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 ${\left \langle f,\psi_{a}(\cdot-x_{j},\cdot-y_{k}) \right \rangle:j,k\in$\mathbb{J}$}$generatedbysingleaveragingfunctionandaveragesampledvalues$\left{\left \langle f,\psi_{x_{j},y_{k}}\right \rangle:j,k\in$\mathbb{J}$\right}$ generated by multiple averaging functions. Two fast reconstruction algorithms for this two types of average sampled values are provided.