1Minimum Risk Wavelet Shrinakge Operator For Poisson Image Denoising

Abstract—The pixel values of images taken by an image sensor are said to be corrupted by Poisson noise. To date, multi-scale Poisson image denoising techniques have processed Haar frame and wavelet coefficients—the modeling of coefficients is enabled by the Skellam distribution analysis. We extend these results by solving for shrinkage operators for Skellam that minimizes the risk functional in the multi-scale Poisson image denoising setting. The minimum risk shrinkage operator of this kind effectively produces denoised wavelet coefficients with minimum attainable L2 error. Index Terms—Frame transform, Poisson distribution, Skella