Optimized Sensing Matrix for Single Pixel Multi-Resolution Compressive Spectral Imaging

Abstract

Compressive spectral imaging (CSI) sensors allow the acquisition of spatial and spectral data using a set of coded projections. The single pixel camera (SPC) is a low-cost CSI architecture capable of sensing high-resolution spectral images, whose potential is diminished by its slow acquisition time due to the large number of required projections. To partially alleviate this issue, dual arm optical systems have been designed such that side information of the scene is captured to guide the reconstruction process. To fully exploit the capabilities of the dual system, the SPC sensing matrix, or equivalently the coding patterns; should be properly designed. Therefore, this work proposes an optimized sensing matrix design for the SPC based on a super-pixel map of the scene, obtained from the side information, such that the number of projections is drastically reduced while the reconstruction quality is improved. Indeed, theoretical analysis based on the restricted isometry property indicates that the error of the reconstruction vanishes when the SPC uses the designed sensing matrix. Simulation and experimental results show that the proposed sensing matrix design improves the reconstruction quality. Specifically, the proposed approach improves image quality in up to 15dB compared with the state of the art sensing matrix designs. Moreover, a fast multi-resolution reconstruction approach is proposed based on the designed matrix, which reduces computation time by two orders of magnitude and does not require an iterative process.