Matching pursuit time-frequency analysis has better time-frequency resolution compared to short-time Fourier transform

continuous wavelet transform

and generalized S transform

but the traditional greed iterative algorithm has lower computation efficiency. The Morlet wavelet is chosen as timefrequency atoms to achieve the matching pursuit due to the good property of scale parameter. The scale parameter has strong control action on the form of time-frequency atom

thus has strong control action on the matching character between signal and time-frequency atom

through comparing and analyzing the forms of timefrequency atoms based on different scale parameters and the projection values of signal onto different time-frequency atoms with the same frequency

phase and time-delay parameters but different scale parameters. The 1D optimization for scale parameter is done with the frequency

phase and time-delay parameters calculated by Hilbert transform as the parameters of time-frequency atoms. Then the parameters are only needed to be fine-adjusted

and the computation efficiency is improved. The effectiveness of algorithm is tested by model data

and the algorithm is also tested on application of denosing and inversion for thin layer thickness.