A New Poisson Noise Filter based on Weights Optimization

TL;DR

This paper introduces a novel Poisson noise image denoising algorithm that optimally determines weights for a weighted linear filter, demonstrating convergence and improved performance over traditional methods.

Contribution

The paper presents a new Poisson noise filter with weights optimized via an oracle approach, improving denoising effectiveness and theoretical convergence guarantees.

Findings

The proposed filter converges at the optimal rate to the true image.

Simulation results show improved performance over conventional filters.

The method effectively estimates weights from observed data.

Abstract

We propose a new image denoising algorithm when the data is contaminated by a Poisson noise. As in the Non-Local Means filter, the proposed algorithm is based on a weighted linear combination of the bserved image. But in contract to the latter where the weights are defined by a Gaussian kernel, we propose to choose them in an optimal way. First some "oracle" weights are defined by minimizing a very tight upper bound of the Mean Square Error. For a practical application the weights are estimated from the observed image. We prove that the proposed filter converges at the usual optimal rate to the true image. Simulation results are presented to compare the performance of the presented filter with conventional filtering methods.