Reconstruction of functions in principal shift-invariant subspaces of mixed Lebesgue spaces

TL;DR

This paper presents a fast algorithm for reconstructing functions in principal shift-invariant subspaces of mixed Lebesgue spaces from nonuniform samples, improving previous results in the field.

Contribution

It introduces a new reconstruction algorithm that guarantees exact recovery under certain sampling density conditions, advancing the theory of sampling in mixed Lebesgue spaces.

Findings

The algorithm enables exact reconstruction with sufficiently dense sampling sets.

It improves upon previous results in nonuniform sampling in mixed Lebesgue spaces.

The method is efficient and applicable to a broad class of functions.

Abstract

In this paper, we discuss to the nonuniform sampling problem in principal shift-invariant subspaces of mixed Lebesgue spaces. We proposed a fast reconstruction algorithm which allows to exactly reconstruct the functions in the principal shift-invariant subspaces as long as the sampling set $X=\{(x_{j},y_{k}):k,j\in \mathbb{J}\}$ is sufficiently dense. Our results improve the result in \cite{LiLiu}.