Learning Dictionaries with Bounded Self-Coherence
Autor: | Sigg, Christian D., Dikk, Tomas, Buhmann, Joachim M. |
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Rok vydání: | 2012 |
Předmět: | |
Druh dokumentu: | Working Paper |
DOI: | 10.1109/LSP.2012.2223757 |
Popis: | Sparse coding in learned dictionaries has been established as a successful approach for signal denoising, source separation and solving inverse problems in general. A dictionary learning method adapts an initial dictionary to a particular signal class by iteratively computing an approximate factorization of a training data matrix into a dictionary and a sparse coding matrix. The learned dictionary is characterized by two properties: the coherence of the dictionary to observations of the signal class, and the self-coherence of the dictionary atoms. A high coherence to the signal class enables the sparse coding of signal observations with a small approximation error, while a low self-coherence of the atoms guarantees atom recovery and a more rapid residual error decay rate for the sparse coding algorithm. The two goals of high signal coherence and low self-coherence are typically in conflict, therefore one seeks a trade-off between them, depending on the application. We present a dictionary learning method with an effective control over the self-coherence of the trained dictionary, enabling a trade-off between maximizing the sparsity of codings and approximating an equiangular tight frame. Comment: 4 pages, 2 figures; IEEE Signal Processing Letters, vol. 19, no. 12, 2012 |
Databáze: | arXiv |
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