Average sampling in mixed shift-invariant subspaces with generators in hybrid-norm spaces

This paper mainly studies the average sampling and reconstruction in shift-invariant subspaces of mixed Lebesgue spaces $L^{p,q}(\mathbb{R}^{d+1})$, under the condition that the generator $\varphi$ of the shift-invariant subspace belongs to a hybrid-norm space of mixed form, which is weaker than the usual assumption of Wiener amalgam space and allows to control the orders $p,q$. First, the sampling stability for two kinds of average sampling functionals are established. Then, we give the corresponding iterative approximation projection algorithms with exponential convergence for recovering the time-varying shift-invariant signals from the average samples.

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

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 [Formula: see text] generated by single averaging function and average sampled values [Formula: see text] generated by multiple averaging functions. Two fast reconstruction algorithms for these two types of average sampled values are provided.