Low rank constraint and spatial spectral total variation for hyperspectral image mixed denoising

- We propose a novel low rank and spatial spectral total variation based HSI mixed denoising model.
- The reason of undesirable jagged distortion caused by the band by band TV regularization is analyzed.
- The model can jointly utilize global low rank and local spatial spectral smooth properties of HSI.
- The iterations based on the ADMM are carried out to solve the optimization problem effectively.
- The proposed model can effectively suppress the jagged distortion while removing the noise.

Due to the environmental and instrumental factors, the hyperspectral image (HSI) is corrupted by various noise, which inevitably affects the subsequent HSI-based applications. Several band by band Total Variation(TV)-regularized low rank based models have been proposed for HSI mixed denoising. However, these methods only utilize the spatial smooth constraint in a separated way, but ignore the local spectral smooth property, which may cause the undesirable jagged spectral distortion. To cope with this problem, we propose a novel low rank constraint and spatial spectral total variation regularization model. First, we adopt the weighted nuclear norm to restore the clean HSI from the mixed noise based on the low rank property. Then, the spatial spectral total variation is modeled as a special regularization to further remove the Gaussian noise and enhance the local spatial and spectral smoothness. Finally, an iterative strategy based on the Alternating Direction Method of Multipliers is designed to solve the derived optimization problem. Extensive experiments demonstrate the superiority of the proposed model in terms of mean PSNR, mean SSIM, mean spectral angle distance and visual quality. Especially, the proposed model is very effective for suppressing the jagged spectral distortion while removing the noise.