Coded aperture snapshot spectral imaging (CASSI) is a technique used to reconstruct three-dimensional hyperspectral images (HSIs) from one or several two-dimensional projection measurements. However, fewer projection measurements or more spectral channels leads to a severly ill-posed problem, in which case regularization methods have to be applied. In order to significantly improve the accuracy of reconstruction, this paper proposes a fast alternating minimization algorithm based on the sparsity and deep image priors (Fama-SDIP) of natural images. By integrating deep image prior (DIP) into the principle of compressive sensing (CS) reconstruction, the proposed algorithm can achieve state-of-the-art results without any training dataset. Extensive experiments show that Fama-SDIP method significantly outperforms prevailing leading methods on simulation and real HSI datasets.
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