2013 | OriginalPaper | Chapter
B-SMART: Bregman-Based First-Order Algorithms for Non-negative Compressed Sensing Problems
Authors : Stefania Petra, Christoph Schnörr, Florian Becker, Frank Lenzen
Published in: Scale Space and Variational Methods in Computer Vision
Publisher: Springer Berlin Heidelberg
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We introduce and study Bregman functions as objectives for non-negative sparse compressed sensing problems together with a related first-order iterative scheme employing non-quadratic proximal terms. This scheme yields closed-form multiplicative updates and handles constraints implicitly. Its analysis does not rely on global Lipschitz continuity in contrast to established state-of-the-art gradient-based methods, hence it is attractive for dealing with very large systems. Convergence and a
O
(
k
− 1
) rate are proved. We also introduce an iterative two-step extension of the update scheme that accelerates convergence. Comparative numerical experiments for non-negativity and box constraints provide evidence for a
O
(
k
− 2
) rate and reveal competitive and also superior performance.