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Learning Dictionaries With Bounded Self-Coherence

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3 Author(s)
Sigg, C.D. ; Swiss Fed. Office of Meteorol. & Climatology (MeteoSwiss), Zurich, Switzerland ; Dikk, T. ; Buhmann, J.M.

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 equi-angular tight frame.

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Signal Processing Letters, IEEE  (Volume:19 ,  Issue: 12 )