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

维尔斯基 有三个主要组成部分，这个研究计划的总体目标是开发新的算法类的统计信号处理和估计的空间和多维数据。 第一个是在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的发展。 正在解决的问题，包括发展的统计对应的新兴理论的多分辨率信号分解和小波变换，迭代，多重网格信号处理算法的调查，以及这些方法的应用范围从逆重建问题的问题，信号或图像分割的主题。 第二是开发处理空间数据的有效算法。 本主题的重点是利用非因果模型的结构，如偏差分方程或马尔可夫随机场描述的，以开发非常有效和高度并行的算法。 正在调查的具体问题包括就业的径向向内和向外递归多维信号处理，并行处理结构的基础上，空间分区的多维信号处理，并制定有效的算法跟踪运动和其他时间变化的时空随机场。 第三是发展统计方法，用于估计或重建多维数据中的几何特征，给出各种数量的不确定测量，例如2-D或3-D中凸对象的支持，或3-D对象的2-D轮廓。

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.