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

In the context of sparse recovery, it is known that most of existingregularizers such as $\ell_1$ suffer from some bias incurred by some leadingentries (in magnitude) of the associated vector. To neutralize this bias, wepropose a class of models with partial regularizers for recovering a sparsesolution of a linear system. We show that every local minimizer of these modelsis sufficiently sparse or the magnitude of all its nonzero entries is above auniform constant depending only on the data of the linear system. Moreover, fora class of partial regularizers, any global minimizer of these models is asparsest solution to the linear system. We also establish some sufficientconditions for local or global recovery of the sparsest solution to the linearsystem, among which one of the conditions is weaker than the best knownrestricted isometry property (RIP) condition for sparse recovery by $\ell_1$.In addition, a first-order feasible augmented Lagrangian (FAL) method isproposed for solving these models, in which each subproblem is solved by anonmonotone proximal gradient (NPG) method. Despite the complication of thepartial regularizers, we show that each proximal subproblem in NPG can besolved as a certain number of one-dimensional optimization problems, whichusually have a closed-form solution. We also show that any accumulation pointof the sequence generated by FAL is a first-order stationary point of themodels. Numerical results on compressed sensing and sparse logistic regressiondemonstrate that the proposed models substantially outperform the widely usedones in the literature in terms of solution quality.

Sparse Recovery via Partial Regularization: Models, Theory and Algorithms