Abstract: The Matching Pursuit(MP) algorithms display good performance of recurring the orthonormal sparse structure of signals, but the signal decomposition process widely ex-hibits pre-echo artifact and local mismatch, so HRP algorithm was proposed by S. Jaggi, et al. to acquire more exact inner structure of signals. Unfortunely HRP algorithm is followed by more huge operation cost. The fast HRP algorithm is advanced at wavelet domain by tak-ing advantage of wavelet multiresolution decomposition, and a parallel algorithm framework is used to further reduce operation time. Theory and simulation trials indicate that HRP algorithm at wavelet domain not only reduces HRP operation cost greatly, but also improves the effect of the wavelet analysis, thus it is a promising technique applied in adaptive signal decomposition and feature extraction.