Robust iterative hard thresholding for compressed sensing
Abstract
Compressed sensing (CS) or sparse signal reconstruction (SSR) is a signal processing technique that exploits the fact that acquired data can have a sparse representation in some basis. One popular technique to reconstruct or approximate the unknown sparse signal is the iterative hard thresholding (IHT) which however performs very poorly under non-Gaussian noise conditions or in the face of outliers (gross errors). In this paper, we propose a robust IHT method based on ideas from $M$-estimation that estimates the sparse signal and the scale of the error distribution simultaneously. The method has a negligible performance loss compared to IHT under Gaussian noise, but superior performance under heavy-tailed non-Gaussian noise conditions.
- Publication:
-
arXiv e-prints
- Pub Date:
- May 2014
- DOI:
- 10.48550/arXiv.1405.1502
- arXiv:
- arXiv:1405.1502
- Bibcode:
- 2014arXiv1405.1502O
- Keywords:
-
- Computer Science - Information Theory;
- Statistics - Applications
- E-Print:
- To appear in Proc. of ISCCSP 2014