Sparse Generalized Fourier Series via Collocation-based Optimization

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.

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Document Details

Document Type
Technical Report
Publication Date
Nov 01, 2014
Accession Number
ADA619307

Entities

People

  • Ashley Prater

Organizations

  • Air Force Research Laboratory

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Air Force
  • Air Force Research Laboratories
  • Classification
  • Coefficients
  • Compressed Sensing
  • Computational Complexity
  • Computations
  • Equations
  • Errors
  • Fourier Series
  • Military Research
  • Optimization
  • Pattern Recognition
  • Polynomials
  • Recognition
  • Rotation

Readers

  • Approximation Theory.
  • Computer Vision.

Technology Areas

  • AI & ML
  • AI & ML - Machine Learning Algorithms