A robust adaptive-thresholding primal-dual sparse recovery for THz imaging

Abstract

Terahertz time-domain spectroscopy (THz-TDS) system is a powerful tool in material spectral analysis and non-destructive testing (NDT). However, the data acquisition is time-consuming due to the point-by-point scanning process, which leads to limitations in THz imaging applications. In this paper, a robust adaptive-thresholding primal-dual sparse recovery (APSR) method is proposed to reconstruct high-resolution THz images and reduce the acquisition time. A sparsity averaging dictionary, which is a concatenate of multiple bases, is applied to improve the robustness and generalization. A reweighted scheme is also adopted to enhance the sparse solution. As a crucial consideration in the sparse recovery method, we propose a robust adaptive threshold estimator based on the median absolute deviation in the sense that the final threshold determines the reconstruction quality and the convergence rate. Meanwhile, together with the Nesterov acceleration technique, a large threshold can be applied at the beginning of the iteration to help accelerate the convergence. Numerical experiments demonstrate that the APSR method can reconstruct THz images with robustness even with low SNR (of 30 dB) and low sampling rate (of 30%) compared to conventional methods. In the real THz-TDS system, our proposed sparse imaging method can successfully recover a composite object with much fewer THz spectra and reduces the acquisition time to 30% at the cost of a relative error of 2.5%, demonstrating the efficiency of our proposed method and the penetrating ability of THz technology in the NDT applications.