A Biconvex Analysis for Lasso $\ell _1$ Reweighting
| Autor: | Sophie M. Fosson |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Signal processing
Noise measurement Computer science Iterative method Applied Mathematics Regular polygon 020206 networking & telecommunications 02 engineering and technology 01 natural sciences 010104 statistics & probability Compressed sensing Lasso (statistics) Signal Processing 0202 electrical engineering electronic engineering information engineering 0101 mathematics Electrical and Electronic Engineering Algorithm |
| Zdroj: | IEEE Signal Processing Letters. 25:1795-1799 |
| ISSN: | 1558-2361 1070-9908 |
| DOI: | 10.1109/lsp.2018.2875251 |
| Popis: | Iterative $\ell _1$ reweighting algorithms are very popular in sparse signal recovery and compressed sensing, since in the practice they have been observed to outperform classical $\ell _1$ methods. Nevertheless, the theoretical analysis of their convergence is a critical point, and generally is limited to the convergence of the functional to a local minimum or to subsequence convergence. In this letter, we propose a new convergence analysis of a Lasso $\ell _1$ reweighting method, based on the observation that the algorithm is an alternated convex search for a biconvex problem. Based on that, we are able to prove the numerical convergence of the sequence of the iterates generated by the algorithm. Furthermore, we propose an alternative iterative soft thresholding procedure, which is faster than the main algorithm. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|