Dynamic Magnetic Resonance Imaging via Nonconvex Low-Rank Matrix Approximation

Xu, Fei; Han, Jingqi; Wang, Yongli; Chen, Ming; Chen, Yongyong; He, Ge; Hu, Yunhong

doi:10.1109/access.2017.2657645

Cited by 23 publications

(12 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Iteration Equation (9) in Theorem 1 can be used to compute the dual sequence {ω t }, since the matrix A has full row rank and the objective function is strictly convex. The matrix A in this problem has different forms with it in NUM, and therefore predetermined routes are not needed when we rewrite Equation (9). Theorem 5.…”

Section: Distributed Newton Methods For Multi-agent Problems In Generamentioning

confidence: 99%

“…Finally, we obtain the desired distributed iteration (20) when substituting Equations (A4)-(A6) into (9).…”

Section: Appendix Bmentioning

confidence: 99%

“…This method makes some improvements in convergence rate over distributed subgradient methods. Compared with conventional centralized methods, the distributed methods have faster computing efficiency and have been widely used in many fields, such as image processing [9,10], computer vision [11], intelligent power grids [12,13], machine learning [14,15], unrelated parallel machine scheduling problems [16], model predictive control (MPC) problems [17], and resource allocation problems in multi-agent communication networks [18,19].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Distributed Newton Methods for Strictly Convex Consensus Optimization Problems in Multi-Agent Networks

2017

View full text Add to dashboard Cite

Abstract:Various distributed optimization methods have been developed for consensus optimization problems in multi-agent networks. Most of these methods only use gradient or subgradient information of the objective functions, which suffer from slow convergence rate. Recently, a distributed Newton method whose appeal stems from the use of second-order information and its fast convergence rate has been devised for the network utility maximization (NUM) problem. This paper contributes to this method by adjusting it to a special kind of consensus optimization problem in two different multi-agent networks. For networks with Hamilton path, the distributed Newton method is modified by exploiting a novel matrix splitting techniques. For general connected multi-agent networks, the algorithm is trimmed by combining the matrix splitting technique and the spanning tree for this consensus optimization problems. The convergence analyses show that both modified distributed Newton methods enable the nodes across the network to achieve a global optimal solution in a distributed manner. Finally, the distributed Newton method is applied to solve a problem which is motivated by the Kuramoto model of coupled nonlinear oscillators and the numerical results illustrate the performance of the proposed algorithm.

show abstract

Section: Distributed Newton Methods For Multi-agent Problems In Generamentioning

confidence: 99%

“…Finally, we obtain the desired distributed iteration (20) when substituting Equations (A4)-(A6) into (9).…”

Section: Appendix Bmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Distributed Newton Methods for Strictly Convex Consensus Optimization Problems in Multi-Agent Networks

2017

View full text Add to dashboard Cite

show abstract

“…where ( ( ( +1) + ( +1) ) − ) represents artifacts, which is subtracted from the updating ( +1) + ( +1) as a residual, resulting in a clearer image [22].…”

Section: Modelingmentioning

confidence: 99%

“…In addition, authors of [20,22] pointed out that, among common nonconvex functions, such as -norm [23], SCAD [24], log [15], MCP [25], ETP [26], and Geman [27], -norm is the best approximation to 0 norm. Inspired by this, we propose a new model as follows:…”

Section: Modelingmentioning

confidence: 99%

Dynamic Magnetic Resonance Imaging Reconstruction Based on Nonconvex Low‐Rank Model

Chen

Yang

Wang

2017

Mathematical Problems in Engineering

View full text Add to dashboard Cite

The quality of dynamic magnetic resonance imaging reconstruction has heavy impact on clinical diagnosis. In this paper, we propose a new reconstructive algorithm based on the + model. In the algorithm, the 1 norm is substituted by the norm to approximate the 0 norm; thus the accuracy of the solution is improved. We apply an alternate iteration method to solve the resulting problem of the proposed method. Experiments on nine data sets show that the proposed algorithm can effectively reconstruct dynamic magnetic resonance images.

show abstract

A singular K-space model for fast reconstruction of magnetic resonance images from undersampled data

Luo

Mou²,

Qin

et al. 2017

Med Biol Eng Comput

View full text Add to dashboard Cite

Reconstructing magnetic resonance images from undersampled k-space data is a challenging problem. This paper introduces a novel method of image reconstruction from undersampled k-space data based on the concept of singularizing operators and a novel singular k-space model. Exploring the sparsity of an image in the k-space, the singular k-space model (SKM) is proposed in terms of the k-space functions of a singularizing operator. The singularizing operator is constructed by combining basic difference operators. An algorithm is developed to reliably estimate the model parameters from undersampled k-space data. The estimated parameters are then used to recover the missing k-space data through the model, subsequently achieving high-quality reconstruction of the image using inverse Fourier transform. Experiments on physical phantom and real brain MR images have shown that the proposed SKM method constantly outperforms the popular total variation (TV) and the classical zero-filling (ZF) methods regardless of the undersampling rates, the noise levels, and the image structures. For the same objective quality of the reconstructed images, the proposed method requires much less k-space data than the TV method. The SKM method is an effective method for fast MRI reconstruction from the undersampled k-space data. Graphical abstract Two Real Images and their sparsified images by singularizing operator.

show abstract

Dynamic Magnetic Resonance Imaging via Nonconvex Low-Rank Matrix Approximation

Cited by 23 publications

References 22 publications

Distributed Newton Methods for Strictly Convex Consensus Optimization Problems in Multi-Agent Networks

Distributed Newton Methods for Strictly Convex Consensus Optimization Problems in Multi-Agent Networks

Dynamic Magnetic Resonance Imaging Reconstruction Based on Nonconvex Low‐Rank Model

A singular K-space model for fast reconstruction of magnetic resonance images from undersampled data

Contact Info

Product

Resources

About