Eigen-vector Coil Sensitivity Map Estimation
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Solution Overview
Problem
Current methods for estimating coil sensitivity maps in MRI are inefficient, particularly when dealing with dynamic objects, as they require high computation costs and are restricted to explicit reconstructions, with unclear optimization criteria and lacking detailed mathematical derivations.
Innovation Solution
The eigenvector approach constructs a matrix from coil calibration data, using sliding blocks to derive a generalized eigenvalue system, reducing computational and storage costs by employing Hermitian eigenvalue systems and equivalent representations, and optimizing coil sensitivity maps through correlation maximization.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If joint estimation approaches are used to compensate for object motion, then measurement precision is improved, but computation cost increases significantly
Solution Approach 1:
The patent divides the coil sensitivity estimation problem into independent spatial location sub-problems. At each spatial location, the estimation is performed separately using local calibration data, avoiding the need for global joint estimation across the entire image volume. This segmentation reduces computational complexity while maintaining accuracy.
Solution Approach 2:
The patent extracts and utilizes only the necessary calibration data from the center of k-space, separating the essential information needed for sensitivity estimation from the rest of the data. This extraction approach focuses computational resources on the most relevant data portions, reducing overall computation cost.
2Adaptability or versatility
If explicit reconstruction methods are used, then coil sensitivity maps can be directly obtained, but the method is restricted and less versatile
Solution Approach 1:
The patent introduces an intermediary eigenvalue decomposition step that bridges implicit and explicit reconstruction approaches. By computing coil sensitivity maps as eigenvectors of a correlation matrix, the method provides a reliable explicit solution while maintaining compatibility with various reconstruction frameworks, thus improving versatility without sacrificing reliability.
3Measurement precision
If large matrices are computed for eigenvector approach, then coil sensitivity maps can be obtained, but storage costs and computation burden increase
Solution Approach 1:
The patent extracts only the essential eigenvalue and eigenvector information needed for coil sensitivity estimation, rather than computing and storing complete large matrices. By focusing on the dominant eigenvectors corresponding to largest eigenvalues, the method achieves accurate sensitivity maps with reduced storage requirements.
Solution Approach 2:
The computation is segmented into smaller operations performed at each spatial location independently. Instead of handling one large global matrix, the method processes local correlation matrices of manageable size, reducing both storage needs and computational burden while maintaining overall accuracy.
Data Source
AI summary
A method for estimating a coil sensitivity map for a magnetic resonance (MR) image includes providing a matrix A of sliding blocks of a 3D image of coil calibration data, calculating a left singular matrix V∥ from a singular value decomposition of A corresponding to τ leading singular values, calculating P=V∥V∥H, calculating a matrix that is an inverse Fourier transform of a zero-padded matrix P, and solving MHcr=(Sr)Hcr for cr, where cr is a vector of coil sensitivity maps for all coils at spatial location r, andM=((11…100…0………00…0)(00…011…1………00…0)…(00…000…0………11…1)).