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Sparse Generalized Fourier Series via Collocation-based Optimization.

机译：基于配置优化的稀疏广义Fourier级数。

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摘要

Generalized Fourier series with orthogonal polynomial bases have useful applications in several fields, including differential equations, pattern recognition, and image and signal processing. However, computing the generalized Fourier series can be a challenging problem, even for relatively well behaved functions. In this paper, a method for approximating a sparse collection of Fourier - like coefficients is presented that uses a collocation technique combined with an optimization problem inspired by recent results in compressed sensing research. The discussion includes approximation error rates and numerical examples to illustrate the effectiveness of the method. One example displays the accuracy of the generalized Fourier series approximation for several test functions, while the other is an application of the generalized Fourier series approximation to rotation - invariant pattern recognition in images.

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作者
Prater, A.;
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年度 2014
页码 1-10
总页数 10
原文格式 PDF
正文语种 eng
中图分类工业技术;
关键词
Fourier series; Optimization; Polynomials; Coefficients; Computerized simulation; Differential equations; Experimental design; Feature extraction; Gaussian noise; Invariance; Linear regression analysis; Multivariate analysis; Pattern recognition; Signal processing; Special functions(mathematics); Test and evaluation; Vector analysis; Generalized fourier series; Orthogonal polynomials; Hermite polynomials; Rotation invariant pattern recognition; L1 minimization; Sparse recovery; Pe62788f; Wuafrl93sfinho;

机译：傅里叶级数;优化;多项式;系数;计算机模拟;微分方程;实验设计;特征提取;高斯噪声;不变性;线性回归分析;多变量分析;模式识别;信号处理;特殊函数（数学）;测试与评估;向量分析;广义Fourier级数;正交多项式; Hermite多项式;旋转不变模式识别; L1最小化;稀疏恢复; pe62788f; Wuafrl93sfinho;

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专利

1. Laplacian singular spectrum associated to the canonical metric on P-1 and the theory of the series of generalized Bessel-Fourier series [J] . Hajli Mounir Journal de Mathematiques Pures et Appliquees . 2015,第2期

机译：与P-1上的规范度量相关的Laplacian奇异谱和广义Bessel-Fourier级数序列的理论
2. Approximation of functions belonging to the generalized Lipschitz class by $C^1cdot N_p$ summability method of conjugate series of Fourier series [J] . V. N. Mishra, K. Khatri, L. N. Mishra Matematicki Vesnik . 2014,第2期

机译：傅立叶级数共轭级数的$ C ^ 1 cdot N_p $可加性方法逼近广义Lipschitz类的函数
3. On the trigonometric approximation of signals belonging to generalized weighted Lipschitz W(L~r, ξ(t))(r ≥ 1)-class by matrix (C~1 · N_p) operator of conjugate series of its Fourier series [J] . Lakshmi Narayan Mishra, Vishnu Narayan Mishra, Kejal Khatri, Applied mathematics and computation . 2014,第Null期

机译：用傅立叶级数共轭系列的矩阵（C〜1·N_p）算子对属于广义加权Lipschitz W（L〜r，ξ（t））（r≥1）类的信号进行三角逼近
4. Sparse generalized Fourier series via collocation-based optimization [C] . Prater Ashley IEEE Applied Imagery Pattern Recognition Workshop . 2014

机译：通过基于搭配的优化实现稀疏广义傅里叶级数
5. FUNCTIONS OF GENERALIZED BOUNDED VARIATION AND FOURIER SERIES. [D] . ISAZA, PEDRO. 1986

机译：广义有界变化和傅里叶级数的函数。
6. On the Approximation of Generalized Lipschitz Function by Euler Means of Conjugate Series of Fourier Series [O] . Jitendra Kumar Kushwaha 2013

机译：傅立叶级数共轭级数的欧拉均值逼近广义Lipschitz函数
7. Sparse generalized Fourier series via collocation-based optimization [O] . Prater, Ashley 2015

机译：基于配置优化的稀疏广义Fourier级数

Sparse Generalized Fourier Series via Collocation-based Optimization.

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