CAREER: An Integrated Study of Image Estimation and Compression Problems

该项目的主要目标是开发一种分析的、多学科的方法来研究和教育图像处理，整合通常单独处理的工程问题的重要方面。特别是，本研究结合了图像数据和物理传感器的现实统计模型，并寻求基于基本统计原理的估计和压缩问题的解决方案。该项目的教育部分旨在通过培养学生的多学科和分析技能，并使他们接触复杂工程问题的多个方面，为他们的工程事业做好更好的准备。这个主题体现在这个项目的各个层面：首先，鼓励有积极性的本科生参与研究。其次，本科图像和视频处理课程和实验练习可以让学生学习，可视化和吸收基本概念。第三，开设高级研究生统计图像处理课程，目的是整合、应用和巩固信息论、估计理论和统计光学的概念。第四，正在开发一个交互式虚拟图像处理实验室，作为两个远程学习项目的一部分。该项目的研究部分解决了图像恢复和压缩中的关键问题，并量化了使用更精确和更复杂的模型可能带来的好处。所开发的方法也适用于病态统计逆问题，如合成孔径雷达成像、天文成像和断层扫描。复杂性正则化理论在这一研究中起着核心作用。复杂性正则化估计量本质上是压缩形式的，在这种情况下，研究了估计性能与率失真理论之间的基本关系。此外，正在开发用于优化几种图像编码系统的操作率失真性能的新技术。

The main goal of this project is to develop an analytical, multidisciplinary approach to research and education in Image Processing, integrating important aspects of engineering problems that are often treated separately. In particular, this study incorporates realistic statistical models for image data and physical sensors, and seeks solutions to estimation and compression problems based upon fundamental statistical principles. The educational component of this project aims at better preparing students for their engineering careers by developing their multidisciplinary and analytical skills, and exposing them to multiple facets of complex engineering problems. This theme is present at all levels of this project: Firstly, motivated undergraduate students are encouraged to participate in the research. Secondly, an undergraduate Image and Video Processing course and laboratory exercises allow the students to learn, visualize and assimilate fundamental concepts. Thirdly, an advanced graduate Statistical Image Processing course is being developed with the objective of integrating, applying and solidifying concepts taught in Information Theory, Estimation Theory, and Statistical Optics. Fourthly, an interactive, virtual Image Processing lab is being developed as part of two Distance Learning projects. The research component of this project addresses key problems in image restoration and compression and quantifies the benefits that may result from the use of more accurate and sophisticated models. The methodology developed is also applicable to ill-posed statistical inverse problems such as Synthetic Aperture Radar imaging, astronomical imaging, and tomography. Complexity regularization theory plays a central role in this research. Complexity-regularized estimators are inherently in compressed form, and fundamental relationships between estimation performance and rate-distortion theory are explored in that context. Additionally, novel techniques for optimizing for optimizing the operational rate-distortion performance of several image coding systems are being developed.