Uniform Recovery Bounds for Structured Random Matrices in Corrupted Compressed Sensing.

We study the problem of recovering an s-sparse signal x* ∈ Cn from corrupted measurements y = Ax* + z* + w, where z* ∈ Cm is a k-sparse corruption vector whose nonzero entries may be arbitrarily large and w ∈ Cm is a dense noise with bounded energy. The aim is to exactly and stably recover the sparse signal with tractable optimization programs. In this paper, we prove the uniform recovery guarante...