CG Variants for General-Form Regularization with an Application to Low-Field MRI

Abstract

In an earlier paper, we generalized the CGME (Conjugate Gradient Minimal Error) algorithm to the ℓ₂-regularized weighted least-squares problem. Here, we use this Generalized CGME method to reconstruct images from actual signals measured using a low-field MRI scanner. We analyze the convergence of both GCGME and the classical Generalized Conjugate Gradient Least Squares (GCGLS) method for the simple case when a Laplace operator is used as a regularizer and indicate when GCGME is to be preferred in terms of convergence speed. We also consider a more complicated ℓ₁-penalty in a compressed sensing framework.