Double Gaussian mixture model-based terahertz wave dispersion compensation method using convex optimization technique

Terahertz (THz) time-domain pulse detection technique has recently attracted great attention in the nondestructive testing (NDT) field due to its superior detection accuracy and sensitivity for various non-metallic materials. However, the dispersion of the THz wave in the tested material significantly degrades the temporal and spatial resolution of THz detection, which limits its practical applications in the high-resolution measurement. Here, a novel dispersion compensation strategy based on the double Gaussian mixture model (DGMM) is proposed to suppress the dispersion effect in THz echoes. The double overcomplete dictionaries composed of one parametric dispersion dictionary and one parametric non-dispersion dictionary are designed separately by discretizing the estimated parameter vector from observed THz echoes. To obtain the excellent performance of dispersion compensation, the convex optimization technique is employed to sparsely decompose the observed dispersive THz echoes by the appropriate selection of the optimal regularization parameter. Both numerical simulations and experiments can validate the effectiveness of proposed method for the non-overlapping and overlapping dispersive THz echoes.