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

In compressed sensing the goal is to recover a signal from as few as possiblenoisy, linear measurements. The general assumption is that the signal has onlya few non-zero entries. The recovery can be performed by multiple differentdecoders, however most of them rely on some tuning. Given an estimate for thenoise level a common convex approach to recover the signal is basis pursuitdenoising. If the measurement matrix has the robust null space property withrespect to the $\ell_2$-norm, basis pursuit denoising obeys stable and robustrecovery guarantees. In the case of unknown noise levels, nonnegative leastsquares recovers non-negative signals if the measurement matrix fulfills anadditional property (sometimes called the $M^+$-criterion). However, if themeasurement matrix is the biadjacency matrix of a random left regular bipartitegraph it obeys with a high probability the null space property with respect tothe $\ell_1$-norm with optimal parameters. Therefore, we discuss non-negativeleast absolute deviation (NNLAD). For these measurement matrices, we prove auniform, stable and robust recovery guarantee without the need for tuning. Suchguarantees are important, since binary expander matrices are sparse and thusallow for fast sketching and recovery. We will further present a method tosolve the NNLAD numerically and show that this is comparable to state of theart methods. Lastly, we explain how the NNLAD can be used for viral detectionin the recent COVID-19 crisis.

Efficient Tuning-Free $\ell_1$-Regression of Nonnegative Compressible Signals