Mathematical Sciences: Statistical Methods for Incomplete and Biased Data with New Applications

数学科学：不完整和有偏差数据的统计方法及其新应用

• 批准号: 9123166
• 负责人: Yehuda Vardi
• 金额: $ 11万
• 依托单位: Rutgers University New Brunswick
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-08-15 至 1996-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9123166&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Statistical; Methods; Incomplete

The problem of recovering an input signal from a blurred output, in an input-output system with linear distortion, is ubiquitous in science and technology. When the blurred output is not corrupted by statistical noise, the problem is entirely deterministic and amounts to a mathematical inversion of a linear system with positive parameters, subject to positivity con- straints on the solution. By showing that all such linear inverse problems with positivity constraints can be interpreted as statistical estimation problems, extremely simple algorithms can be developed for finding the problems' maximum likelihood solutions. Extensions to specific problems like noise degrada- tion, estimation of blurring parameters (parameters of the point spread function) and regularization techniques will follow. The methodology will be applied to new problems including restoration of images blurred by relative motion between the subject and the camera lens. The blurring of a signal (sound, image, etc.) is common in science and technology, for example the systematic distort observed signal becomes what mathematicians call linear inverse problems with positivity constraints. This research will develop methods of solution which are broadly applicable to such problems. The basis for this approach is to draw on statistical principles and exploit the connection between such linear inverse problems and statistical estimation problems for incomplete data where methods already exist.

从模糊的输入信号中恢复输入信号的问题 在具有线性失真的输入-输出系统中，输出为 在科学和技术中无处不在。 当模糊输出为 不受统计噪声的影响，问题完全在于 确定性和金额的数学反演的线性 系统具有正参数，受正性约束， 对解决方案的约束。 通过证明所有这些线性的 具有正性约束的反问题可以解释为 作为统计估计问题， 可以用来寻找问题的最大可能性 解决方案 针对特定问题的扩展，如噪声退化， 模糊参数（点的参数）的估计 扩展函数）和正则化技术。 的 方法将适用于新的问题，包括恢复 图像模糊的相对运动之间的主题和 照相机透镜。 信号（声音、图像等）的模糊常见于 科学和技术，例如系统的扭曲， 观测到的信号变成了数学家所说的线性逆 积极性约束的问题。 这项研究将发展 解决方案的方法，广泛适用于这些 问题 这种方法的基础是利用统计数据， 原理，并利用这种线性逆之间的联系， 不完全数据的统计估计问题 方法已经存在。