Accession Number : ADA619307


Title :   Sparse Generalized Fourier Series via Collocation-based Optimization


Descriptive Note : Conference paper


Corporate Author : AIR FORCE RESEARCH LAB ROME NY INFORMATION DIRECTORATE


Personal Author(s) : Prater, Ashley


Full Text : https://apps.dtic.mil/dtic/tr/fulltext/u2/a619307.pdf


Report Date : Nov 2014


Pagination or Media Count : 10


Abstract : 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.


Descriptors :   *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


Subject Categories : Numerical Mathematics


Distribution Statement : APPROVED FOR PUBLIC RELEASE