改进经典去噪模型，有效减少图像阶梯效应。
Adaptive double-phase Rudin--Osher--Fatemi denoising model
- 引入自适应双阶段正则项，融合总变差与二次加权项
- 在多种噪声水平下，保持边缘同时显著降低阶梯效应
- 适合科学成像等需保真度与视觉质量的场景
尽管鲁丁-奥斯勒-法蒂（ROF）模型提出已逾30年，其在天文成像等科学应用中仍具重要价值。然而该模型存在阶梯效应等伪影问题。近年来，数学分析领域兴起双相问题研究，一种结合总变差（TV）与带权重的二次增长项的双相积分泛函被提出作为图像恢复的正则化器。本文在此基础上，提出一种自适应的ROF去噪模型变体。该模型旨在减轻经典ROF模型的阶梯效应，同时保留图像边缘特征。我们在合成图像和自然图像上，对多种噪声水平进行了实验测试。结果表明，相比具有类似可解释性的已有模型，在SSIM、PSNR和LPIPS等相似性指标上表现相当或更优，且阶梯效应明显降低。
原文摘要 · Abstract (English)
Even though more than 30 years have passed since the seminal Rudin--Osher--Fatemi (ROF) paper on total variation (TV) denoising, it remains relevant, in particular in scientific applications such as astronomical imaging. However, it is known to suffer from artifacts such as the staircasing effect. Many variants of the model have been proposed with the aim of countering this. Recently, against the backdrop of immense research output on double-phase problems in the mathematical analysis community, a double-phase type integral functional, comprising of TV and a weighted term of quadratic growth, was suggested as a regularizer for image restoration. Here, we propose an adaptive variant of the ROF denoising model based on that regularizer. It is designed to reduce staircasing with respect to the classical ROF model, while preserving the edges of the image in a similar fashion. We implement the model and test its performance on synthetic and natural images over a range of noise levels. Compared to {established} models {with similar interpretability to ROF}, we observe an improved or similar performance in terms of similarity metrics SSIM, PSNR, {and LPIPS}, while the staircasing effect is visibly reduced.
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