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    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.