A Ridgelet Approach to Poisson Denoising

TL;DR

This paper presents a new ridgelet transform-based method for Poisson image denoising, leveraging theoretical insights and adaptive thresholding to effectively reduce noise in images affected by non-Gaussian, signal-dependent Poisson noise.

Contribution

It introduces a novel ridgelet thresholding scheme specifically designed for Poisson noise, combining theoretical modeling with adaptive techniques for improved denoising performance.

Findings

The method effectively reduces Poisson noise in images.

Theoretical model aligns well with numerical experiments.

Demonstrates potential across various scenarios.

Abstract

This paper introduces a novel ridgelet transform-based method for Poisson image denoising. Our work focuses on harnessing the Poisson noise's unique non-additive and signal-dependent properties, distinguishing it from Gaussian noise. The core of our approach is a new thresholding scheme informed by theoretical insights into the ridgelet coefficients of Poisson-distributed images and adaptive thresholding guided by Stein's method. We verify our theoretical model through numerical experiments and demonstrate the potential of ridgelet thresholding across assorted scenarios. Our findings represent a significant step in enhancing the understanding of Poisson noise and offer an effective denoising method for images corrupted with it.