Mathematical Sciences: Statistical Methods in Image Processing

本项目涉及图像处理一般领域中的三个相关问题。首先是Gibbs Ssamer和Metropolis动态算法的效率显著提高，不再将算法限制在局部有界的图像空间。第二种方法是为暗盘的天文图像数据开发一种特殊的估计方法，其中数据具有显著的模糊性(例如，哈勃望远镜数据)。这里，使用适当的低维线性函数提高了效率。第三种是利用马尔可夫随机场模型进行数据压缩，对原始大图像进行细分，形成最优的代表子图像。当只有质量较差的图像数据可用时，统计图像分析使用统计原理来“猜测”真实图像。特定算法的质量取决于所选择的“猜测”有多好以及实现的速度有多快。这个项目专注于通过尝试获取最相关的信息来提高算法的速度，而不是一次处理整个图像。

This project deals with three related problems in the general area of image processing. The first is a dramatic increase in the efficiency of the Gibbs Sampler and Metropolis Dynamic algorithms from restricting the algorithms to a locally bounded image space. The second develops a special estimation method for astronomical image data of a faint disk, where the data has significant blur (e.g., Hubble telescope data). Here the use of a suitable lower dimensional linear function improves efficiency. The third addresses data compression using a Markov random field model and subdividing the original large image and forming optimal representative subimages. Statistical image analysis uses statistical principles to "guess" the real image when only poor quality image data is available. The quality of a particular algorithm is depends upon how good the chosen "guess" is and how quickly it is achieved. This project focusses on increasing the speed of the algorithms by trying to get the most pertinent information rather than working on the whole image at once.