A Guaranteed Convergence Analysis for the Projected Fast Iterative Soft-Thresholding Algorithm in Parallel MRI

TL;DR

This paper establishes a guaranteed convergence criterion for the parallel MRI pFISTA algorithm, providing practical step size recommendations that significantly accelerate sparse image reconstruction.

Contribution

It extends the convergence analysis of pFISTA to parallel MRI models SENSE and SPIRiT, offering reliable step size guidelines for faster reconstructions.

Findings

Guaranteed convergence criterion for parallel MRI pFISTA.

Recommended step sizes improve reconstruction speed by over five times.

Validated convergence and efficiency through in vivo brain image experiments.

Abstract

The boom of non-uniform sampling and compressed sensing techniques dramatically alleviates the lengthy data acquisition problem of magnetic resonance imaging. Sparse reconstruction, thanks to its fast computation and promising performance, has attracted researchers to put numerous efforts on it and has been adopted in commercial scanners. To perform sparse reconstruction, choosing a proper algorithm is essential in providing satisfying results and saving time in tuning parameters. The pFISTA, a simple and efficient algorithm for sparse reconstruction, has been successfully extended to parallel imaging. However, its convergence criterion is still an open question. And the existing convergence criterion of single-coil pFISTA cannot be applied to the parallel imaging pFISTA, which, therefore, imposes confusions and difficulties on users about determining the only parameter - step size. In this work, we provide the guaranteed convergence analysis of the parallel imaging version pFISTA to solve the two well-known parallel imaging reconstruction models, SENSE and SPIRiT. Along with the convergence analysis, we provide recommended step size values for SENSE and SPIRiT reconstructions to obtain fast and promising reconstructions. Experiments on in vivo brain images demonstrate the validity of the convergence criterion. Besides, experimental results show that compared to using backtracking and power iteration to determine the step size, our recommended step size achieves more than five times acceleration in reconstruction time in most tested cases.