RUI: Adaptive Kernels for Partial Differential Equation Models in Image Denoising: Construction and Algorithms

研究人员为图像去噪中的扩散PDE模型构建了自适应核，并开发了基于核的去噪算法。自适应内核是一种能够根据本地窗口内的图像内容自适应地改变其内核特征的内核。离散核滤波器是一种广泛应用于工业图像处理的滤波器；非迭代滤波器可以实现实时去噪。所提出的自适应核主要来源于PDE模型。由于Rudin-Osher-Fatemi的影响，有相当多的PDE模型用于图像去噪。在大量数值分析结果的基础上，开发了高精度、稳定的算法。然而，大多数数值偏微分方程算法涉及迭代或逆矩阵。它们是时间和/或内存消耗，因此不适合实时预处理降噪。研究者研究了一些流行的PDE模型的自适应核的构造，从这些核设计参数自适应滤波器，并开发了它们的实现算法，重点是极快的单次滤波过程。研究者创建GUI软件来执行基于核算法的降噪，这提供了一个适合工业需求的开发工具包。无限小方法是开发自适应核的主要工具。他还运用贝叶斯决策理论建立了自适应滤波器参数的最优选择规则，用于控制降噪质量。这项研究支持了国家对纳米技术和信息技术的兴趣，因为低成本安全摄像机、移动数字电视、移动视频电话对数字图像/视频的需求，所有这些都用于国土安全和国防部的应用。这项研究还影响了正在兴起的特征保留降噪技术。像网络摄像头这样的在线视频通常会产生低质量的图像。即使在低光或人造光环境中使用的高质量数码相机和摄像机也会产生噪音。保留特征的降噪技术为增强这些低质量图像提供了一种低成本的解决方案。市场上有许多类型的软件用于图像清理和计算机增强，但是移动视频和类似的产品需要可以内置到设备中的实时处理。对这些技术的安全需求非常高，特别是在美国边境地区，而解决方案的数量却很低。这个项目弥合了高度发达的理论和不发达的工业应用之间的鸿沟。

The investigator constructs adaptive kernels for diffusion PDE models in image denoising and develops kernel-based denoising algorithms. An adaptive kernel is a kernel that adaptively changes its kernel characteristics depending on the image content within a local window. Discrete kernels are filters, which are widely used in industrial image processing; and non-iterative filters can realize the real-time denoising. The proposed adaptive kernels are mainly derived from PDE models. Due to Rudin-Osher-Fatemi's influential work, there are a considerable number of PDE models for image denoising. Based on the extensive results in numerical analysis, highly accurate and stable algorithms have been developed. However, most numerical PDE algorithms involve either iteration or inverse matrices. They are time and/or memory consuming and therefore not suitable for real-time pre-processing noise reduction. The investigator studies the construction of adaptive kernels for some popular PDE models, designs parametric adaptive filters from these kernels, and develops algorithms for their implementations with emphasis on the extremely fast single-pass filter process. The investigator creates the GUI software to perform noise reduction based on the kernel-based algorithms, which provide a development kit suitable for industrial demands. The infinitesimal method is the main tool for the development of the adaptive kernels. He also applies Bayesian Decision Theory to create the rule for the optimal selection of the parameters in the adaptive filters, which are used to control the quality of noise reduction. This research support the national interest in NANOTECHNOLOGY and INFORMATION TECHNOLOGY due to the demand for digital images/videos for low-cost security cameras, mobile digital TV, cell-video phones, all of which are used for HOMELAND SECURITY and DEPARTMENT OF DEFENSE applications. The research also impacts feature-preserve noise reduction techniques, which is on the rise. On-line videos such as web-cams generally produce low-quality pictures. Even high-quality digital cameras and camcorders used in low-light or artificial-light environments produce noise. Feature-preserve noise reduction techniques provide a low-cost solution for enhancing these low-quality images. There are many types of software on the market for picture cleaning and computer enhancement, however mobile videos and similar products require real-time processing that can be built into the devices. The security demand for these techniques is very high, especially in U.S. Border areas, while the number of solutions are low. This project bridges the gulf between the highly developed theory and the underdeveloped industrial applications.