Abstract: In order to solve the problem of inaccurate location of complex terahertz echo signal caused by multi-layer reflection,material dispersion absorption and noise of blade samples with thermal barrier coatings, a time sliced sparse dispersion model based on sparse representation is proposed to locate the complex terahertz echoes. Considering the influence of material dispersion on the pulse spreading of terahertz time domain echo signal, the corresponding terahertz sparse dispersion dictionary is established based on the convolution model of terahertz echo signal. The sparse pulse response function can be reconstructed by spectral projected gradient convex optimization algorithm to locate the delay time of complex echo signal. In addition, the evaluation indicators composed of the root mean square error and sparsity are introduced to quantitatively assess the performance of the proposed method on THz echoes from the two dimensions of reconstruction accuracy and sparsity. Then, theoretical simulation and thermal barrier coating experimental results indicate that the proposed method has better reconstruction accuracy and sparsity, and the echo location performance is better than that of frequency wavelet domain deconvolution and sparse reconstruction method without considering dispersion. It is more suitable for precise localization of complex terahertz echo signal, and provides a new way for the processing of complex terahertz signal.

Key words: terahertz detection, sparse representation, time sliced sparse dispersion, thermal barrier coatings, echo localization