MRI Image Reconstruction Using K-Space Weighting and Block-Toeplitz Matrices
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Solution Overview
Problem
Current MRI image reconstruction methods from under-sampled k-space data face challenges of extended computational time and high memory usage, leading to reduced image quality and increased patient discomfort due to longer scan times.
Innovation Solution
The method involves iteratively reconstructing image-space data using a non-linear conjugate gradient process with a k-space weighting matrix and a block-Toeplitz matrix, which accelerates the solution process and reduces computational time and memory usage by applying a diagonal weighting matrix to the data fidelity term, enabling near-optimal convergence and improved image quality.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If data acquisition time is increased to improve image quality, then image quality improves, but patient discomfort increases and scan time is extended
Solution Approach 1:
The patent applies partial action by intentionally under-sampling k-space data (acquiring fewer data points than the full Nyquist rate would require). This reduces scan time while iterative reconstruction algorithms compensate for the missing data to produce acceptable quality images, resolving the contradiction between scan time and image quality
Solution Approach 2:
The patent changes the sampling parameters in k-space by using non-uniform or reduced sampling patterns instead of complete uniform sampling. This parameter change enables faster acquisition while iterative reconstruction methods adjust to produce quality images from the modified data set
2Loss of time
If k-space data is under-sampled to reduce scan time, then scan time is reduced, but signal-to-noise ratio decreases and image degradation occurs
Solution Approach 1:
The patent employs iterative reconstruction algorithms that use feedback loops to progressively refine the image reconstruction. Each iteration uses the previous result to guide further optimization, allowing the system to recover image quality from under-sampled data by continuously adjusting the reconstruction based on the sampling pattern and observed data
Solution Approach 2:
The patent applies preliminary action by pre-calculating or pre-planning the under-sampling pattern and density compensation functions before actual image reconstruction. This preliminary preparation enables the iterative algorithm to work more efficiently and recover image quality without requiring complete k-space sampling
3Manufacturing precision
If various techniques are used to enhance image quality from under-sampled data, then image quality improves, but computational time and memory usage increase
Solution Approach 1:
The patent segments the computational task by separating the reconstruction process into distinct components: forward modeling of the under-sampling pattern, application of density compensation functions, and iterative optimization steps. This segmentation allows each component to be optimized independently and processed more efficiently
Solution Approach 2:
The patent changes computational parameters by using efficient matrix representations and optimization algorithms that reduce the computational complexity of iterative reconstruction. By adjusting convergence criteria, regularization parameters, and using appropriate basis functions, the system achieves good image quality with reduced computational burden
Data Source
AI summary
A set of image-space data is reconstructed from a set of k-space data. The set of image-space data is generated by minimizing a cost functional by an iterative non-linear conjugate gradient process. The iterative process may be accelerated by introducing k-space weighting to the cost functional. With proper choice of k-space weighting, a block-Toeplitz matrix is generated which permits use of Fast Fourier Transform techniques. An image is rendered from the set of image-space data.