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In this article, we consider the extension of Shannon sampling series reconstruction theorem for nonhomogeneous random fields using local averages sampling, which helps improve certain earlier results. The upper bound of mean square truncation sampling approximation error is more precise, and we establish one approximation result in the almost sure sense. [ABSTRACT FROM AUTHOR]

In this paper, we mainly investigate the average sampling problem for the homogeneous random fields in a reproducing kernel subspace of mixed Lebesgue space. Based on the counterpart sampling result for the deterministic signals in the same space, a mean square convergence result for recovering the homogeneous random fields by the iterative reconstruction algorithm is obtained. [ABSTRACT FROM AUTHOR]

In this paper, a lower bounded of sequences on classical sampling theorem for random signals is given and is used to extend the applicable range of frame. The convergence property of sampling series, the estimate of truncation error both in mean square sense and for almost sure results on sampling theorem for multidimensional random signals from asymmetrical average sampling are analyzed. Using the new results on frames recently, the famous Shannon sampling theorem on multidimensional random signals has been extended with a new idea. [ABSTRACT FROM AUTHOR]