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

For a large class of random matrices $A$ with i.i.d. entries we show that the$\ell_1$-quotient property holds with probability exponentially close to 1. Incontrast to previous results, our analysis does not require concentration ofthe entrywise distributions. We provide a unified proof that recoverscorresponding previous results for (sub-)Gaussian and Weibull distributions.Our findings generalize known results on the geometry of random polytopes,providing lower bounds on the size of the largest Euclidean ball contained inthe centrally symmetric polytope spanned by the columns of $A$. At the sametime, our results establish robustness of noise-blind $\ell_1$-decoders forrecovering sparse vectors $x$ from underdetermined, noisy linear measurements$y = Ax + w$ under the weakest possible assumptions on the entrywisedistributions that allow for recovery with optimal sample complexity even inthe noiseless case. Our analysis predicts superior robustness behavior formeasurement matrices with super-Gaussian entries, which we confirm by numericalexperiments.

A Quotient Property for Matrices with Heavy-Tailed Entries and its Application to Noise-Blind Compressed Sensing