Discrete Shearlets as a Sparsifying Transform in Low-Rank Plus Sparse Decomposition for Undersampled (k, t)-Space MR...

Area of Science:

• Medical Imaging
• Signal Processing
• Biomedical Engineering

Background:

• Magnetic resonance imaging (MRI) requires robust methods for analyzing complex dynamic data.
• Traditional sparsifying transforms face challenges in accurately representing discontinuities and edges in MRI.
• Low-rank plus sparse (L+S) decomposition is a promising technique for separating signal components.

Purpose of the Study:

• To evaluate discrete shearlets as a sparsifying transform within an L+S decomposition framework for undersampled MRI data.
• To compare the performance of discrete shearlets against other sparsifying transforms, specifically in dynamic contrast-enhanced (DCE) and small bowel imaging.
• To assess the accuracy of motion estimation and the isolation of physiological signals like bowel motility.

Main Methods:

• Implementation of an L+S decomposition algorithm utilizing discrete shearlets.
• Evaluation on simulated dynamic contrast-enhanced (DCE) and small bowel MRI datasets.
• Comparison of reconstruction performance against the k-t FOCUSS algorithm.
• Analysis of motion estimation accuracy and motility metrics derived from the sparse component.

Main Results:

• Discrete shearlets successfully separated low-rank (background, periodic motion) from sparse components (enhancement, bowel motility) in both DCE and small bowel data.
• Motion estimated from the low-rank component of DCE data showed higher fidelity to ground truth deformations compared to other methods.
• Bowel motility metrics derived from the sparse component of free-breathing data were comparable to breath-holding data, even with significant undersampling.
• The discrete shearlet-based L+S decomposition demonstrated robust performance in isolating rapid/random bowel motility.

Conclusions:

• Discrete shearlets are a highly effective sparsifying transform for L+S decomposition in undersampled MRI.
• The proposed method accurately separates physiological motion and enhancement, improving quantitative analysis.
• This approach holds significant potential for improving the quality and interpretability of dynamic MRI studies, particularly for gastrointestinal applications.