Support driven reweighted ℓ1 minimization
Title | Support driven reweighted ℓ1 minimization |
Publication Type | Conference |
Year of Publication | 2012 |
Authors | Hassan Mansour, Ozgur Yilmaz |
Conference Name | ICASSP |
Keywords | ICASSP |
Abstract | In this paper, we propose a support driven reweighted ℓ1 minimization algorithm (SDRL1) that solves a sequence of weighted ℓ1 problems and relies on the support estimate accuracy. Our SDRL1 algorithm is related to the IRL1 algorithm proposed by Candes, Wakin, and Boyd. We demonstrate that it is sufficient to find support estimates with good accuracy and apply constant weights instead of using the inverse coefficient magnitudes to achieve gains similar to those of IRL1. We then prove that given a support estimate with sufficient accuracy, if the signal decays according to a specific rate, the solution to the weighted ℓ1 minimization problem results in a support estimate with higher accuracy than the initial estimate. We also show that under certain conditions, it is possible to achieve higher estimate accuracy when the intersection of support estimates is considered. We demonstrate the performance of SDRL1 through numerical simulations and compare it with that of IRL1 and standard ℓ1 minimization. |
URL | https://slim.gatech.edu/Publications/Public/Conferences/ICASSP/2012/MansourYilmazICASSPwL1/MansourYilmazICASSPwL1.pdf |
Citation Key | mansour2012ICASSsupport |