Robustness Of Sampling And Reconstruction In High Dimensional Mixed Lebesgue Spaces

Sampling theory is not only the theoretical basis of modern communication system but also one of the powerful basis tools in signal analysis.The stability of the sampling and re-construction determines whether the signal can be recovered accurately from its sample.In this paper,we study the robustness of nonuniform sampling and reconstruction in high dimensional mixed Lebesgue spaces （?）.First,based on the two existing non-uniform sampling methods in the classical Lebesgue space （?）,we discuss the robustness of the generator and sampling function in the mixed Lebesgue translation invariant subspaces （?）.Then,we study the robustness of generator and sampling in translation invariant subspace （?）for two more general average sampling methods.