Recovering Sparse Signals With a Certain Family of Nonconvex Penalties and DC Programming

By Gilles Gasso, Alain Rakotomamonjy, Stéphane Canu. IEEE Transactions on Signal Processing, 2009

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Sparse Regularization via Convex Analysis (2017, unknown): “, [11], [13], [15], [16], [19], [25], [30], [31], [38], [39], [43], [47], [58], [64], [66].”
Combinatorial Penalties: Structure preserved by convex relaxations (2017, background): “For example, `α-quasi-norms [24, 14] or more generally penalties of the form Φ(w) = ∑d i=1 φ(|wi|), where φ is a monotone concave penalty [12, 8, 16] can be more advantageous than the `1-norm.”
A Generalized Iterated Shrinkage Algorithm for Non-convex Sparse Coding (2013, methodology): “Given x ( k ) , IRL1 [8, 21] updates x by solving the following problem using the existing (cid:2) 1 -minimization algorithms [1, 3, 41].”
Generalized Nonconvex Nonsmooth Low-Rank Minimization (2014, methodology): “A common method is DC (Difference of Convex functions) programming [14].”
A General Iterative Shrinkage and Thresholding Algorithm for Non-convex Regularized Optimization Problems (2013, methodology): “One commonly used approach to solve problem (1) is the Multi-Stage (MS) convex relaxation (or CCCP, or DC programming) (Zhang, 2010b; Yuille & Rangarajan, 2003; Gasso et al., 2009).”
Sparse Modeling for Image and Vision Processing (2014, background): “A natural way of dealing with such penalties when they appear in the objective function is to use an approach called DC-programming, where DC stands for “difference of convex” [see Gasso et al., 2009, for a review].”