A Convergence Analysis for Projected Fast Iterative Soft-thresholding Algorithm under Radial Sampling MRI

Radial sampling is a fast magnetic resonance imaging technique. The projected fast iterative soft-thresholding algorithm (pFISTA) has shown the advantage to solved tight frame sparse reconstruction model for removing undersampling image artifacts. 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 and an optimal step size was further suggested to allow the fastest convergence. Verifications were made in vivo data of static brain imaging and dynamic contrast-enhanced (DCE) liver imaging, demonstrating that the recommended parameter allowed fast convergence in radial MRI.