Bregman iteration was introduced to TV restoration a few years ago and improved the performance significantly. Later it was found that this same idea gave what appeared to be state-of-the-art fast algorithms for L1 based optimization arising in compressive sensing and elsewhere. Not only has this idea been around since 1967, but every new variant recently invented seems to be closely related and indeed often a special case of a known techniques. So why is it so important now? The answer seems to be in the nature of L1 itself. Errors cancel beautifully. This is joint work with Wotao Yin and other collaborators.
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