CHAPTER 12 Sparsity in Redundant Dictionaries

Complex signals such as audio recordings or images often include structures that are not well represented by few vectors in any single basis. Indeed, small dictionaries such as bases have a limited capability of sparse expression. Natural languages build sparsity from large redundant dictionaries of words, which evolve in time. Biological perception systems also seem to incorporate robust and redundant representations that generate sparse encodings at later stages. Larger dictionaries incorporating more patterns can increase sparsity and thus improve applications to compression, denoising, inverse problems, and pattern recognition.

Finding the set of M dictionary vectors that approximate a signal ...

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