In this paper, a convolution sparse coding method based on global structure characteristics and spectral correlation is proposed for the reconstruction of compressive spectral images. The proposed method uses the convolution kernel to operate the global image, which can better preserve image structure information in the spatial dimension. To take full exploration of the constraints between spectra, the coefficients corresponding to the convolution kernel are constrained by the norm to improve spectral accuracy. And, to solve the problem that convolutional sparse coding is insensitive to low frequency, the global total-variation (TV) constraint is added to estimate the low-frequency components. It not only ensures the effective estimation of the low-frequency but also transforms the convolutional sparse coding into a de-noising process, which makes the reconstructing process simpler. Simulations show that compared with the current mainstream optimization methods (DeSCI and Gap-TV), the proposed method improves the reconstruction quality by up to 7 dB in PSNR and 10% in SSIM, and has a great improvement in the details of the reconstructed image.
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