Generalized Orthogonal Matching Pursuit With Singular Value Decomposition

Matching pursuit (MP) is an algorithm that can represent signal sparsely, and this advantage makes MP popular in signal processing. However, MP algorithm is a greedy algorithm which means it cannot deal with a large family of signals like seismic data which becomes larger and larger with development of data acquisition technologies. Generalized orthogonal MP (GOMP) is an improved algorithm which helps to reduce the cost of the calculation greatly. Fast MP algorithm is a method that can build dynamic dictionary by making full use of the characteristics of the original signal. In this study, singular value decomposition (SVD) is involved into the GOMP algorithm with dynamic dictionary to improve its efficiency. Compared with conventional MP, the proposed method picks multiatoms at each iteration. It has advantage in calculation speed and can reconstruct the original signal more exactly. Synthetic and field data examples are utilized to demonstrate the feasibility, computational efficiency, and precision of the proposed method.