Estimation and Signal Processing for Spatial Data: Efficient Algorithms, Inverse Problems, and Computational Vision and Geometry

空间数据的估计和信号处理：高效算法、反问题以及计算视觉和几何

• 批准号: 8700903
• 负责人: Alan Willsky
• 金额: $ 40.99万
• 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: 1987
• 资助国家: 美国
• 起止时间: 1987-08-01 至 1991-01-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8700903&HistoricalAwards=false
• 关键词: Estimation; Signal; Processing; Spatial; Data

This research focuses on estimation and signal processing for spatial data. Three major areas are considered. The first deals with efficient algorithms for the processing of spatial data. Problems to be addressed include (i) the employment of novel notions of recursion as well as spatial decompositions to develop recursive and highly parallel algorithms for the estimation of 2-D processes described by noncausal models and for other 2-D digital filtering applications; and (ii) the exploitation of the symmetries present in some classes of random fields (e.g. isotropic fields) to develop efficient procedures for recursive and spectral estimation. The second deals with the development of algorithms for inverse and signal reconstruction problems in several dimensions. Among the problems to be investigated are (i) the development of efficient and generalized-tomographic methods for exact and approximate solution of 2-D and 3-D inverse scattering problems; and (ii) the development of system- identification-based approaches to inverse problems with particular emphasis on algorithms that work at multiple spatial scales. The third area deals with computational vision and geometry. A number of research problems are described including (i) the development of estimation-based algorithms for problems of computational vision such as motion and depth estimation; and (ii) the investigation of system and estimation-theoretic formulations of problems in computational geometry such as the reconstruction of objects given uncertain measurements of various quantities such as the support of a convex object, its silhouette, its interior, etc. This research focuses on estimation and signal processing for spatial data. The three major areas considered are (i) efficient algorithms for the processing of spatial data (ii) the development of algorithms for inverse and signal reconstruction problems in two and three dimensions and (iii) questions related to computational vision and geometry.

本研究的重点是估计和信号处理， 空间数据 考虑了三个主要领域。 第一部分涉及 空间数据处理的有效算法。 问题要 （一）使用新的递归概念 以及空间分解，以开发递归和高度 并行算法的估计2-D过程描述的 非因果模型和其他2-D数字滤波应用; (ii)利用存在于某些类的对称性， 随机场（例如各向同性场），以制定有效的程序 用于递归和谱估计。 第二个问题涉及 反求和信号重构算法的开发 几个方面的问题。 在有待调查的问题中， （一）发展高效、通用的层析成像技术 二维和三维反演的精确和近似解法 散射问题;及（ii）系统的发展- 基于识别的方法来反问题与特定的 强调在多个空间尺度上工作的算法。 的 第三个领域涉及计算视觉和几何。 一些 研究的问题，包括（一）发展 基于估计的算法的计算视觉问题， 作为运动和深度估计;以及（ii）系统的调查 计算问题的估计理论公式 几何学，如物体的重建， 各种量的测量，如凸的支撑， 物体、其轮廓、其内部等。 本研究的重点是估计和信号处理， 空间数据 考虑的三个主要方面是：（i）效率 算法的空间数据处理（二）的发展 算法的逆和信号重建问题，在两个和 三个维度和（iii）与计算视觉有关的问题 和几何学