Subsampled terahertz data reconstruction based on spatio-temporal dictionary learning

TL;DR

This paper introduces a spatio-temporal dictionary learning approach for reconstructing incomplete 3D terahertz data, significantly improving data recovery accuracy from limited observations in terahertz imaging applications.

Contribution

It proposes a novel joint sparse recovery and dictionary learning method for effective denoising and reconstruction of subsampled terahertz data, enhancing accuracy over existing techniques.

Findings

Achieved 19 dB SNR with only 5% data observation for layered structures.

Obtained 98.8% and 99.9% accuracy in thickness and depth measurements.

Validated effectiveness on model and pharmaceutical terahertz datasets.

Abstract

In this paper, the problem of terahertz pulsed imaging and reconstruction is addressed. It is assumed that an incomplete (subsampled) three dimensional THz data set has been acquired and the aim is to recover all missing samples. A sparsity-inducing approach is proposed for this purpose. First, a simple interpolation is applied to incomplete noisy data. Then, we propose a spatio-temporal dictionary learning method to obtain an appropriate sparse representation of data based on a joint sparse recovery algorithm. Then, using the sparse coefficients and the learned dictionary, the 3D data is effectively denoised by minimizing a simple cost function. We consider two types of terahertz data to evaluate the performance of the proposed approach; THz data acquired for a model sample with clear layered structures (e.g., a T-shape plastic sheet buried in a polythene pellet), and pharmaceutical tablet data (with low spatial resolution). The achieved signal-to-noise-ratio for reconstruction of T-shape data, from only 5% observation was 19 dB. Moreover, the accuracies of obtained thickness and depth measurements for pharmaceutical tablet data after reconstruction from 10% observation were 98.8%, and 99.9%, respectively. These results, along with chemical mapping analysis, presented at the end of this paper, confirm the accuracy of the proposed method.