Spatial-spectral encoding and dictionary optimization in compressive single-pixel hyperspectral imaging based on mutual coherence minimization.

A single-pixel detector based hyperspectral system provides an effective way to obtain the spatial-spectral information of target scenes. However, complex spectral dispersion and the substantial number of measurements not only increase the complexity of the system but also decrease the sampling efficiency and the reconstruction accuracy. In this paper, we propose a compressive sensing (CS) theory based single-pixel hyperspectral imaging system. Based on structured illumination, the spatial information is modulated by binary spatial patterns displayed on a liquid crystal on silicon (LCoS), while polarizing elements at specific angles, acting as a serious of filters, modulate the spectral dimension, effectively avoiding spectral dispersion. In terms of sampling efficiency, the application of CS significantly decreases the number of measurements required compared to the Nyquist-Shannon sampling theorem. Besides, to improve the reconstruction accuracy, mutual coherence minimization is employed to optimize the pre-trained dictionary, spatial patterns and filters. Furthermore, a two-step encoding method based on macro-pixel segmentation is proposed to address the issue of low resolution constrained by the size of the dictionary. Compared to the unoptimized system and dictionary, the proposed method achieves more accurate reconstruction results in both spectral and spatial dimensions. This work may provide opportunities for high-resolution single-pixel hyperspectral imaging systems based on CS.