Smooth Local Low-Rank (LLR) Reconstruction Software v1.0

https://github.com/ralobos/smooth_LLR

Overview

This MATLAB software reproduces the reconstruction experiments presented in [1]. It performs reconstruction of retrospectively undersampled dynamic MRI k-space data using a smooth Huber-based local low-rank regularizer. The key innovation is the use of smooth regularizers that enable standard optimization algorithms (such as nonlinear conjugate gradient) to solve the inverse problem efficiently.

Contents

Main Scripts

• example_smooth_LLR.m - Main reconstruction script for dynamic MRI undersampled data
• example_smooth_LLR_fast_step_size.m - Reconstruction using a heuristic fast step-size selection strategy

References

[1] R. A. Lobos, J. Salazar Cavazos, R. R. Nadakuditi, J. A. Fessler.
Smooth optimization using global and local low-rank regularizers
arXiv:2505.06073, SIAM Journal on Imaging Sciences, (In press).