A Non-iterative Reconstruction Algorithm for Single Pixel Spectral Imaging with Side Information

Compressive spectral imaging (CSI) allows the acquisition of spatial information of a scene along multiple spectral bands using fewer projected measurements than traditional scanning methods. In general, to obtain high resolution spatial and spectral information, expensive detectors and sophisticated optical devices are required. Fortunately, the single-pixel camera (SPC) is a low-cost optical architecture since it uses a light sensor compared to CSI architectures with larger sensors. However, this advantage is overshadowed by the large number of projections needed to recover the spectral image, which entails large acquisition times. Alternatively, high-resolution spectral images can be obtained using SPC with side-information, without significantly increasing acquisition costs. However, this approach retrieves improved resolution images applying iterative and computationally expensive algorithms. This paper proposes a non-iterative method that combines the spectral information of SPC and the side information of a multispectral image to recover high resolution spatial and spectral information. The proposed fast compressive spectral imaging (FCSI) reconstruction method exploits the fact that the spatial-spectral data lie in a low dimensional subspace. This methodology allows to reduce the number of required measurements in the SPC as well as the computation time of the reconstruction. Simulations and experimental results show the effectiveness of the proposed method compared to similar approaches, both in reconstruction quality and sample complexity.