# Robust Signal Recovery With Highly Coherent Measurement Matrices

• Published 2017 in IEEE Signal Processing Letters

#### Abstract

By embedding an <inline-formula><tex-math notation="LaTeX">$\ell _{p}$</tex-math></inline-formula>-norm noise constraint for <inline-formula><tex-math notation="LaTeX">$p\geq 2$</tex-math></inline-formula> into the recently emerged <inline-formula><tex-math notation="LaTeX">$\ell _{1-2}$</tex-math></inline-formula> method, in this letter, we study theoretically and numerically an <inline-formula><tex-math notation="LaTeX">$\ell _{1-2}/\ell _{p}$</tex-math> </inline-formula> method for recovery of general noisy signals from highly coherent measurement matrices. In particular, the obtained theoretical results not only improve the condition deduced in <xref ref-type="bibr" rid="ref1">[1]</xref> for Gaussian noisy signal recovery but also provide a new theoretical guarantee for generally non-Gaussian noisy signal recovery. What is more, to better boost the recovery performance, a partial sum <inline-formula><tex-math notation="LaTeX">$\ell _{1-2}/\ell _{p}$</tex-math></inline-formula> method is also proposed latter. This improved method, together with the previous <inline-formula><tex-math notation="LaTeX"> $\ell _{1-2}/\ell _{p}$</tex-math></inline-formula> method, becomes more competitive when compared with some of the state-of-the-art methods in recovering noisy signals from highly coherent measurement matrices.

DOI: 10.1109/LSP.2016.2626308

### Cite this paper

@article{Wang2017RobustSR, title={Robust Signal Recovery With Highly Coherent Measurement Matrices}, author={Wendong Wang and Jianjun Wang and Zili Zhang}, journal={IEEE Signal Processing Letters}, year={2017}, volume={24}, pages={304-308} }