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1.
PeerJ Comput Sci ; 9: e1242, 2023.
Artigo em Inglês | MEDLINE | ID: mdl-37346506

RESUMO

Tensor eigenproblems have wide applications in blind source separation, magnetic resonance imaging, and molecular conformation. In this study, we explore an alternating direction method for computing the largest or smallest Z-eigenvalue and corresponding eigenvector of an even-order symmetric tensor. The method decomposes a tensor Z-eigenproblem into a series of matrix eigenproblems that can be readily solved using off-the-shelf matrix eigenvalue algorithms. Our numerical results show that, in most cases, the proposed method converges over two times faster and could determine extreme Z-eigenvalues with 20-50% higher probability than a classical power method-based approach.

2.
Magn Reson Imaging ; 87: 38-46, 2022 04.
Artigo em Inglês | MEDLINE | ID: mdl-34968699

RESUMO

Recently, deep learning approaches with various network architectures have drawn significant attention from the magnetic resonance imaging (MRI) community because of their great potential for image reconstruction from undersampled k-space data in fast MRI. However, the robustness of a trained network when applied to test data deviated from training data is still an important open question. In this work, we focus on quantitatively evaluating the influence of image contrast, human anatomy, sampling pattern, undersampling factor, and noise level on the generalization of a trained network composed by a cascade of several CNNs and a data consistency layer, called a deep cascade of convolutional neural network (DC-CNN). The DC-CNN is trained from datasets with different image contrast, human anatomy, sampling pattern, undersampling factor, and noise level, and then applied to test datasets consistent or inconsistent with the training datasets to assess the generalizability of the learned DC-CNN network. The results of our experiments show that reconstruction quality from the DC-CNN network is highly sensitive to sampling pattern, undersampling factor, and noise level, which are closely related to signal-to-noise ratio (SNR), and is relatively less sensitive to the image contrast. We also show that a deviation of human anatomy between training and test data leads to a substantial reduction of image quality for the brain dataset, whereas comparable performance for the chest and knee dataset having fewer anatomy details than brain images. This work further provides some empirical understanding of the generalizability of trained networks when there are deviations between training and test data. It also demonstrates the potential of transfer learning for image reconstruction from datasets different from those used in training the network.


Assuntos
Processamento de Imagem Assistida por Computador , Redes Neurais de Computação , Encéfalo/diagnóstico por imagem , Humanos , Processamento de Imagem Assistida por Computador/métodos , Imageamento por Ressonância Magnética/métodos , Razão Sinal-Ruído
3.
Math Biosci Eng ; 18(4): 4162-4192, 2021 05 12.
Artigo em Inglês | MEDLINE | ID: mdl-34198431

RESUMO

In this paper, a mathematical model has been formulated for the transmission dynamics of citrus Huanglongbing considering latent period as the time delay factor. Existence of the equilibria and their stability have been studied on the basis of basic reproduction number in two cases τ=0 and τ>0. The results show that stability changes occur through Hopf bifurcation in the delayed system. Optimal control theory is then applied to investigate the optimal strategy for curtailing the spread of the disease using three time-dependent control variables determined from sensitivity analysis. By using Pontryagin's Maximum Principle, we obtain the optimal integrated strategy and prove the uniqueness of optimal control solution. Analytical and numerical findings suggest that it is feasible to implement control techniques while minimizing the cost of implementation of optimal control strategies.


Assuntos
Modelos Biológicos , Modelos Teóricos , Número Básico de Reprodução , Simulação por Computador
4.
Med Biol Eng Comput ; 57(9): 1933-1946, 2019 Sep.
Artigo em Inglês | MEDLINE | ID: mdl-31254175

RESUMO

A direct application of the compressed sensing (CS) theory to dynamic magnetic resonance imaging (MRI) reconstruction needs vectorization or matricization of the dynamic MRI data, which is composed of a stack of 2D images and can be naturally regarded as a tensor. This 1D/2D model may destroy the inherent spatial structure property of the data. An alternative way to exploit the multidimensional structure in dynamic MRI is to employ tensor decomposition for dictionary learning, that is, learning multiple dictionaries along each dimension (mode) and sparsely representing the multidimensional data with respect to the Kronecker product of these dictionaries. In this work, we introduce a novel tensor dictionary learning method under an orthonormal constraint on the elementary matrix of the tensor dictionary for dynamic MRI reconstruction. The proposed algorithm alternates sparse coding, tensor dictionary learning, and updating reconstruction, and each corresponding subproblem is efficiently solved by a closed-form solution. Numerical experiments on phantom and synthetic data show significant improvements in reconstruction accuracy and computational efficiency obtained by the proposed scheme over the existing method that uses the 1D/2D model with overcomplete dictionary learning. Graphical abstract Fig. 1 Comparison between (a) the traditional method and (b) the proposed method based on dictionary learning for dynamic MRI reconstruction.


Assuntos
Algoritmos , Processamento de Imagem Assistida por Computador/métodos , Imageamento por Ressonância Magnética/métodos , Humanos , Imagens de Fantasmas
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