Poissonian Blurred Hyperspectral Imagery Denoising Based on Variable Splitting and Penalty Technique

Poisson noise is one of the significant sources of noise present in hyperspectral imagery (HSI). In most of the existing denoising methods, Poisson noise is first transformed into Gaussian noise through the Anscombe transform and then removed. However, the use of Anscombe transform can give rise to transform errors that affect the final denoising results. In addition, blurs often contaminate the HSI during the imaging procedure, which makes it more difficult to remove the Poisson noise. In view of the above problems, under the maximum a posteriori (MAP) model, we propose a Poissonian blurred HSI denoising based on variable splitting and penalty technique (named as VSPT) to directly remove the Poissonian blurred HSI noise without using the Anscombe transform. By finding the minimum value of the negative logarithmic Poisson log-likelihood combined with the total variation (TV), the proposed method transforms the problem into two subproblems, which are easier to solve: 1) a TV regularized deconvolution problem and 2) an ordinary convex optimization problem. The experimental results show that the proposed VSPT method can effectively remove Poisson noise in HSI contaminated by blurs during the imaging procedure.