  In this paper, a convolutional sparse coding method based on global structure
characteristics and spectral correlation is proposed for the reconstruction of
compressive spectral images. The spectral data is regarded as the convolution
sum of the convolution kernel and the corresponding coefficients, using the
convolution kernel operates the global image information, preserving the
structure information of the spectral image in the spatial dimension. To take
full exploration of the constraints between spectra, the coefficients
corresponding to the convolution kernel are constrained by the L_(2,1)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, the proposed method can improve the
reconstruction quality by up to 4 dB in PSNR and 10% in SSIM, and has a great
improvement in the details of the reconstructed image.
