Random Sampling Using Shannon Interpolation and Poisson Summation Formulae

TL;DR

This paper presents a method for random sampling recovery using Shannon interpolation and Poisson summation, introducing efficient matrix filling techniques and demonstrating results on various signals.

Contribution

It introduces a fast matrix filling technique based on Shannon interpolation and Poisson summation for random sampling recovery, with practical implementation and numerical validation.

Findings

Effective recovery of various signals demonstrated

Efficient matrix filling technique developed

Potential for future theoretical and practical applications

Abstract

This report mainly focused on the basic concepts and the recovery methods for the random sampling. The recovery methods involve the orthogonal matching pursuit algorithm and the gradient-based total variation strategy. In particular, a fast and efficient observation matrix filling technique was implemented by the classic Shannon interpolation and Poisson summation formulae. The numerical results for the trigonometric signal, the Gaussian-modulated sinusoidal pulse, and the square wave were demonstrated and discussed. The work may give some help for future work in theoretical study and practical implementation of the random sampling.