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

Pollak摘要这项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：给定一张以数字数组形式存储在计算机上的图片(例如，医学图像)，目标是设计一种算法来自动将图像分割成有意义的区域(例如，肿瘤和健康组织)。更广泛地说，这项研究的动机是许多应用-例如，在医学成像和遥感领域-其特征是图像的高复杂性和低质量(例如，由于成像过程的不完善而引起的噪声、模糊或杂乱)。从这些图像中提取和恢复对象是具有挑战性的重要问题。由于好的中间退化模型通常非常复杂甚至不可用，这些问题必须以这样一种方式来解决，即所产生的算法对退化的精确结构不敏感。然而，当精确建模成为可能时，算法应该足够灵活，以利用这一点。此外，在许多感兴趣的应用中，海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的尺度空间估计框架。它建立在最近的非线性尺度空间图像分析方法的基础上，与最优估计和滑模控制建立了重要的联系，从而产生了一维信号和二维图像的有效分割和恢复方法。对这些方法的理论分析揭示了它们的稳健性，它们对各种问题的适用性，以及它们允许快速数值格式的事实。正在研究一些实际的图像处理问题，特别是皮肤镜图像的分析(用于提高皮肤癌筛查的准确性的皮肤病变的放大图像)。

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).