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The generalized minimax concave (GMC) penalty is a nonconvex sparse regularizer which can preserve the overall-convexity of the sparse least squares problem. In this paper, we study the solution path of a special but important instance of the GMC model termed the scaled GMC (sGMC) model. We show that despite the nonconvexity of the regularizer, there exists a solution path of the sGMC model which is piecewise linear as a function of the regularization parameter, and we propose an efficient algorithm for computing a solution path of this type.

Compressed sensing aims to retrieve sparse signals from very few samples. It relies on dedicated reconstruction algorithms and well-chosen measurement matrices. In combination with network coding, which operates traditionally over finite fields, it leverages the benefits of both techniques. However, compressed sensing has been primarily investigated over the real field. F2OMP is one of the few recovery algorithms to reconstruct signals over finite fields. However, its use in practical cases is limited since its performance depends mainly on binary matrices for signal recovery.

In recent years approximate message passing algorithms have gained a lot of attention and different versions have been proposed for coping with various system models. This paper focuses on vector approximate message passing (VAMP) for generalized linear models. While this algorithm is originally derived from a message passing point of view, we will review it from an estimation theory perspective and afterwards adapt it for a quantized compressed sensing application. Finally, numerical results are presented to evaluate the performance of the algorithm.

Most existing work in designing sensing matrices for compressive recovery is based on optimizing some quality factor, such as mutual coherence, average coherence or the restricted isometry constant (RIC), of the sensing matrix. In this paper, we report anomalous results that show that such a design is not always guaranteed to improve reconstruction results.