A convergence analysis for projected fast iterative soft-thresholding algorithm under radial sampling MRI

Abstract

Radial sampling is a fast magnetic resonance imaging technique. Further imaging acceleration can be achieved with undersampling but how to reconstruct a clear image with fast algorithm is still challenging. Previous work has shown the advantage of removing undersampling image artifacts using the tight-frame sparse reconstruction model. This model was further solved with a projected fast iterative soft-thresholding algorithm (pFISTA). However, the convergence of this algorithm under radial sampling has not been clearly set up. In this work, the authors derived a theoretical convergence condition for this algorithm. This condition was approximated by estimating the maximal eigenvalue of reconstruction operators through the power iteration. Based on the condition, an optimal step size was further suggested to allow the fastest convergence. Verifications were made on the prospective in vivo data of static brain imaging and dynamic contrast-enhanced liver imaging, demonstrating that the recommended parameter allowed fast convergence in radial MRI.