English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Learning optimal dictionaries for sparse coding has exposed characteristicsparse features of many natural signals. However, universal guarantees of thestability of such features in the presence of noise are lacking. Here, weprovide very general conditions guaranteeing when dictionaries yielding thesparsest encodings are unique and stable with respect to measurement ormodeling error. We demonstrate that some or all original dictionary elementsare recoverable from noisy data even if the dictionary fails to satisfy thespark condition, its size is overestimated, or only a polynomial number ofdistinct sparse supports appear in the data. Importantly, we derive theseguarantees without requiring any constraints on the recovered dictionary beyonda natural upper bound on its size. Our results also yield an effectiveprocedure sufficient to affirm if a proposed solution to the dictionarylearning problem is unique within bounds commensurate with the noise. Wesuggest applications to data analysis, engineering, and neuroscience and closewith some remaining challenges left open by our work.

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