Eigenvectors of matrices on a network have been used for understanding influence of a vertex and spectral clustering. For matrices with small geodesic-width and their given eigenvalues, we propose preconditioned gradi...
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Eigenvectors of matrices on a network have been used for understanding influence of a vertex and spectral clustering. For matrices with small geodesic-width and their given eigenvalues, we propose preconditioned gradient descent algorithms in this paper to find eigenvectors. We also consider synchronous implementation of the proposed algorithms at vertex/agent level in a spatially distributed network in which each agent has limited data processing capability and confined communication range. (c) 2022 Elsevier B.V. All rights reserved.
For tomography reconstruction, the iteration methods based on spare regularization have recently emerged and are proven effective especially in the situation that projection data is insufficient or noisy in low radiat...
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ISBN:
(纸本)9780819493057
For tomography reconstruction, the iteration methods based on spare regularization have recently emerged and are proven effective especially in the situation that projection data is insufficient or noisy in low radiation dose. Because iterative tomography reconstruction algorithms have heavy computational demanding especially for clinical data sets and is far from being close to real-time reconstruction. So there is incentive to develop fast algorithms of the optimization problem. We present new accelerating iterative shrinkage algorithms for sparse-based tomography reconstruction, which base on the existing shrinkage algorithms and combine with traditional algebra methods, linear search method and preconditioning techniques to solve large dense linear systems. We give two different weighted matrixes as the preconditioner and get the different convergence speeds. From the experimental results it can be seen that using the sparsity in the transform domain as the regularization term can greatly improve the visual effect of the reconstructed images compared with corresponding algebraic algorithms, and the linear search method can obviously accelerates the converge rate.
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