2012/05/30 by Hassan Mansour, Özgür Yılmaz, Mansour, Hassan +2
Computer Science · Decision Sciences · Engineering · Mathematics · #FOS: Computer and information sciences #Image and Signal Denoising Methods #Information Theory (cs.IT) #Probabilistic and Robust Engineering Design #Sparse and Compressive Sensing Techniques #cs.IT #math.IT
paper · pdf · doi:10.48550/arxiv.1205.6846
Proc. of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), March, 2012
arxiv created 2012/05/30 · openalex publication_date 2012/05/30 · arxiv updated 2012/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 Candès, 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.