Abstract: During the imaging process of the diffractive optic imaging spectrometer, infocus images are often blurred by other defocused images. The existing recovery algorithms only utilize the spatial information and show limitations on these ill-posed inverse problems. In this paper, a regularization method based on the multichannel spectral-spatial total variation prior is proposed to reconstruct diffractive spectral images. First, an observation model of the degraded spectral images is constructed carefully, relying on the principle of diffractive spectral imaging. Then, a reconstruction model is established by combining the spatial and spectral prior information under the maximum posteriori framework. The proposed model makes full use of the local spatial smoothness and local spectral smoothness of the diffractive spectral images. Meanwhile, the ADMM (alternating direction method of multipliers) is employed to efficiently optimize the model. A large number of experiments demonstrate that this new restoration model has better performance in terms of average peak signal-to-noise ratio, average structural similarity, average spectral angular distance and visual quality compared with other restoration methods. In addition, for the ill-conditioned problem with cross-channel blurs and noise interference, this model can suppress noise, preserve edge information, and reduce jagged spectral distortion while ensuring the solution speed.

Key words: diffractive optic imaging spectrometer, total variation, local spatial-spectral smoothness, alternating direction method of multipliers (ADMM), image restoration