Iterative Phase Reconstruction for Half Fourier MRI
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Solution Overview
Problem
Existing MRI methods, such as half Fourier imaging, face significant reconstruction errors due to off-resonance effects and technical imperfections, especially in regions with rapid phase variation, as they directly replace the phase image with estimates, leading to inaccurate phase reconstruction and poor image quality.
Innovation Solution
A data acquisition method for 3D MRI that undersamples the k-space in specific regions, using symmetric and asymmetric parts with varying sampling densities, and an image reconstruction method that iteratively minimizes a cost function with a phase constraint term to improve phase estimation accuracy, employing nonlinear conjugate gradient methods and sparsifying transforms.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If half Fourier imaging is used to shorten measurement time, then productivity is improved, but measurement precision deteriorates due to reconstruction errors in regions with rapid phase variation
Solution Approach 1:
The patent applies iterative feedback by using the reconstructed image from initially acquired data to estimate phase, then using this phase estimate to synthesize missing k-space data, reconstructing again, and repeating the process until convergence. This feedback loop continuously improves phase reconstruction accuracy while maintaining the time savings of half-Fourier imaging.
Solution Approach 2:
The patent performs preliminary phase estimation from the initially acquired k-space data before synthesizing the missing data. This preliminary action provides an initial phase map that guides the subsequent data synthesis and iterative refinement process, enabling accurate phase reconstruction without acquiring all k-space data upfront.
2Device complexity
If direct phase replacement is used to synthesize unacquired data, then device complexity is reduced, but measurement precision deteriorates due to inaccurate phase estimation in regions with rapid phase variation
Solution Approach 1:
Instead of direct single-step phase replacement, the patent implements iterative feedback where the reconstructed image is continuously refined by re-estimating phase and re-synthesizing missing data. This feedback mechanism progressively improves phase estimation accuracy in regions with rapid phase variation while maintaining algorithmic simplicity at each iteration step.
Solution Approach 2:
The patent transforms the static direct replacement approach into a dynamic iterative process. The phase estimation and data synthesis operations are performed repeatedly with updating inputs, allowing the system to adapt and converge to accurate phase values even in complex regions with rapid phase variation.
3Ease of operation
If conventional phase correction methods are used, then ease of operation is improved, but reliability deteriorates due to destruction of conjugate symmetry and reconstruction errors
Solution Approach 1:
The patent maintains ease of operation through automated iterative feedback that preserves conjugate symmetry at each iteration step. The method automatically refines phase estimates and re-synthesizes data while maintaining the fundamental symmetry properties of k-space, ensuring reliable reconstruction without manual intervention or complex manual corrections.
Solution Approach 2:
The patent applies prior cushioning by iteratively refining the phase estimation before final image reconstruction. Each iteration预先 (in advance) corrects phase errors and preserves conjugate symmetry, cushioning against the accumulation of reconstruction errors that would otherwise degrade image quality and reliability.
Data Source
Figure 1a~3d
AI summary
A method for accelerating magnetic resonance imaging, comprising: In 3D MRI, the k-space in the phase encoding plane is divided into two symmetric parts and three asymmetric parts. Different sampling densities are applied in different parts. Images are reconstructed by iteratively minimizing a cost function when random sampling is applied in each part. A phase constraint term is added into the cost function to improve the quality of the reconstruction by exploiting the conjugate symmetry of k-space.