Fast local reconstruction methods for nonuniform sampling in shift-invariant spaces

作     者：Gröchenig, K Schwab, H 

作者机构：Univ Connecticut Dept Math Storrs CT 06269 USA Univ Vienna Dept Math NUHAG A-1090 Vienna Austria 

出 版 物：《SIAM JOURNAL ON MATRIX ANALYSIS AND APPLICATIONS》 (工业与应用数学会矩阵分析和应用杂志)

年 卷 期：2003年第24卷第4期

页      面：899-913页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：shift-invariant space nonuniform sampling banded matrix localization data segmentation denoising 

摘      要：We present a new method for the fast reconstruction of a function f from its samples f(x(j)) under the assumption that f belongs to a shift-invariant space V (phi). If the generator phi has compact support, then the reconstruction is local, quite in contrast to methods based on band-limited functions. Using frame theoretic arguments, we show that the matrix of the corresponding linear system of equations is a positive-definite banded matrix. This special structure makes possible the fast local reconstruction algorithm in O(S(2)J) operations, where J is the number of samples and S is the support length of the generator phi. Further optimization can be achieved by means of data segmentation. Ample numerical simulation is provided.