Terahertz Single-Pixel Imaging Optimized Through Sparse Representation of an Overcomplete Dictionary

Terahertz (THz) single-pixel imaging has received major research attention because of the lack of a suitable high-resolution array detector for THz imaging applications. Improving both imaging speed and quality has become a research hotspot for this field in recent years. In this study, a terahertz single-pixel imaging system with Hadamard spatial encoding was constructed by using optically induced semiconductor materials to perform THz wave modulation. Sparse coding was added to the system's reconstruction algorithm to enhance imaging quality. Numerous image patches were then collected from a natural image set to train an overcomplete dictionary and each patch in the measured image was reconstructed through sparse representation. To validate the effectiveness of the proposed algorithm, the reconstruction performances of different algorithms were compared under various conditions (i.e., with sampling rates varying from 5 to 100% and with noise levels within a signal-to-noise ratio range of 10-50 dB). The proposed algorithm, in combination with sparse representation of an overcomplete dictionary, showed a higher peak signal-to-noise ratio and a lower mean square error than both the inverse Hadamard transform (IHT) and TVAL3 algorithms. Finally, THz imaging experiments were performed to validate the algorithm's reconstruction performance at sub-Nyquist sampling rates. The experimental and simulation results coincided closely, thus indicating that the use of the proposed algorithm enhances the signal-to-noise ratio of the reconstructed image, reduces its mean square error, and retains greater image detail. The proposed algorithm was demonstrated to be the preferred choice for THz single-pixel imaging applications.