期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 68, 期 -, 页码 519-528出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2020.2964239
关键词
Sparse representation; convolutional sparse coding; parallel proximal algorithm; convex optimization
资金
- European Research Council under EUs 7th Framework Program, ERC [320649]
- Israel Science Foundation (ISF) [1770/14]
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, patch-based, 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 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.
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