This paper proposes a compressed sensing method based on overcomplete learned dictionaries for experimental 3D ultrasound (US) imaging. Two undersampling patterns suited for 3D US imaging are investigated in ex vivo 3...
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ISBN:
(纸本)9781479981823
This paper proposes a compressed sensing method based on overcomplete learned dictionaries for experimental 3D ultrasound (US) imaging. Two undersampling patterns suited for 3D US imaging are investigated in ex vivo 3D US volume acquisitions: a spatially uniform random acquisition and a line-wise random acquisition. The overcomplete dictionary was learned using the K-SVD algorithm on patches extracted from 3D US datasets. The CS reconstruction problem was solved through the l(1) minimization using the spectral projected gradient algorithm and was performed by removing 20% to 80% of the original samples according to the two undersampling patterns. Besides the K-SVD dictionary we include the Fourier basis and the discrete cosine transform to our experiments for comparison. The approach is evaluated on 3D US experimental data acquired from ex vivo pig brains and sheep hearts. Reconstructions from 50% of the samples of the original 3D volume show little information loss in terms of normalized root mean squared errors.
Improving numerical forecasting skill in the atmospheric and oceanic sciences by solving optimization problems is an important issue. One such method is to compute the conditional nonlinear optimal perturbation(CNOP),...
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Improving numerical forecasting skill in the atmospheric and oceanic sciences by solving optimization problems is an important issue. One such method is to compute the conditional nonlinear optimal perturbation(CNOP), which has been applied widely in predictability studies. In this study, the Differential Evolution(DE) algorithm, which is a derivative-free algorithm and has been applied to obtain CNOPs for exploring the uncertainty of terrestrial ecosystem processes, was employed to obtain the CNOPs for finite-dimensional optimization problems with ball constraint conditions using Burgers' equation. The aim was first to test if the CNOP calculated by the DE algorithm is similar to that computed by traditional optimization algorithms, such as the spectralprojectedgradient(SPG2) algorithm. The second motive was to supply a possible route through which the CNOP approach can be applied in predictability studies in the atmospheric and oceanic sciences without obtaining a model adjoint system, or for optimization problems with non-differentiable cost functions. A projection skill was first explanted to the DE algorithm to calculate the CNOPs. To validate the algorithm, the SPG2 algorithm was also applied to obtain the CNOPs for the same optimization problems. The results showed that the CNOPs obtained by the DE algorithm were nearly the same as those obtained by the SPG2 algorithm in terms of their spatial distributions and nonlinear evolutions. The implication is that the DE algorithm could be employed to calculate the optimal values of optimization problems, especially for non-differentiable and nonlinear optimization problems associated with the atmospheric and oceanic sciences.
In this paper, a restrained optimal perturbation method is firstly proposed to solve the backward heat conduction problem, the initial temperature distribution will be identified from the overspecified data, a regular...
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In this paper, a restrained optimal perturbation method is firstly proposed to solve the backward heat conduction problem, the initial temperature distribution will be identified from the overspecified data, a regularization term is introduced in the objective functional for overcoming the ill-posedness of this problem, spectral projected gradient algorithm is used to solve the optimal problem, and we give the sensitivity analysis of the initial value. The results of numerical experiments are also presented. (C) 2013 Elsevier Inc. All rights reserved.
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