Nonlinear Least Squares in RN

被引：13

作者：

Aldroubi, Akram ^{[1
]}

Zaringhalam, Kourosh ^{[1
]}

机构：

[1] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

来源：

ACTA APPLICANDAE MATHEMATICAE | 2009年 / 107卷 / 1-3期

基金：

美国国家科学基金会;

关键词：

Signal modeling; Signal processing; Image processing; Compressed sampling; Compressed sensing; ROBUST UNCERTAINTY PRINCIPLES; OVERCOMPLETE DICTIONARIES; FINITE RATE; RECONSTRUCTION; SIGNALS; SEGMENTATION; INNOVATION;

D O I：

10.1007/s10440-008-9398-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Recent research and new paradigms in mathematics, engineering, and science assume nonlinear signal models of the form M = (i is an element of I) V-i consisting of a union of subspaces Vi instead of a single subspace M = V. These models have been used in sampling and reconstruction of signals with finite rate of innovation, the Generalized Principle Component Analysis and the subspace segmentation problem in computer vision, and problems related to sparsity, compressed sensing, and dictionary design. In this paper, we develop an algorithm that searches for the best nonlinear model of the form M = (sic)(i=1)(l) V-i subset of R-N that is optimally compatible with a set of observations F = {f(1), ... , f(m)} subset of R-N. When l = 1 this becomes the classical least squares optimization. Thus, this problem is a nonlinear version of the least squares problem. We test our algorithm on synthetic data as well as images.

引用

页码：325 / 337

页数：13

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