EPIGRAPHICALLY-RELAXED LINEARLY-INVOLVED GENERALIZED MOREAU-ENHANCED MODEL FOR LAYERED MIXED NORM REGULARIZATION

This paper proposes an epigraphically-relaxed linearly-involved generalized Moreau-enhanced (ER-LiGME) model for layered mixed norm regularization. Group sparse and low-rank (GSpLr)-aware modeling using l1/nuclear-norm-based layered mixed norms has succeeded in precise high dimensional signal recovery, e.g., images and videos. Our previous work significantly expands the potential of the GSpLr-aware modeling by epigraphical relaxation (ER). It enables us to handle a (even non-proximable) deeply-layered mixed norm minimization by decoupling it into a norm and multiple epigraphical constraints (if each proximity operator is available). One problem with typical SpLr modeling is that it suffers from the underestimation effect due to the ℓ1 and nuclear norm regularization. To circumvent this problem, LiGME penalty functions, which modify conventional sparsity and low-rankness promoting convex functions to nonconvex ones while keeping overall convexity, have been proposed conventionally. In this work, we integrate the ER technique with the LiGME model to realize deeply-layered (possibly non-proximable) mixed norm regularization and show its effectiveness in denoising and compressed sensing reconstruction.