Robust signal recovery with highly coherent measurement matrices

By embedding an ell-norm noise constraint for into the recently emerged method, in this letter, we study theoretically and numerically an 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 [1] 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 method is also proposed latter. This improved method, together with the previous method, becomes more competitive when compared with some of the state-of-the-art methods in recovering noisy signals from highly coherent measurement matrices.