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

As a natural extension of compressive sensing and the requirement of somepractical problems, Phaseless Compressed Sensing (PCS) has been introduced andstudied recently. Many theoretical results have been obtained for PCS with theaid of its convex relaxation. Motivated by successful applications of nonconvexrelaxed methods for solving compressive sensing, in this paper, we try toinvestigate PCS via its nonconvex relaxation. Specifically, we relax PCS in thereal context by the corresponding $\ell_p$-minimization with $p\in (0,1)$. Weshow that there exists a constant $p^\ast\in (0,1]$ such that for any fixed$p\in(0, p^\ast)$, every optimal solution to the $\ell_p$-minimization alsosolves the concerned problem; and derive an expression of such a constant$p^\ast$ by making use of the known data and the sparsity level of theconcerned problem. These provide a theoretical basis for solving this class ofproblems via the corresponding $\ell_p$-minimization.

A Theoretical Perspective of Solving Phaseless Compressed Sensing via Its Nonconvex Relaxation