Orthogonal Matching Pursuit : Recursive Function Approximation with Applications to WaveletDecompositionY

In this paper we describe a recursive algorithm to compute representations of functions with respect to nonorthogonal and possibly overcomplete dictionaries of elementary building blocks e.g. aane (wavelet) frames. We propose a modiication to the Matching Pursuit algorithm of Mallat and Zhang (1992) that maintains full backward orthogonality of the residual (error) at every step and thereby leads to improved convergence. We refer to this modiied algorithm as Orthogonal Matching Pursuit (OMP). It is shown that all additional computation required for the OMP algorithm may be performed recursively.