Discrete Sampling Theorem, Sinc-lets and Other Peculiar Properties of Sampled Signals

TL;DR

This paper introduces a discrete sampling theorem applicable to finite, band-limited signals in various orthogonal domains, demonstrating novel properties and applications like image super-resolution and reconstruction from projections.

Contribution

It formulates a new discrete sampling theorem and explores its implications, including the existence of signals sharply bounded in space and transform domains, with practical applications.

Findings

Successful image super-resolution from multiple chaotic samples

Existence of signals sharply bounded in space and transform domains

Introduction of Sinc-lets and peculiar properties of sampled signals

Abstract

Discrete sampling theorem is formulated that refers to discrete signals specified by a finite number of their samples and band-limited in a domain of a certain orthogonal transform. Conditions of the recoverability of such signals from their sparse samples are discussed for different transforms and applications are illustrated by examples of image super-resolution from multiple chaotically sampled frames and in image reconstruction from projections. Experimental evidence is presented of the existence of discrete signals sharply bounded both in space and DFT or DCT domains and of the family of the corresponding basis functions