Variational PDE Models and Computational Methods in Image Processing

Chan9973341研究员和他的同事研究了在将变分和偏微分方程方法应用于图像处理问题时出现的建模和计算问题，并开发了有效的新算法。这些问题是计算密集型的，需要准确有效的方法。他们考虑了基于全变分的对偶图像复原方法、多通道图像的盲解卷积方法、边缘锐化图像的ENO小波压缩方法、简化的Mumford-Shah模型和多通道扩展图像复原与分割方法以及新的无边缘停止的活动轮廓模型。课程包括图像恢复、压缩、多光谱图像、分割和活动轮廓。在医学和化学成像、天文成像和多光谱自动目标识别方面的应用也在不断追求。图像处理跨越了工程学科、物理和医学科学。在医学和生物技术领域的应用范围从计算机断层扫描到分子结构的微观图像处理。在环境领域，卫星成像已被用于绘制自然资源和环境污染地图。在制造领域，成像系统被用来自动检测缺陷。在所有这些应用中，一个关键的过程是图像恢复，即清除被噪声和模糊污染的图像。这是这个项目的中心主题。由于大量的像素和可能的图像序列(例如视频)，这些问题是非常计算密集的。解决这些问题需要聪明的数学算法和高性能的计算机。除此之外，在当前的通信革命和信息高速公路的使用中，正在传输更多的图像，需要更好的数学算法来压缩和消除传输中出现的噪声和其他失真。

Chan9973341 The investigator and his colleaques study modeling and computational questions that arise in applying variational and partial differential equation methods to problems of image processing, and they develop effective new algorithms. These problems are computationally intensive and accurate and efficient methods are needed. They consider dual methods for image restoration by total variation, blind deconvolution of multi-channel images, ENO-wavelet compression of images with sharp edges, reduced Mumford-Shah models and multi-channel extensions for image restoration and segmentation, and new active contour models without edge-stopping. Topics of study include image restoration, compression, multispectral images, segmentation, and active contours. Applications in medical and chemical imaging, astronomical imaging, and multispectral automatic target recognition are pursued. Image processing arises across engineering disciplines and the physical and medical sciences. Applications in the medical sciences and biotechnology field range from computer tomography to processing of microscopic images of molecular structures. In the enviromental area, satellite imaging has been used to map natural resources as well as enviromental pollution. In the area of manufacturing, imaging systems are used to detect defects automatically. In all of these applications, a key process is that of image restoration, namely, cleaning up an image polluted by noise and blurring. This is a central subject of this project. These problems are very computationally intensive due to the large number of pixels and the possibility of sequences of images (e.g. videos). Solving them requires clever mathematical algorithms as well as high performance computers. Beyond this, in the current revolution in commmunication and the use of the information highway, more images are being transmitted and better mathematical algorithms are needed to compress and remove noise and other distortions occuring in the transmission.