Nonuniform average sampling in multiply generated shift-invariant subspaces of mixed Lebesgue spaces

Abstract

In this paper, we study nonuniform average sampling problem in multiply generated shift-invariant subspaces of mixed Lebesgue spaces. We discuss two types of average sampled values: average sampled values $\{⟨f,{\psi }_a(\cdot -x_j,\cdot -y_k)⟩:j,k\in \mathbb{J}\}$ generated by single averaging function and average sampled values $\left\{⟨f,{\psi }_{x_j,y_k}⟩:j,k\in \mathbb{J}\right\}$ generated by multiple averaging functions. Two fast reconstruction algorithms for this two types of average sampled values are provided.

16 pages. arXiv admin note: text overlap with arXiv:1801.05715