CAREER: Robust and Efficient Restoration and Segmentation of Signals and Images: A Non-linear Scale-Space Approach

波拉克摘要本研究解决了从数字信号和图像中提取信息的各种问题。 一个典型的例子是图像分割：给定一张存储在计算机上的数字数组（例如，医学图像），目的是设计一种算法来自动地将图像分割成有意义的区域（例如，进入肿瘤和健康组织）。 更一般地说，这项研究是由许多应用的动机-例如，在医学成像和遥感领域-其特点是高复杂性和低质量的图像（由于，例如，噪声，模糊，或杂波，这是由成像过程的不完善引起的）。 由于良好的模型的干预退化往往是非常复杂的，甚至是不可用的，这些问题必须解决的方式，所得到的算法是不敏感的退化的精确结构。 然而，当精确建模成为可能时，算法应该足够灵活以利用它。此外，在许多感兴趣的应用中，大量的数据使得快速的方法特别有价值。本项目正在开发一种适用于此类问题的新型尺度空间估计框架。 建立在最近的非线性尺度空间方法的图像分析的基础上，它与最优估计和滑动模式控制建立了重要的联系，从而产生了有效的方法来分割和恢复1-D信号和2-D图像。 这些方法的理论分析揭示了它们的鲁棒性，它们对广泛问题的适用性，以及它们承认快速数值方案的事实。 正在研究一些实际的图像处理问题，特别是皮肤镜图像（用于提高皮肤癌筛查准确性的皮肤病变放大图片）的分析。

Pollak ABSTRACTThis research addresses various problems of extracting information from digital signals and images. A prototypical example is that of image segmentation: given a picture stored on a computer as an array of numbers (e.g., a medical image), the objective is to design an algorithm to automatically partition the image into meaningful regions (e.g., into a tumor and healthy tissue). More generally, this research is motivated by many applications---for example, in the areas of medical imaging and remote sensing---which are characterized by high complexity and poor quality of images (due to, for instance, noise, blurring, or clutter, which are caused by imperfections of the imaging process).Extracting and restoring objects from such images are challenging and important problems. Since good models of the intervening degradations are often very complex or even unavailable, these problems must be addressed in such a way that the resulting algorithms are insensitive to the precise structure of degradations. When precise modeling is possible, however, the algorithms should be flexible enough to take advantage of it. In addition, the large quantity of data in many applications of interest makes methods that are fast particularly valuable.This project is developing develop a novel scale-space estimation framework applicable to such problems. Built on the foundation of recent non-linear scale-space approaches to image analysis, it is making important links with optimal estimation and sliding-mode control, thereby producing efficient methods for segmentation and restoration of 1-D signals and 2-D images. Theoretical analysis of these methods reveals their robustness, their applicability to a wide range of problems, and the fact that they admit fast numerical schemes. A number of practical image processing problems are being pursued, in particular, analysis of dermatoscopic imagery (magnified pictures of skin lesions used to improve the accuracy of screening for skin cancer).