In the processing of signals defined over graph domains, it is highly desirable to have algorithms that can be implemented in a decentralised manner, whereby each node only needs to exchange information within a local...
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In the processing of signals defined over graph domains, it is highly desirable to have algorithms that can be implemented in a decentralised manner, whereby each node only needs to exchange information within a localized subgraph of nodes. The most common example is when the subgraph consist of immediate neighbors and this allows for distributed processing. Many graph signal operators, in their original forms, are not amenable to distributed processing. To overcome this deficiency, a polynomial approximation is usually applied to the original operator to yield a distributed operator which is a matrix polynomial of the graph shift matrix. This approach however is only applicable when the original operator is a function of the graph shift matrix. In this paper, we propose a generalized approach to approximate graph signal operators that are not necessary functions of the shift matrix. The key idea here is to restrict the approximated matrixinverse to have small geodesic-width so that multiplication with the small geodesic-width matrix can be implemented in a decentralised manner. Furthermore, to increase the accuracy of the approximated operator, an iterative algorithm which also has the decentralised property and low computational complexity, is proposed. We apply the proposed approach to signal inpainting and signal reconstruction in filter banks. Numerical results verify the effectiveness of the proposed algorithm. The proposed algorithms can also be used to efficiently solve linear system of equations. (C) 2019 Elsevier B.V. All rights reserved.
The reconstruction of time-varying signals on graphs is a prominent problem in graph signal processing community. By imposing the smoothness regularization over the time-vertex domain, the reconstruction problem can b...
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The reconstruction of time-varying signals on graphs is a prominent problem in graph signal processing community. By imposing the smoothness regularization over the time-vertex domain, the reconstruction problem can be formulated into an unconstrained optimization problem that minimizes the weighted sum of the data fidelity term and regularization term. In this paper, we propose an approximate Newton method to solve the problem in a distributed manner, which is applicable for spatially distributed systems consisting of agents with limited computation and communication capacity. The algorithm has low computational complexity while nearly maintains the fast convergence of the second-order methods, which is evidently better than the existing reconstruction algorithm based on the gradient descent method. The convergence of the proposed algorithm is explicitly proved. Numerical results verify the validity and fast convergence of the proposed algorithm.
In this paper, we propose a new low-complexity optimal transmitting antenna selection algorithm for multiple-input multiple-output (MIMO) systems. Different from the conventional optimal antenna selection methods, our...
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ISBN:
(纸本)9781467331227
In this paper, we propose a new low-complexity optimal transmitting antenna selection algorithm for multiple-input multiple-output (MIMO) systems. Different from the conventional optimal antenna selection methods, our proposed algorithm can approximate the inversematrix subject to an error tolerance. However, the antenna selection optimality can often be obtained as the same outcome from the exact matrixinverse. Furthermore, our proposed matrix inverse approximation algorithm can be greatly expedited by using parallel computing. With significantly reduced complexity using many microprocessors, our proposed method is very appealing to the future MIMO technologies.
For many expensive deterministic computer simulators, the outputs do not have replication error and the desired metamodel (or statistical emulator) is an interpolator of the observed data. Realizations of Gaussian spa...
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For many expensive deterministic computer simulators, the outputs do not have replication error and the desired metamodel (or statistical emulator) is an interpolator of the observed data. Realizations of Gaussian spatial processes (GP) are commonly used to model such simulator outputs. Fitting a GP model to n data points requires the computation of the inverse and determinant of n x n correlation matrices, R, that are sometimes computationally unstable due to near-singularity of R. This happens if any pair of design points are very close together in the input space. The popular approach to overcome near-singularity is to introduce a small nugget (or jitter) parameter in the model that is estimated along with other model parameters. The inclusion of a nugget in the model often causes unnecessary over-smoothing of the data. In this article, we propose a lower bound on the nugget that minimizes the over-smoothing and an iterative regularization approach to construct a predictor that further improves the interpolation accuracy. We also show that the proposed predictor converges to the GP interpolator.
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