Accelerating Convergence of Proximal Methods for Compressed Sensing using Polynomials with Application to MRI

Résumé : This work aims to accelerate the convergence of iterative proximal methods when applied to linear inverse problems that arise in compressed sensing applications by designing a preconditioner using polynomials. By leveraging polynomials, the preconditioner targets the eigenvalue spectrum of the normal operator derived from the linear measurement operator in a manner that does not assume any explicit structure, and can thus be applied various applications of interest. The efficacy of the preconditioner is validated on four varied MRI applications, where it seen to achieve faster convergence while achieving similar reconstruction quality.