Variations on the Convolutional Sparse Coding Model 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 highdimensional 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   ell _1  ell _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.

Distributed compressed video sensing based on convolutional sparse coding This paper discusses a Distributed Compressed Video Sensing (DCVS) framework using Convolutional Sparse Coding (CSC). CSC is a technique to represent a signal as convolutions of filters and corresponding coefficients. Conventional block based DCVS methods divide a given video sequence into key and nonkey frames. The key frames are decoded independently like still images, and the nonkey frames use Side Information (SI) generated with previously decoded key frames. The sparse dictionaries of the nonkey frames are designed with the SIs. However, in CSC based methods, a nonkey frame can use the dictionary of the nearest key frame in the temporal domain since the dictionary filters, namely features, are robuster against motions than those of block based methods.