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.

翻译：本文介绍了一种基于脊波变换的新型泊松图像去噪方法。我们的工作重点在于利用泊松噪声独特的非加性和信号依赖性特性，从而区别于高斯噪声。该方法的核心是一种新的阈值方案，该方案基于对泊松分布图像脊波系数的理论洞察以及由Stein方法引导的自适应阈值处理。我们通过数值实验验证了理论模型，并展示了脊波阈值处理在不同场景下的潜力。我们的研究结果显著增进了对泊松噪声的理解，并为受其污染的图像提供了一种有效的去噪方法。