Abstract: For the extremely high complexity of usual algorithms for sparse decomposition, a new group matching pursuit algorithm is presented based on a redundant dictionary with several orthonormal bases. The algorithm adopts the the idea of iterative group matching pursuit and selects the optimal basis from the dictionary by comparing the matching degree between the signal or the residua and every basis. Each operation of decomposing results in a few important coefficients by using the fast calculating algorithm of orthogonal decomposition. After several such iterations, the original signal is approximated with a few coefficients eventually. Simulation results show that the calculating speed of the algorithm in this paper increases by about thirty times compared with MP’s. Moreover, this algorithm can avoid over-matching.

Key words: sparse decomposition, redundant dictionary, matching pursuit algorithm, signal compression