Sparsity Constrained Estimation in Image Processing and Computer Vision

Over the past decade, sparsity has emerged as a dominant theme in signal processing and big data applications. In this chapter, we formulate and solve new flavors of sparsity-constrained optimization problems built on the family of spike-and-slab priors. First, we develop an efficient Iterative Convex Refinement solution to the hard non-convex problem of Bayesian signal recovery under sparsity-inducing spike-and-slab priors. We also offer a Bayesian perspective on sparse representation-based classification via the introduction of class-specific priors. This formulation represents a consummation of ideas developed for model-based compressive sensing into a general framework for sparse model-based classification.