CG Variants for General-Form Regularization with an Application to Low-Field MRI
Merel L. de Leeuw den Bouter (TU Delft - Numerical Analysis)
Martin B. Gijzen (TU Delft - Numerical Analysis)
R.F. Remis (TU Delft - Signal Processing Systems)
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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.