / amplitude correction parameters.

[0064] Step 5: Perform Hankel structure low-rank joint iteration on the high-order parity phase / amplitude joint error model for ultra-low field EPI corresponding to the optimal high-order parity phase / amplitude correction parameters in the compromise to suppress residual structured artifacts; After obtaining the compromise-optimal high-order parity phase / amplitude correction parameters, the Hankel matrix is ​​constructed in blocks for the high-order parity phase / amplitude joint error model for ultra-low field EPI, and low-rank joint iteration processing is performed. This process is then used to iteratively optimize the correction parameters, forming a joint iteration mechanism of the high-order parity phase / amplitude joint error model and low-rank constraints for ultra-low field EPI. This improves the suppression of residual Nyquist artifacts in low signal-to-noise ratio scenarios. The low-rank constraint can be expressed as:

[0065] in, This represents the Hankel matrix construction operator. This represents the singular value contraction operator. This represents the unHankelization and overlapping block averaging operations.

[0066] To avoid low-rank processing from disrupting the central k-space, this invention further employs a central protection weight for mixing:

[0067] in, For the phase model correction results, For low-rank mixing intensity, As a central protection weight, This indicates point-by-point multiplication.

[0068] Step 6: After the low-rank joint iteration of the Hankel structure, adaptive interpolation resampling is used to further correct the non-integer sampling misalignment; Following the low-rank joint iteration of the Hankel structure, this invention further employs adaptive interpolation resampling for correction. This step primarily targets local residual artifacts that are difficult to completely eliminate even after higher-order phase correction and low-rank correction. Adaptive interpolation resampling performs complex interpolation on the k-space along the readout direction or phase encoding direction, and determines the local resampling offset with the goal of minimizing parity-even complex consistency. The cost function of adaptive interpolation resampling can be expressed as:

[0069] in, Indicates the candidate offset The sampling line after resampling This represents the prediction line constructed from adjacent odd and even lines. As weight, It is a very small constant.

[0070] Step 7: After completing adaptive interpolation resampling, perform phase-preserving amplitude soft suppression on the residual N / 2 artifacts in the image domain; After completing adaptive interpolation resampling, this invention does not use simple half-field complex copy subtraction, but instead constructs a high-confidence artifact region outside the main protected area, and only performs soft suppression on the amplitude of the high-confidence artifact region towards the background level, while preserving the original complex phase.

[0071] Let the current complex image be The amplitude is Phase is The background target threshold is Then, amplitude soft suppression can be expressed as:

[0072] Finally, the complex image is recovered (i.e., the image after artifact removal):

[0073] Step 8: Perform a safety evaluation on the higher-order parity phase / amplitude correction parameters obtained in Steps 5, 6, and 7, and select the optimal higher-order parity phase / amplitude correction parameters for image reconstruction; This invention performs a security evaluation on the higher-order parity phase / amplitude correction parameters obtained in steps five, six, and seven. For each higher-order parity phase / amplitude correction parameter obtained in steps five, six, and seven, the preservative energy, background noise variation, residual ghost intensity, and relative change in the central k-space are calculated, and a security scoring function is constructed. The final result is selected from the candidate set that satisfies the safety constraints.

[0074] This mechanism enables the invention to have higher stability under low signal-to-noise ratio and complex interference conditions, and avoids image distortion due to over-optimization.

[0075] After determining the optimal higher-order parity phase / amplitude correction parameters for the safety scoring function, these parameters are substituted into the aforementioned higher-order parity phase / amplitude joint correction model to obtain the final corrected two-dimensional complex k-space, denoted as... Subsequently, a two-dimensional discrete inverse Fourier transform is performed on the finally corrected two-dimensional complex k-space to obtain the final complex reconstructed image:

[0076] Where represents the two-dimensional discrete inverse Fourier transform, M and N represent the number of sampling points in the phase encoding direction and readout direction, respectively, x and y represent the spatial location index in the reconstructed image, and j represents the imaginary unit.

[0077] In the above processing flow, to reduce the dependence on manual adjustment of processing parameters between different ultra-low field EPI data, this invention sets up a parameter adaptive recommendation module based on data quality self-assessment. This parameter adaptive recommendation module can run before performing higher-order odd-even phase / amplitude correction, multi-objective optimization, Hankel structure low-rank processing, adaptive interpolation resampling, and image domain residual artifact suppression, or it can update the recommended parameters based on intermediate evaluation results during processing.

[0078] First, an initial image reconstruction is performed on the input two-dimensional complex EPI k-space. Based on the input k-space data and the initially reconstructed image, data quality features are extracted, including initial signal-to-noise ratio, EMI anomalous sampling ratio, central k-space energy proportion, central k-space energy variation degree, and initial odd-even complex inconsistency degree, forming a data quality feature vector. These data quality features are then normalized to reduce the impact of differences in the numerical scales of different features on the parameter recommendation results.

[0079] Subsequently, based on the normalized data quality feature vector, initial recommended parameters adapted to the current data quality are generated through preset parameter recommendation rules, historical optimal parameter matching, regression mapping models, or combinations thereof. The recommended parameters include one or more of the following: the search range of higher-order odd-even phase / amplitude correction parameters, the weight of the comprehensive evaluation function, Hankel low-rank processing parameters, center k-space protection parameters, adaptive interpolation resampling parameters, image domain amplitude soft suppression parameters, and security evaluation thresholds.

[0080] Centered on the initial recommended parameters, multiple sets of candidate parameter combinations are generated within their allowable variation range. For each set of candidate parameters, a rapid pre-evaluation process is performed to correct candidates or reduce the number of iterations, and the parity of the k-space, the intensity of residual Nyquist artifacts, the degree of damage to the main signal, the change in background noise, and the relative change in the central k-space are calculated. Candidate parameters that meet the requirements of main signal preservation, background noise control, and central k-space stability are included in the safe candidate set, and a comprehensive score is calculated for each candidate parameter in the safe candidate set.

[0081] Finally, the candidate parameters with the best comprehensive score are selected from the set of safe candidates as the recommended parameters for the current ultra-low field EPI data. These recommended parameters are then automatically written into the high-order odd-even phase / amplitude correction, multi-objective optimization, Hankel structure low-rank processing, adaptive interpolation resampling, image domain residual artifact suppression, and safety evaluation modules to execute the subsequent complete correction process. If no candidate parameters meet the safety requirements, a preset conservative parameter combination is automatically invoked or a manual confirmation mode is entered, thereby avoiding overcorrection caused by abnormal data quality or parameter recommendation deviations.

[0082] Figure 1 This invention demonstrates that it is not a single image domain post-processing method, but rather addresses the problems of low signal-to-noise ratio, significant environmental electromagnetic interference, and complex phase / amplitude errors of odd and even echoes in ultra-low field MRI. Starting from the root cause of the inconsistency between odd and even echoes in the k-space of EPI, it constructs a robust closed-loop correction process for ultra-low field EPI through preprocessing, error modeling, evaluation optimization, structural constraints, residual suppression, and safe backoff.

[0083] Figure 2 Each group of images, from left to right, consists of the original image, the final corrected image, and a difference map / residual artifact map. As can be seen from the figures, under the acquisition conditions of 0.068T ultra-low field MRI with low signal-to-noise ratio and significant environmental interference, the original EPI images contain varying degrees of Nyquist artifacts or background artifacts. After processing using the method of this invention, the half-field artifacts and residual signals caused by the inconsistency between odd and even echoes are significantly reduced, and the main structure remains basically stable. Figure 2Taking the experimental data in (f) as an example, the ULF-Universal comprehensive evaluation index decreased from 0.2399 before processing to 0.1141 in the final result, a decrease of approximately 52.4%; the energy ratio (GSR) of the FOV / 2ghost region decreased from 0.210358 to 0.093664, a decrease of approximately 55.47%. The difference map / residual artifact map further demonstrates that the correction effect of this invention is mainly concentrated in the artifact region and the residual inconsistency region, rather than simply weakening the overall image brightness. It achieves relatively stable Nyquist artifact suppression under low signal-to-noise ratio and complex interference conditions. Compared with the GSR evaluation caliber commonly used in existing EPI Nyquist artifact correction studies, this invention achieves a higher amplitude of artifact reduction under ultra-low field complex acquisition conditions, demonstrating good robustness and engineering applicability.

[0084] Depend on Figure 3 As can be seen, the k-space center energy is preserved after correction, indicating that this invention does not reduce artifacts by simply weakening image brightness or destroying central k-space information. Simultaneously, the red and blue residual signals in the odd-even line residual map are significantly weakened after correction. Taking the mean absolute residual as an example, Mean(|Residual|) decreases from 7.451172 before correction to 4.830566 after correction, a decrease of approximately 35.17%. This demonstrates that this invention can reduce the complex inconsistency of odd-even echoes in ultra-low field MRI EPI data at the k-space level, thereby improving the root cause of Nyquist artifacts.

[0085] Figure 4 The green rectangle represents the main signal region of interest (ROI), used to characterize the signal intensity of the real imaging target in the image; the red rectangle represents the upper half-field of view (FOV / 2) ghost region ROI, and the orange rectangle represents the lower half-field of view (FOV / 2) ghost region ROI, used to statistically analyze the residual signal intensity of the Nyquist artifact regions in each half-field of view. By using the same location and size of the main ROI and ghost ROI in both the original and corrected images, the changes in Nyquist artifacts relative to the main signal before and after processing can be quantitatively compared, thus avoiding reliance solely on subjective visual judgment to evaluate the artifact removal effect.

[0086] Example 4 The present invention also provides an ultra-low field MRI EPI Nyquist artifact elimination system, comprising: Module 1: Preprocessing for abnormal noise and electromagnetic interference to perform center protection on two-dimensional complex EPI k-space data; The second module is used to establish a high-order odd-even phase / amplitude joint error model for ultra-low field EPI based on the two-dimensional complex EPI k-space data preprocessed with abnormal noise and electromagnetic interference. The third module is used to construct a complex consistency evaluation index for the odd-even k-space for high-order odd-even phase / amplitude joint correction models. The fourth module is used to construct a multi-objective security optimization model based on the parity k-space complex number consistency evaluation index, and to solve for the compromise optimal high-order parity phase / amplitude correction parameters. The fifth module is used to perform Hankel structure low-rank joint iteration on the high-order parity phase / amplitude joint error model for ultra-low field EPI corresponding to the compromise optimal high-order parity phase / amplitude correction parameters in order to suppress residual structured artifacts.

[0087] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0088] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0089] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0090] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0091] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit its scope of protection. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that after reading the present invention, they can still make various changes, modifications or equivalent substitutions to the specific implementation of the invention, but these changes, modifications or equivalent substitutions are all within the scope of protection of the pending claims of the invention.

Claims

1. A method for eliminating Nyquist artifacts in ultra-low field MRI EPI, characterized in that, Includes the following steps: Step 1: Perform center protection preprocessing on the two-dimensional complex EPI k-space data to remove abnormal noise and electromagnetic interference; Step 2: Based on the two-dimensional complex EPI k-space data after preprocessing for abnormal noise and electromagnetic interference, establish a high-order odd-even phase / amplitude joint error model for ultra-low field EPI; Step 3: For the high-order parity phase / amplitude joint correction model, construct a parity k-space complex number consistency evaluation index; Step 4: Construct a multi-objective security optimization model based on the parity k-space complex number consistency evaluation index, and solve for the compromise optimal high-order parity phase / amplitude correction parameters; Step 5: Perform Hankel structure low-rank joint iteration on the high-order parity phase / amplitude joint error model for ultra-low field EPI corresponding to the optimal high-order parity phase / amplitude correction parameters in the compromise to suppress residual structured artifacts.

2. The method for eliminating Nyquist artifacts in ultra-low field MRI EPI according to claim 1, characterized in that, Step one specifically involves: Acquire the two-dimensional complex EPI k-space data K(m,n) to be processed in ultra-low field MRI, where m represents the sampling line number of the phase encoding direction and n represents the sampling point number of the readout direction; Robust preprocessing is performed on the two-dimensional complex EPI k-space data K(m,n). Isolated spikes, abnormal sampling rows and columns are identified based on the robust statistics of k-space amplitude, and repair is performed by interpolation of the neighborhood complex median or adjacent normal sampling lines. Phase-preserving soft threshold suppression is applied to the peripheral noise outside the central k-space protection zone of the two-dimensional complex EPI k-space data.

3. The method for eliminating Nyquist artifacts in ultra-low field MRI EPI according to claim 1, characterized in that, Step two specifically involves: Considering the effects of slow drift of the main magnetic field, non-ideal gradient response, eddy current residue and unstable receiving link under ultra-low field conditions, the zero-order phase, first-order linear phase, inter-line slow drift, second-order nonlinear phase bending and parity amplitude difference are incorporated into a unified parity phase / amplitude joint error model. Let the symbols for odd and even echoes be... Where odd-numbered sampling lines are taken as +1 and even-numbered sampling lines are taken as -1, the higher-order phase error between odd and even echoes is expressed as: in, This represents the higher-order phase error between odd and even echoes. This indicates the zero-order phase difference between odd and even echoes. This indicates the first-order phase or equivalent subpixel displacement of the readout direction. This represents the slow drift coefficient along the sampling line direction. This represents the second-order nonlinear phase curvature coefficient of the readout direction. For normalized sampling line coordinates, To normalize the readout direction coordinates, It is a second-order Legendre polynomial; The second-order Legendre polynomial is expressed as: Introducing logarithmic amplitude difference of odd and even echoes To compensate for potential amplitude inconsistencies during forward and reverse readout, the higher-order parity phase / amplitude joint error model for ultra-low field EPI is expressed as: 。 4. The method for eliminating Nyquist artifacts in ultra-low field MRI EPI according to claim 1, characterized in that, Step three specifically involves: In the complex domain of k-space, the consistency of even and odd sampling lines is evaluated. For even sampling lines, a prediction line is constructed using their two adjacent odd sampling lines: And define the complex residual between the even-numbered line and the predicted line: Define the parity term for complex residuals from the above formula: in The reliability weight for complex consistency evaluation, with a value range of [value range missing]. ε is a preset positive number set to prevent the denominator from being zero or too small; Define the phase consistency term: in,( ) Represents complex conjugation, Re( ) indicates taking the real part of a complex number; Define the amplitude consistency term: Define image focusing evaluation terms: in N I This represents the total number of image pixels involved in the calculation. To normalize the image energy distribution; set up This refers to the k-space after step one processing, before parity / even phase / amplitude correction is performed. To define the k-space conservation weights, we define the k-space energy preservation term: Based on the consistency of complex numbers in the even-odd k-space, combined with the consistency of complex residuals in the even-odd k-space... Phase consistency Amplitude consistency Image focusing and k-space energy preservation term A comprehensive no-reference evaluation function suitable for ultra-low field EPI is constructed, and its expression is: in, All are non-negative weighting coefficients, used to adjust the relative importance of each evaluation sub-item in the comprehensive no-reference evaluation function.

5. The method for eliminating Nyquist artifacts in ultra-low field MRI EPI according to claim 1, characterized in that, Step four specifically involves: The parameter optimization objective of the multi-objective safety optimization model is set as simultaneously minimizing the parity consistency term, residual artifact term, main damage term, background noise term, and center k-space variation term, as expressed below: A multidimensional parameter search space is constructed based on the preset value range of the higher-order odd-even phase / amplitude correction parameters, and several initial candidate parameters that can uniformly cover the search space are generated using Sobol sequences, Halton sequences or other low-difference sequences. Substitute each set of initial candidate parameters into the high-order odd-even phase / amplitude joint correction model to obtain the corresponding candidate correction results, and calculate the objective function values ​​of each item of the multi-objective security optimization model to form the initial sample set required for parameter optimization. Based on the initial sample, an approximate prediction model between the parameters and each objective function is fitted. New candidate parameters are selected through multi-objective Bayesian optimization iteration, and random weight scalarization is used to coordinate the relative importance between different optimization objectives. After iteration, all candidate parameters are sorted in a non-dominated manner to obtain the Pareto candidate solution set, and the compromise optimal higher-order parity phase / amplitude correction parameters are determined.

6. The method for eliminating Nyquist artifacts in ultra-low field MRI EPI according to claim 1, characterized in that, Step five specifically involves: After obtaining the compromise-optimal high-order parity phase / amplitude correction parameters, the high-order parity phase / amplitude joint error model for ultra-low field EPI is divided into blocks to construct the Hankel matrix and complete low-rank joint iteration processing. This is then used to iteratively optimize the correction parameters, forming a joint iteration mechanism of the high-order parity phase / amplitude joint error model and low-rank constraints for ultra-low field EPI. This improves the suppression of residual Nyquist artifacts in low signal-to-noise ratio scenarios. The low-rank constraint is expressed as follows: in, This represents the Hankel matrix construction operator. This represents the singular value contraction operator. This represents the unHankelization and overlapping block averaging operations; To avoid low-rank processing from disrupting the central k-space, a further mixing process using centrally protected weights is employed: in, For the phase model correction results, For low-rank mixing intensity, As a central protection weight, This indicates point-by-point multiplication.

7. The method for eliminating Nyquist artifacts in ultra-low field MRI EPI according to claim 1, characterized in that, It also includes the following steps: Step 6: After the low-rank joint iteration of the Hankel structure, adaptive interpolation resampling is used to further correct the non-integer sampling misalignment; Step 7: After completing adaptive interpolation resampling, perform phase-preserving amplitude soft suppression on the residual N / 2 artifacts in the image domain; Step 8: Perform a safety evaluation on the higher-order parity phase / amplitude correction parameters obtained in Steps 5, 6, and 7, and select the optimal higher-order parity phase / amplitude correction parameters for image reconstruction.

8. The method for eliminating Nyquist artifacts in ultra-low field MRI EPI according to claim 7, characterized in that, Steps six and seven are specifically as follows: Adaptive interpolation resampling is used to perform complex interpolation on the k-space along the readout direction or the phase encoding direction, and the local resampling offset is determined with the goal of minimizing the parity of complex numbers. The cost function of adaptive interpolation resampling is expressed as: in, Indicates the candidate offset The sampling line after resampling This represents the prediction line constructed from adjacent odd and even lines. As weight, A preset positive number is set to prevent the denominator from being zero or the value from being too small; After adaptive interpolation resampling, a high-confidence artifact region is constructed outside the main protected area. Soft suppression of the amplitude of this high-confidence artifact region is applied only to the background level, while preserving the original complex phase. The soft suppression is expressed as: in, The current complex image is, For amplitude, For phase, The background target threshold.

9. The method for eliminating Nyquist artifacts in ultra-low field MRI EPI according to claim 7, characterized in that, Step eight is as follows: For each of the higher-order odd-even phase / amplitude correction parameters obtained in steps five, six, and seven, the main energy preservation, background noise variation, residual ghost intensity, and relative change in the center k-space are calculated, and a security scoring function is constructed. The final result is selected from the candidate set that satisfies the safety constraints: After determining the optimal higher-order parity phase / amplitude correction parameters for the safety scoring function, these parameters are substituted into the higher-order parity phase / amplitude joint correction model to obtain the final corrected two-dimensional complex k-space, denoted as . A two-dimensional discrete inverse Fourier transform is performed on the finally corrected two-dimensional complex k-space to obtain the final complex reconstructed image: Where represents the two-dimensional discrete inverse Fourier transform, M and N represent the number of sampling points in the phase encoding direction and readout direction, respectively, x and y represent the spatial location index in the reconstructed image, and j represents the imaginary unit.

10. An ultra-low field MRI EPI Nyquist artifact elimination system, characterized in that, include: Module 1: Preprocessing for abnormal noise and electromagnetic interference to perform center protection on two-dimensional complex EPI k-space data; The second module is used to establish a high-order odd-even phase / amplitude joint error model for ultra-low field EPI based on the two-dimensional complex EPI k-space data preprocessed with abnormal noise and electromagnetic interference. The third module is used to construct a complex consistency evaluation index for the odd-even k-space for high-order odd-even phase / amplitude joint correction models. The fourth module is used to construct a multi-objective security optimization model based on the parity k-space complex number consistency evaluation index, and to solve for the compromise optimal high-order parity phase / amplitude correction parameters. The fifth module is used to perform Hankel structure low-rank joint iteration on the high-order parity phase / amplitude joint error model for ultra-low field EPI corresponding to the compromise optimal high-order parity phase / amplitude correction parameters in order to suppress residual structured artifacts.

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