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/

Zendy Plus

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

Zendy Tools

Zendy Open

We consider an important problem in signal processing, which consists infinding the sparsest solution of a linear system $\Phi x=b$. This problem hasapplications in several areas, but is NP-hard in general. Usually analternative convex problem is considered, based on minimizing the (weighted)$\ell_{1}$ norm. For this alternative to be useful, weights should be chosen asto obtain a solution of the original NP-hard problem. A well known algorithmfor this is the Re-Weighted $\ell_{1}$, proposed by Cand\`es, Wakin and Boyd.In this article we introduce a new methodology for updating the weights of aRe-Weighted $\ell_{1}$ algorithm, based on identifying these weights asLagrange multipliers. This is then translated into an algorithm withperformance comparable to the usual methodology, but allowing an interpretationof the weights as Lagrange multipliers. The methodology may also be used for anoisy linear system, obtaining in this case a Re-Weighted LASSO algorithm, witha promising performance according to the experimental results.

Re-Weighted $\ell_1$ Algorithms within the Lagrange Duality Framework: Bringing Interpretability to Weights