Sparse Approximation to the Dirac-{\delta} Distribution

TL;DR

This paper introduces the POAFD method for fast sparse approximation of the Dirac delta distribution, which can enhance signal and image processing tasks by providing efficient representations.

Contribution

It proposes a novel pre-orthogonal adaptive Fourier decomposition approach for approximating the Dirac delta, improving computational efficiency and potential applications.

Findings

POAFD achieves rapid approximation of the Dirac delta.

The method offers sparse representations beneficial for signal analysis.

Potential applications include system identification and image processing.

Abstract

The Dirac-{\delta} distribution may be realized through sequences of convlutions, the latter being also regarded as approximation to the identity. The present study proposes the so called pre-orthogonal adaptive Fourier decomposition (POAFD) method to realize fast approximation to the identity. The type of sparse representation method has potential applications in signal and image analysis, as well as in system identification.