A new method for signal sparse decomposition

Increasing attention has been paid to the signal sparse representation based on overcomplete dictionaries in the fields of signal processing. The sparsity degree of decomposed signal is directly related with the dictionary chosen, and the computation speed depends on the sparse decomposition algorithm and the scale of dictionary. Almost all sparse decomposition algorithms available suffer from enormous computational complexity, which severely affects the practicability of these algorithms and limits the development of sparse representation upon an overcomplete dictionary. This paper presents a new method for decomposing a signal upon overcomplete dictionary. This method first constructs a special concatenate dictionary with several orthogonal bases and presents a iterative group matching search algorithm. The experiments results show that our algorithm can reduce the computation burden greatly and is more efficient than MP. This paper also proposes a method to determine a near optimal value of the total number of coefficients.