This paper develops a new class of algorithms for signal recovery in the distributed compressive sensing (DCS) framework. DCS exploits both intra-signal and inter-signal correlations through the concept of joint spars...
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ISBN:
(纸本)9781424442959
This paper develops a new class of algorithms for signal recovery in the distributed compressive sensing (DCS) framework. DCS exploits both intra-signal and inter-signal correlations through the concept of joint sparsity to further reduce the number of measurements required for recovery. DCS is well-suited for sensor network applications due to its universality, computational asymmetry, tolerance to quantization and noise, and robustness to measurement loss. In this paper we propose recovery algorithms for the sparse common and innovation joint sparsity model. Our approach leads to a class of efficient algorithms, the Texas Hold 'Em algorithms, which are scalable both in terms of communication bandwidth and computational complexity.
This paper addresses the topic of fitting reduced data represented by the sequence of interpolation points (Formula Presented) in arbitrary Euclidean space Em. The parametric curve γ together with its knots (Formula ...
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Convolutional Neural Networks (CNNs) have received substantial attention as a highly effective tool for analyzing medical images, notably in interpreting endoscopic images, due to their capacity to provide results equ...
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We introduce a machine-learning-based framework for constructing continuum non-Newtonian fluid dynamics model directly from a micro-scale description. Polymer solution is used as an example to demonstrate the essentia...
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Large-scale interconnected uncertain systems commonly have large state and uncertainty dimensions. Aside from the heavy computational cost of performing robust stability analysis in a centralized manner, privacy requi...
Large-scale interconnected uncertain systems commonly have large state and uncertainty dimensions. Aside from the heavy computational cost of performing robust stability analysis in a centralized manner, privacy requirements in the network can also introduce further issues. In this paper, we utilize IQC analysis for analyzing large-scale interconnected uncertain systems and we evade these issues by describing a decomposition scheme that is based on the interconnection structure of the system. This scheme is based on the so-called chordal decomposition and does not add any conservativeness to the analysis approach. The decomposed problem can be solved using distributed computational algorithms without the need for a centralized computational unit. We further discuss the merits of the proposed analysis approach using a numerical experiment.
In this note we construct an upper estimate on the maximum angles of triangles generated by the longest-edge bisection algorithms applied to a triangle. This upper bound considerably improves upon one inherited from t...
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We consider an online version of the conflict-free coloring of a set of points on the line, where each newly inserted point must be assigned a color upon insertion, and at all times the coloring has to be conflict-fre...
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We consider an online version of the conflict-free coloring of a set of points on the line, where each newly inserted point must be assigned a color upon insertion, and at all times the coloring has to be conflict-free, in the sense that in every interval I there is a color that appears exactly once in I. We present several deterministic and randomized algorithms for achieving this goal, and analyze their performance, that is, the maximum number of colors that they need to use, as a function of the number n of inserted points. We first show that a natural and simple (deterministic) approach may perform rather poorly, requiring Ω(√n) colors in the worst case. We then modify this approach, to obtain an efficient deterministic algorithm that uses a maximum of Θ(log2 n) colors. Next, we present two randomized solutions. The first algorithm requires an expected number of at most O(log 2 n) colors, and produces a coloring which is valid with high probability, and the second one, which is a variant of our efficient deterministic algorithm, requires an expected number of at most O(log n log log n) colors but always produces a valid coloring. We also analyze the performance of the simplest proposed algorithm when the points are inserted in a random order, and present an incomplete analysis that indicates that, with high probability, it uses only O(log n) colors. Finally, we show that in the extension of this problem to two dimensions, where the relevant ranges are disks, n colors may be required in the worst case. The average-case behavior for disks, and cases involving other planar ranges, are still open.
Compressive sensing (CS) is an emerging approach for acquisition of signals having a sparse or compressible representation in some basis. While CS literature has mostly focused on problems involving 1-D and 2-D signal...
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ISBN:
(纸本)9781424442959
Compressive sensing (CS) is an emerging approach for acquisition of signals having a sparse or compressible representation in some basis. While CS literature has mostly focused on problems involving 1-D and 2-D signals, many important applications involve signals that are multidimensional. We propose the use of Kronecker product matrices in CS for two purposes. First, we can use such matrices as sparsifying bases that jointly model the different types of structure present in the signal. Second, the measurement matrices used in distributed measurement settings can be easily expressed as Kronecker products. This new formulation enables the derivation of analytical bounds for sparse approximation and CS recovery of multidimensional signals.
Multidimensional arrays have proven to be useful in watermarking, therefore interest in this subject has increased in the previous years along with the number of publications. For one dimensional arrays (sequences), l...
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Multidimensional arrays have proven to be useful in watermarking, therefore interest in this subject has increased in the previous years along with the number of publications. For one dimensional arrays (sequences), linear complexity is regarded as standard measure of complexity. Although linear complexity of sequences has been widely studied, only recently, we have extended it to the study of multidimensional arrays. In this paper, we show that the concept of multidimensional linear complexity is a powerful tool, by examining the results for selected constructs. We have obtained the linear complexity of logartihmic Moreno-Tirkel arrays and we show that they show high multidimensional linear complexity. Finally, we explicitly provide the minimal generators for quadratic Moreno-Tirkel arrays. The results show that these techniques are effective in finding the multidimensional linear complexity of the constructions, representing only a small fraction of the applicability of multidimensional linear complexity. The study of multidimensional arrays provides new ways to understand sequences and set the basis for forthcoming proof of the three years old conjectures related with CDMA sequences.
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