Dictionary preconditioning for orthogonal matching pursuit in the presence of noise

Since orthogonal matching pursuit (OMP) may fail to identify correct atoms if the cumulative coherence of dictionary is too high, Schnass and Vandergheynst modified OMP algorithm by using a sensing dictionary in sensing step and proposed an method for designing sensing dictionary in noiseless case. However, only contaminated observations are available in most practical situations. In this letter, we provide the sufficient condition under which the modified OMP can be guaranteed to identify correct atoms in noisy case and propose a method to designing sensing dictionary. Finally, simulation results are presented to demonstrate the effectivity of the proposed method.