Generalized sampling is a numerically stable framework for obtaining reconstructions of signals in different bases and frames from their samples. For example, one can use wavelet bases for reconstruction given frequency measurements.In this paper, we will introduce a carefully documented toolbox for performing generalized sampling in Julia. Julia is a new language for technical computing with focus on performance, which is ideally suited to handle the large size problems often encountered in generalized sampling. The toolbox provides specialized solutions for the setup of Fourier bases and wavelets.The performance of the toolbox is compared to existing implementations of generalized sampling in MATLAB.
We introduce new estimation methods for a sub-class of the Gaussian scale mixture models for wavelet trees by Wainwright, Simoncelli & Willsky that rely on modern results for composite likelihoods and approximate Bayesian inference. Our methodology is illustrated for denoising and edge detection problems in two-dimensional images.
Robert Jacobsen, Bd. 1: Biographische Skizzen, hrsg. vom Museum Würth durch Lothar Romain undC. Sylvia Weber, Sigmaringen (Thorbecke) 1992, 119 S.
Robert Jacobsen, Bd. 2: Werke aus 50 Jahren, hrsg. vom Museum Würth durch Lothar Romain und C. Sylvia Weber, Sigmaringen (Thorbecke) 1992, 135 S.
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