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 Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Sparse signal restoration is usually formulated as the minimization of a quadratic cost function |y-Ax ||22 where \mbi A is a dictionary and \mbi x is an unknown sparse vector. It is well-known that imposing an &#x2113;0 constraint leads to an NP-hard minimization problem. The convex relaxation approach has received considerable attention, where the &#x2113;0-norm is replaced by the &#x2113;1-norm. Among the many effective &#x2113;1 solvers, the homotopy algorithm minimizes ||y-Ax ||22+&#x03BB;||x||1 with respect to x for a continuum of &#x03BB;'s. It is inspired by the piecewise regularity of the &#x2113;1-regularization path, also referred to as the homotopy path. In this paper, we address the minimization problem ||y-Ax||22+&#x03BB;||x||0 for a continuum of &#x03BB;'s and propose two heuristic search algorithms for &#x2113;0-homotopy. Continuation Single Best Replacement is a forward-backward greedy strategy extending the Single Best Replacement algorithm, previously proposed for &#x2113;0-minimization at a given &#x03BB;. The adaptive search of the &#x03BB;-values is inspired by &#x2113;1-homotopy. &#x2113;0 Regularization Path Descent is a more complex algorithm exploiting the structural properties of the &#x2113;0-regularization path, which is piecewise constant with respect to &#x03BB;. Both algorithms are empirically evaluated for difficult inverse problems involving ill-conditioned dictionaries. Finally, we show that they can be easily coupled with usual methods of model order selection.

ieee transactions on signal processing

Homotopy Based Algorithms for <formula formulatype="inline"><tex Notation="TeX">$\ell _{\scriptscriptstyle 0}$</tex></formula>-Regularized Least-Squares

Homotopy Based Algorithms for $\ell _{\scriptscriptstyle 0}$-Regularized Least-Squares