Local Regularization for EPI Geometric Distortion Correction
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Solution Overview
Problem
Echo-planar imaging (EPI) in MR imaging suffers from geometric distortion due to inhomogeneity in the main magnet (B0) magnetic field and low bandwidth in the phase-encoding direction, leading to noise-sensitive inverse method results with prominent noise 'hot spots'.
Innovation Solution
Employ a locally-regularized pseudoinverse distortion matrix, using B0 field maps and local identity matrices to correct geometric distortion directly on complex image data, reducing noise amplification and distortion.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If the inverse method is used to correct geometric distortion, then distortion correction is achieved, but noise hot spots are amplified
Solution Approach 1:
The patent applies local quality by using a locally-regularized pseudoinverse distortion matrix that incorporates local identity matrices. This allows different regions of the image to be corrected with different levels of regularization, preserving distortion correction accuracy in regions where it is most needed while suppressing noise amplification in regions where the distortion is less severe or where noise suppression is prioritized.
Solution Approach 2:
The patent changes the parameter of the distortion matrix by using a pseudoinverse rather than a true inverse, and by introducing regularization parameters through local identity matrices. This parameter change transforms the correction process from a noise-amplifying operation to a noise-suppressing operation while maintaining distortion correction effectiveness.
2Manufacturing precision
If the inverse distortion matrix is used, then geometric distortion is corrected, but noise sensitivity increases
Solution Approach 1:
The patent applies beforehand cushioning by incorporating regularization terms into the distortion matrix inversion process. The local identity matrices act as a pre-established cushion that prevents excessive noise amplification before the correction process can amplify noise, thereby stabilizing the correction against noise sensitivity.
Solution Approach 2:
The patent uses an intermediary approach by introducing a pseudoinverse distortion matrix that mediates between the distorted image and the true image. This pseudoinverse, regularized by local identity matrices, acts as a buffer that reduces the direct impact of noise while still achieving effective distortion correction.
3Manufacturing precision
If standard inverse method is applied, then distortion is removed, but image quality deteriorates due to noise hot spots
Solution Approach 1:
The patent applies local quality by differentiating the correction approach across different image regions. The locally-regularized pseudoinverse distortion matrix allows aggressive correction in regions with severe distortion while applying milder correction in regions where noise suppression is more important, thereby maintaining overall image quality.
Solution Approach 2:
The patent uses a composite approach by combining the distortion matrix with local identity matrices to create a regularized pseudoinverse. This composite structure integrates the distortion correction capability with noise suppression properties, achieving both distortion removal and image quality preservation.
Data Source
AI summary
Systems and methods include determination of a field map representing inhomogeneity of a main magnetic field of a magnetic resonance scanner within a subject, determination of a pixel shift map based on the field map, operation of the magnetic resonance scanner to generate an image of the subject, determination of a portion of the pixel shift map corresponding to a phase-encoding line of the image, determination of a distortion matrix corresponding to the portion of the pixel shift map, determination of a locally-regularized pseudoinverse distortion matrix based on the distortion matrix, and correction of the line of the image based on the locally-regularized pseudoinverse distortion matrix.