Polynomial Preconditioners for Regularized Linear Inverse Problems

SIAM Journal on Imaging Sciences, Volume 17, Issue 1, Page 116-146, March 2024.
Abstract. This work aims to accelerate the convergence of proximal gradient methods used to solve regularized linear inverse problems. This is achieved by designing a polynomial-based preconditioner that targets the eigenvalue spectrum of the normal operator derived from the linear operator. The preconditioner does not assume any explicit structure on the linear function and thus can be deployed in diverse applications of interest. The efficacy of the preconditioner is validated on three different Magnetic Resonance Imaging applications, where it is seen to achieve faster iterative convergence (around [math] faster, depending on the application of interest) while achieving similar reconstruction quality.