On the uniqueness and stability of dictionaries for sparse representation of noisy signals

• DOI: 10.48550/arxiv.1606.06997
• Publication Date: 2016-01-01
• Authors: Charles J. Garfinkle; Christopher J. Hi...
• Keywords: SPARK (programming language); Neural coding; Dictionary Learning; Noisy data; Representation

Learning optimal dictionaries for sparse coding has exposed characteristic features of many natural signals. However, universal guarantees the stability such in presence noise are lacking. Here, we provide very general conditions guaranteeing when yielding sparsest encodings unique and stable with respect to measurement or modeling error. We demonstrate that some all original dictionary elements recoverable from noisy data even if fails satisfy spark condition, its size is overestimated, only a polynomial number distinct supports appear data. Importantly, derive these without requiring any constraints on recovered beyond upper bound size. Our results also yield an effective procedure sufficient affirm proposed solution learning problem within bounds commensurate noise. suggest applications analysis, engineering, neuroscience close remaining challenges left open by our work.