Application of tree-based searches to matching pursuit

Matching pursuit (MP) uses a greedy search to construct a subset of vectors, from a larger set, which best represents a signal of interest. We extend this search for the best subset by keeping the K vectors which maximize the selection criterion at each iteration. This is termed the MP:K algorithm and represents a suboptimal search through the tree of all possible subsets where each node is limited to having K children. As a more suboptimal search, we can use the M-L search to select a subset of dictionary vectors, leading to the MP:M-L algorithm. We compare the computation and storage requirements for three variants of the MP algorithm using these searches. Through simulations, the significantly improved performance obtained using the MP:K and MP:M-L algorithms is demonstrated. We conclude that the modified matching pursuit (MMP) algorithm offers the best compromise between performance and complexity using these search techniques.