Terahertz nondestructive stratigraphic reconstruction of paper stacks based on adaptive sparse deconvolution

Abstract

Characterizing the number of sheets in a stack of paper typically involves mechanical separation of the individual sheets. Here, we explore an nondestructive method that can be applied to the intact paper stack. Namely, terahertz time-of-flight tomography, together with post signal-processing technique sparse deconvolution based on a two-step iterative shrinkage-thresholding algorithm (SD/TWIST), is employed to reconstruct the stratigraphy of stacks of sheets of paper with multilayered structure in a nondestructive and noncontact manner. The double-Gaussian mixture model (DGMM) is also incorporated to suppress dispersion in the reflected THz echoes. The effectiveness and accuracy of the proposed adaptive sparse-deconvolution method are verified experimentally and numerically. Compared with the commonly used frequency wavelet-domain deconvolution (FWDD) method and previous implementations of sparse deconvolution based on an iterative-shrinkage and thresholding algorithm (SD/IST), the proposed sparse-deconvolution approach can provide a clearer and rapid stratigraphic reconstruction of the paper stacks studied, while ensuring accurate thickness information for each paper sheet in the presence of noise, revealing the potential usage of real-time THz tomographic-image processing.