A new algorithm on hierarchical sparse signal reconstruction

Reconstructing signals that have a sparse representation has been studied in the recent years. However, most of the work dealing with this problem requires a low-coherent dictionary matrix. This article presents a novel procedure for sparse signal reconstruction with high coherent dictionary by partitioning the dictionary in the preprocessing step and addressing the reconstruction of hierarchical sparse signals via a new matching pursuit algorithm. We analyse the performance of the proposed algorithm in the noiseless case and show that given the same conditions as required for OMP, it achieves at least the same reconstruction performance as OMP. Numerical simulation and experimental results show that by exploiting the hierarchical sparse structure of the signal, the proposed method outperforms those traditional methods.