Generalized Sampling in Julia

TL;DR

This paper introduces a Julia toolbox for generalized sampling, enabling stable signal reconstruction in various bases, with performance advantages over MATLAB implementations, especially for large-scale problems.

Contribution

The paper presents a new Julia toolbox for generalized sampling, optimized for large problems and includes specialized Fourier and wavelet solutions.

Findings

Julia toolbox offers improved performance over MATLAB implementations.

The toolbox effectively handles large-scale generalized sampling problems.

Specialized solutions for Fourier bases and wavelets are included.

Abstract

Generalized sampling is a numerically stable framework for obtaining reconstructions of signals in different bases and frames from their samples. In this paper, we will introduce a carefully documented toolbox for performing generalized sampling in Julia. Julia is a new language for technical computing with focus on performance, which is ideally suited to handle the large size problems often encountered in generalized sampling. The toolbox provides specialized solutions for the setup of Fourier bases and wavelets. The performance of the toolbox is compared to existing implementations of generalized sampling in MATLAB.