Compressive spectral image super-resolution by using singular value decomposition

Compressive sensing (CS) has been recently applied to the acquisition and reconstruction of spectral images (SI). This field is known as compressive spectral imaging (CSI). The attainable resolution of SI depends on the sensor characteristics, whose cost increases in proportion to the resolution. Super-resolution (SR) approaches are usually applied to low-resolution (LR) CSI systems to improve the quality of the reconstructions by solving two consecutive optimization problems. In contrast, this work aims at reconstructing a high resolution (HR) SI from LR compressive measurements by solving a single convex optimization problem based on the fusion of CS and SR techniques. Furthermore, the truncated singular value decomposition is used to alleviate the computational complexity of the inverse reconstruction problem. The proposed method is tested by using the coded aperture snapshot spectral imager (CASSI), and the results are compared to HR-SI images directly reconstructed from LR-SI images by using an SR algorithm via sparse representation. In particular, a gain of up to 1.5 dB of PSNR is attained with the proposed method.