In this paper, we address the problem of recovering signals from undersampled data where such signals are not sparse in an orthonormal basis, but in an overcomplete dictionary. We show that if the combined matrix obeys a certain restricted isometry property and if the signal is sufficiently sparse, the reconstruction that relies on p minimization with 0

Nonconvex optimization; Orthonormal basis; Over-complete dictionaries; Redundant dictionaries; Restricted isometries; Restricted isometry properties; Sparse signal recoveries; Under-sampled

HeFei University of Technology