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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]

We present a technique to recover and refine the depth map from a single image captured by a conventional camera in this paper. Our method builds on the universal imaging principle: only scene at the focus distance will converge to a single sharp point on imaging sensor but other scene will yield different blur effects varying with its distance from the camera lens. We first estimate depth values at edge locations via spectrum contrast and then recover the full depth map using a depth matting optimization method. Due to the fact that some blur textures such as soft shadows or blur patterns will produce ambiguity results during the procedure of depth estimation, we use a total variation-based image smoothing method to smooth the original image, a smoothed image with detailed texture being suppressed can be generated. Taking this smoothed image as reference image, a guided filter is used to refine the final depth map. [ABSTRACT FROM AUTHOR]

The Nyquist–Shannon sampling theorem is on the reconstruction of a band-limited signal from its uniformly sampled samples. The higher the signal bandwidth gets, the more challenging the uniform sampling may become. To deal with this problem, signal reconstruction from local averages has been studied in the literature. In this paper, we obtain an improved Nyquist–Shannon sampling theorem from general local averages. In practice, the measurement apparatus gives a weighted average over an asymmetrical interval. As a special case, for local averages from symmetrical interval, we show that the sampling rate is much lower than that of a result by Gröchenig. Moreover, we obtain two exact dual frames from local averages, one of which improves a result by Sun and Zhou. At the end of this paper, as an example application of local average sampling, we consider a reconstruction algorithm: the piecewise linear approximations. [ABSTRACT FROM AUTHOR]

The WKS sampling theorem is a fundamental result in the field of telecommunication and signal processing. It is a perfect example of the synthesis of traditionally distinct disciplines in mathematics, engineering analysis, and the sciences. The theorem recovers a bandlimited signal from its samples at uniformly points, which purpose is to analyze deterministic functions, or deterministic signals. However, there are a few counterparts of this theorem for random signals so far. This article gives a new WKS sampling principle on random signals from local averages with probability 1. [ABSTRACT FROM AUTHOR]

Abstract: This work is concerned with approximation of a signal from local averages. It improves a result of Butzer and Lei [P.L. Butzer, J. Lei, Approximation of signals using measured sampled values and error analysis, Commun. Appl. Anal. 4 (2000) 245–255]. [Copyright &y& Elsevier]