In this paper, we present a telegraph diffusion model with variable exponents for image despeckling. Moving beyond the traditional assumption of a constant exponent in the telegraph diffusion framework, we explore three distinct variable exponents for edge detection. All of these depend on the gray level of the image or its gradient. We rigorously prove the existence and uniqueness of weak solutions of our model in a functional setting and perform numerical experiments to assess how well it can despeckle noisy gray-level images. We consider both a range of natural images contaminated by varying degrees of artificial speckle noise and synthetic aperture radar (SAR) images. We finally compare our method with the nonlocal speckle removal technique and find that our model outperforms the latter at speckle elimination and edge preservation.

翻译：本文提出了一种用于图像去斑的变指数电报扩散模型。该研究突破了电报扩散框架中传统恒定指数的假设，探索了三种不同的边缘检测变指数方案。这些指数均依赖于图像的灰度值或其梯度信息。我们在函数空间框架下严格证明了该模型弱解的存在唯一性，并通过数值实验评估了其对含噪灰度图像的去斑性能。实验数据涵盖不同程度人工斑纹噪声污染的自然图像集以及合成孔径雷达（SAR）图像。最终，我们将本方法与经典的非局部去斑技术进行对比，发现所提模型在斑纹消除与边缘保持方面均表现出更优的性能。