Probabilistic matching pursuit with Gabor dictionaries

We propose a probabilistic extension of the matching pursuit adaptive signa l processing algorithm introduced by Mallat and others, In adaptive signal processing, signals are expanded in terms of a large linearly dependent "di ctionary" of functions rather than in terms of an orthonormal basis. Matchi ng pursuit is a simple greedy algorithm for generating an expansion of a gi ven signal. In probabilistic matching pursuit multiple random expansions ar e obtained as estimates for a given signal. The new algorithm is illustrate d in the context of signal denoising. Although most of the random expansion s generated by probabilistic matching pursuit are poorer estimates for the signal than those obtained by matching pursuit, our final estimate, obtaine d as an expected value computed by means of an ergodic average, can improve the result obtained by MP in some denoising situations. One of the major u nderlying ideas is a novel notion of coherence between a signal and the dic tionary. Several simulated examples are presented. (C) 2000 Elsevier Scienc e B.V. All rights reserved.