Majee Sudeb, Ray Rajendra K, Majee Ananta K
IEEE Trans Image Process. 2022;31:1963-1977. doi: 10.1109/TIP.2022.3149230. Epub 2022 Feb 18.
In this work, we propose a non-linear hyperbolic-parabolic coupled Partial Differential Equation (PDE) based model for image despeckling. Here, a separate equation is used to calculate the edge variable, which improves the quality of edge information in the despeckled images. The existence of the weak solution of the present system is achieved via Schauder fixed point theorem. We used a generalized weighted average finite-difference scheme and the Gauss-Seidel iterative technique to solve the coupled system. Numerical studies are reported to show the effectiveness of the proposed approach with respect to standard PDE-based and nonlocal methods available in the literature. Numerical experiments are performed over gray-level images degraded by artificial speckle noise. Additionally, we investigate the noise removal efficiency of the proposed algorithm when applied to real synthetic aperture radar (SAR) and Ultrasound images. Overall, our study confirms that in most cases, the present model performs better than the other PDE-based models and shows competitive performance with the nonlocal technique. To the best of our knowledge, the proposed despeckling approach is the first work that utilizes the advantage of the non-linear coupled hyperbolic-parabolic PDEs for image despeckling.
在这项工作中，我们提出了一种基于非线性双曲 - 抛物耦合偏微分方程（PDE）的图像去斑模型。在此，使用一个单独的方程来计算边缘变量，这提高了去斑图像中边缘信息的质量。通过绍德尔不动点定理证明了当前系统弱解的存在性。我们使用广义加权平均有限差分格式和高斯 - 赛德尔迭代技术来求解耦合系统。报告了数值研究结果，以表明所提出的方法相对于文献中可用的基于标准偏微分方程的方法和非局部方法的有效性。对由人工散斑噪声退化的灰度图像进行了数值实验。此外，我们研究了所提出的算法应用于真实合成孔径雷达（SAR）和超声图像时的去噪效率。总体而言，我们的研究证实，在大多数情况下，当前模型比其他基于偏微分方程的模型表现更好，并且与非局部技术相比具有竞争力。据我们所知，所提出的去斑方法是第一项利用非线性耦合双曲 - 抛物偏微分方程优势进行图像去斑的工作。
