Statistical Signal Processing and Estimation for Spatial andMultidimensional Data: Multiresolution Methods, Efficient Algorithms and Geometric Reconstruction

空间和多维数据的统计信号处理和估计：多分辨率方法、高效算法和几何重建

基本信息

批准号：
9015281
负责人：
Alan Willsky
金额：
$ 19.5万
依托单位：
Massachusetts Institute of Technology
依托单位国家：
美国
项目类别：
Continuing grant
财政年份：
1991
资助国家：
美国
起止时间：
1991-03-15 至 1994-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=9015281&HistoricalAwards=false
关键词：
Statistical Signal Processing Estimation Spatial

项目摘要

Willsky There are three major components of this research program which has as its overall objective the development of new classes of algorithms for statistical signal processing and estimation of spatial and multidimensional data. The first is the development of statistical models and methods for multiscale signal analysis and processing in one and several dimensions. Problems that are being addressed include the development of a statistical counterpart to the emerging theory of multiresolution signal decompositions and wavelet transforms, the investigation of iterative, multigrid signal processing algorithms, and applications of these methods to topics ranging from inverse reconstruction problems to problems of signal or image segmentation. The second is the development of efficient algorithms for processing spatial data. This topic focuses on the exploitation of the structure of noncausal models, such as those described by partial difference equations or Markov random fields, in order to develop extremely efficient and highly parallel algorithms. Specific problems being investigated include the employment of radially inward and outward recursions for multidimensional signal processing, parallel processing structures based on spatial partitioning of multidimensional signal processing, and the development of efficient algorithms for tracking motion and other temporal changes in space-time random fields. The third is the development of statistical methods for estimating or reconstructing geometric features in multidimensional data given uncertain measurements of various quantities, such as the support of a convex object in 2-D or 3-D, or the 2-D silhouette of 3-D objects.

Willsky该研究计划的三个主要组成部分是其总体目标，即用于统计信号处理以及空间和多维数据估计的新算法的开发。首先是开发一个和几个维度的多尺度信号分析和处理的统计模型和方法。正在解决的问题包括开发与多分辨率信号分解和小波变换的新兴理论的发展，对迭代，多机信号处理算法的调查以及这些方法的应用以及主题，从反相反的问题到信号问题的主题或图像分割。第二个是开发用于处理空间数据的有效算法。该主题着重于对非因果模型的结构的开发，例如部分差异方程或马尔可夫随机场所描述的结构，以开发出极其有效且高度平行的算法。正在研究的具体问题包括用于多维信号处理的径向内和外部递归，基于多维信号处理的空间分配以及用于跟踪运动运动的有效算法的开发以及空间随机场中的其他时间变化的发展。第三是开发用于在多维数据中估算或重建几何特征的统计方法，其中不确定了各种数量的测量，例如2-D或3-D中的凸对象的支持，或3--的2-D Silhouette的2-D Silhouette D对象。