Variations on the CSC model

Abstract

Over the past decade, the celebrated sparse representation model has achieved impressive results in various signal and image processing tasks. A convolutional version of this model, termed convolutional sparse coding (CSC), has been recently reintroduced and extensively studied. CSC brings a natural remedy to the limitation of typical sparse enforcing approaches of handling global and high-dimensional signals by local, patchbased, processing. While the classic field of sparse representations has been able to cater for the diverse challenges of different signal processing tasks by considering a wide range of problem formulations, almost all available algorithms that deploy the CSC model consider the same 1 − 2 problem form. As we argue in this paper, this CSC pursuit formulation is also too restrictive as it fails to explicitly exploit some local characteristics of the signal. This work expands the range of formulations for the CSC model by proposing two convex alternatives that merge global norms with local penalties and constraints. The main contribution of this work is the derivation of efficient and provably converging algorithms to solve these new sparse coding formulations.

Rethinking the CSC Model for Natural Images

“…The first application we mention is cartoon-texture separation, where the goal is to blindly decompose an image into its texture and cartoon parts. Recent papers have achieved successful results by incorporating the CSC model [28,34]. Curiously, these algorithms model the cartoon image via the Total-Variation smoothness assumption, while using the CSC to model only the texture.…”

“…The CSC model has shown great success in several natural image processing tasks such as image separation, image fusion, and super-resolution, matching or outperforming local-based methods [26,28,[32][33][34]. Interestingly, one can find two common properties to all these success stories.…”