Improved Computational Efficiency of Locally Low Rank MRI Reconstruction Using Iterative Random Patch Adjustments

Area of Science:

• Medical Imaging
• Image Reconstruction
• Regularization Techniques

Background:

• Locally low-rank (LLR) regularization is effective for MRI reconstruction, leveraging correlations within image patches.
• Conventional LLR methods use overlapping patches, leading to high computational costs and limiting practical MRI applications.

Purpose of the Study:

• To present and analyze an alternative LLR regularization formulation for MRI reconstruction.
• To introduce a novel LLR method with iterative random patch adjustments (LLR-IRPA) to reduce computational load.
• To provide a mathematical framework and justification for the LLR-IRPA approach.

Main Methods:

• Developed LLR regularization with iterative random patch adjustments (LLR-IRPA).
• Shifted a single set of non-overlapping patches iteratively to achieve shift-invariance and avoid artifacts.
• Compared LLR-IRPA against a state-of-the-art LLR algorithm using overlapping patches.

Main Results:

• LLR-IRPA demonstrated comparable reconstruction results to overlapping patch methods.
• The LLR-IRPA approach significantly reduced computational load.
• Theoretical results confirmed the effective shift invariance of LLR-IRPA.
• Reconstruction examples were shown for undersampled acquisitions and T1 parameter mapping.

Conclusions:

• LLR-IRPA offers a computationally efficient alternative for MRI reconstruction.
• The method achieves effective shift invariance without the drawbacks of overlapping patches.
• LLR-IRPA shows promise for accelerated MRI and quantitative parameter mapping.