CIF: Small: Multidimensional Signal Processing With Box Splines

CIF：小：使用箱形样条进行多维信号处理

• 批准号: 1018149
• 负责人: Alireza Entezari
• 金额: $ 33.43万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-01 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1018149&HistoricalAwards=false
• 关键词: CIF; Small; Multidimensional; Signal; Processing; CIF; Small; Multidimensional; Signal; Processing

AbstractThis research develops a novel framework for interpolation and approximation of multivariate data.The research introduces a method for construction of non-separable multivariate splines that are geometricallytailored for general sampling lattices with emphasis on sphere packing and covering latticesin multidimensions. These multivariate splines lead to the design of multidimensional signal processingtools, that have proven degree of continuity and approximation order for sampling lattices.The splines under investigation, called Voronoi splines, are B-spline-like elements that inherit thegeometry of any sampling lattice from its Voronoi cell and form basis for reconstruction. Furthermore,the relationship of the proposed splines with the well-known multivariate box splines are investigatedand used for evaluation purposes. Compared to other polyhedral splines, Voronoi splines form shiftinvariantspaces for approximation. This property makes them uniquely suitable for multidimensionalsignal processing.

摘要这项研究开发了一个新型的插值和近似多元数据的框架。该研究介绍了一种构建不可分离的多元花样条的方法，该方法是对一般采样晶格的几何绘制，重点是对球体包装的一般抽样，并覆盖了多维的lattices。这些多元键素导致了多维信号处理工具的设计，这些晶状体已被证明具有连续性和近似顺序，用于采样晶格。所调查的花键称为voronoi spline，是b-spline的类似B-Spline类似的元素，可继承其voronoi Cell和Recontruction的任何采样lattice lattice lattice lattice lattice lattice的几何。此外，研究了所提出的花键与众所周知的多元盒子花键的关系，并用于评估目的。与其他多面体花纹相比，Voronoi花纹形成shiftInvariantSpaces以进行近似。此属性使它们独特地适合多维分子认证处理。