A Non-Local Means Filter for Removing the Poisson Noise

TL;DR

This paper introduces a Non-Local Means-based algorithm tailored for removing Poisson noise in images, providing theoretical guarantees of convergence and demonstrating competitive performance through simulations.

Contribution

It develops a novel Non-Local Means Poisson Filter with proven convergence and optimal rate, extending the classic method to Poisson noise.

Findings

The filter effectively reduces Poisson noise in images.

Theoretical proof of convergence at the optimal rate.

Simulation results show high competitiveness with existing methods.

Abstract

A new image denoising algorithm to deal with the Poisson noise model is given, which is based on the idea of Non-Local Mean. By using the "Oracle" concept, we establish a theorem to show that the Non-Local Means Filter can effectively deal with Poisson noise with some modification. Under the theoretical result, we construct our new algorithm called Non-Local Means Poisson Filter and demonstrate in theory that the filter converges at the usual optimal rate. The filter is as simple as the classic Non-Local Means and the simulation results show that our filter is very competitive.