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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

In the past decade, sparse and low-rank recovery have drawn much attention inmany areas such as signal/image processing, statistics, bioinformatics andmachine learning. To achieve sparsity and/or low-rankness inducing, the$\ell_1$ norm and nuclear norm are of the most popular regularization penaltiesdue to their convexity. While the $\ell_1$ and nuclear norm are convenient asthe related convex optimization problems are usually tractable, it has beenshown in many applications that a nonconvex penalty can yield significantlybetter performance. In recent, nonconvex regularization based sparse andlow-rank recovery is of considerable interest and it in fact is a main driverof the recent progress in nonconvex and nonsmooth optimization. This papergives an overview of this topic in various fields in signal processing,statistics and machine learning, including compressive sensing (CS), sparseregression and variable selection, sparse signals separation, sparse principalcomponent analysis (PCA), large covariance and inverse covariance matricesestimation, matrix completion, and robust PCA. We present recent developmentsof nonconvex regularization based sparse and low-rank recovery in these fields,addressing the issues of penalty selection, applications and the convergence ofnonconvex algorithms. Code is available at https://github.com/FWen/ncreg.git.

A Survey on Nonconvex Regularization Based Sparse and Low-Rank Recovery in Signal Processing, Statistics, and Machine Learning