The l(1)-Analysis in Phase Retrieval with Redundant Dictionary

摘要

This article presents new results concerning the recovery of a signal from the magnitude only measurements where the signal is not sparse in an orthonormal basis but in a redundant dictionary, which we call it phase retrieval with redundant dictionary for short. To solve this phaseless problem, we analyze the -analysis model. Firstly we investigate the noiseless case with presenting a null space property of the measurement matrix under which the -analysis model provides an exact recovery. Secondly we introduce a new property (S-DRIP) of the measurement matrix. By solving the -analysis model, we prove that this property can guarantee a stable recovery of real signals that are nearly sparse in overcomplete dictionaries.