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Titlebook: Compressed Sensing and its Applications; Second International Holger Boche,Giuseppe Caire,Rudolf Mathar Book 2017 Springer International Pu

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Weak Phase Retrieval,e equivalent. In this paper, we make a detailed study of a weakening of these concepts to weak phase retrieval and weak phaseless reconstruction. We will give several necessary and/or sufficient conditions for frames to have these weak properties. We will prove three surprising results: (1) Weak pha
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A Randomized Tensor Train Singular Value Decomposition,r matrices, it provides a fundamental but expensive tool for tensor computations. In the present work, we examine generalizations of randomized matrix decomposition methods to higher-order tensors in the framework of the hierarchical tensor representation. In particular we present and analyze a rand
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Versatile and Scalable Cosparse Methods for Physics-Driven Inverse Problems,scribed as a . (generative) model of the signal of interest from a low number of elementary signals taken in a dictionary, is now widely used. In many inverse problems of this kind, it happens that an alternative model, the . hypothesis (stating that the result of some linear . of the signal is spar
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Total Variation Minimization in Compressed Sensing, addition to summarizing the results in the area, we illustrate why an approach that is common for synthesis sparse signals fails and different techniques are necessary. Lastly, we discuss a generalization of recent results for Gaussian measurements to the subgaussian case.
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https://doi.org/10.1007/b137883endent on the dimension .. Hence the curse of dimensionality – the bane of high-dimensional approximation – is mitigated to a significant extent. We also discuss several practical issues, including unknown noise (due to truncation or numerical error), and highlight a number of open problems and challenges.
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