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

This paper considers the exact recovery of $k$-sparse signals in thenoiseless setting and support recovery in the noisy case when some priorinformation on the support of the signals is available. This prior supportconsists of two parts. One part is a subset of the true support and anotherpart is outside of the true support. For $k$-sparse signals $\mathbf{x}$ withthe prior support which is composed of $g$ true indices and $b$ wrong indices,we show that if the restricted isometry constant (RIC) $\delta_{k+b+1}$ of thesensing matrix $\mathbf{A}$ satisfies \begin{eqnarray*}\delta_{k+b+1}<\frac{1}{\sqrt{k-g+1}}, \end{eqnarray*} then orthogonal matchingpursuit (OMP) algorithm can perfectly recover the signals $\mathbf{x}$ from$\mathbf{y}=\mathbf{Ax}$ in $k-g$ iterations. Moreover, we show the abovesufficient condition on the RIC is sharp. In the noisy case, we achieve theexact recovery of the remainder support (the part of the true support outsideof the prior support) for the $k$-sparse signals $\mathbf{x}$ from$\mathbf{y}=\mathbf{Ax}+\mathbf{v}$ under appropriate conditions. For theremainder support recovery, we also obtain a necessary condition based on theminimum magnitude of partial nonzero elements of the signals $\mathbf{x}$.

A sharp recovery condition for sparse signals with partial support information via orthogonal matching pursuit