A Modified Greedy Algorithm for Wavelet Coefficients Reconstruction

A modified greedy algorithm called Multi-Tree-based Orthogonal Matching Pursuit (MTOMP) is presented for wavelet coefficients reconstruction in this paper. The proposed algorithm treats the tree model in the wavelet domain as an additional prior information, selects from multiple trees some optimal nodes where wavelet coefficients´ coordinates would be added into the estimated support set, and then refines the estimated support set renewed according to a backtracking method, so as to reconstruct the wavelet coefficients more accurately with fewer iterations on the condition that the sparsity level is unknown. The analytical theory and simulation results show that the proposed algorithm can achieve better reconstruction performances and it is superior to other greedy algorithms both visually and objectively with reducing the computational complexity and improving the reconstruction efficiency.