Weighted Best Linear Prediction and Its Randomized Acceleration for Poisson Image Denoising

Photon-limited Poisson image denoising is a pressing problem and faces great challenges in some fields such as emission tomography, low-exposure x-ray imaging, fluorescence microscopy, and infrared astronomy. Currently, the post- processing best linear prediction method (BLP) based on co- variance estimation of non-local similar image patches has been proposed and achieved good results in Poisson image denoising. However, the calculation of similarity is inaccurate in the photon limited case, which leads to the inaccuracy of similarity patches- based covariance estimation as well. To remedy this, we propose a new BLP method based on weighted covariance estimation (WBLP). This method searches for similar patches in a large window for each reference patch, which brings a large amount of computation. To solve this problem, we introduce a randomized acceleration technique to speed up our method.