Plastic Flow as an Energy Minimization Problem. Numerical Experiments

In this work, we try to develop a fast converging method for segmentation assisted deformable registration. The segmentation step consists of a piece-wise constant Mumford-Shah energy model while reg- istration is driven by the sum of squared distances of both initial images and segmented mask with a diffusion regularization. In order to solve this energy minimization problem, a second order Gauss-Newton opti- mization method is used. For the numerical experiments we used CT data sets from the EMPIRE10 challenge. In this preliminary study, we show high accuracy of our algorithm.

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Semantic parsing as an energy minimization problem

1997 IEEE International Conference on Intelligent Processing Systems (Cat. No.97TH8335) ◽

10.1109/icips.1997.669157 ◽

2002 ◽

Author(s):

S.W.K. Chan

Keyword(s):

Minimization Problem ◽

Energy Minimization ◽

Semantic Parsing

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The energy minimization problem for two-level dissipative quantum systems

Journal of Mathematical Physics ◽

10.1063/1.3479390 ◽

2010 ◽

Vol 51 (9) ◽

pp. 092705 ◽

Cited By ~ 15

Author(s):

B. Bonnard ◽

O. Cots ◽

N. Shcherbakova ◽

D. Sugny

Keyword(s):

Minimization Problem ◽

Energy Minimization ◽

Quantum Systems ◽

Dissipative Quantum Systems

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Convergence Theorems for Modified Inertial Viscosity Splitting Methods in Banach Spaces

Mathematics ◽

10.3390/math7020156 ◽

2019 ◽

Vol 7 (2) ◽

pp. 156 ◽

Cited By ~ 1

Author(s):

Chanjuan Pan ◽

Yuanheng Wang

Keyword(s):

Strong Convergence ◽

Banach Spaces ◽

Minimization Problem ◽

Numerical Experiments ◽

Splitting Method ◽

Splitting Methods ◽

Strong Convergence Theorem ◽

Accretive Operators ◽

Convex Minimization Problem ◽

Inertial Extrapolation

In this article, we study a modified viscosity splitting method combined with inertial extrapolation for accretive operators in Banach spaces and then establish a strong convergence theorem for such iterations under some suitable assumptions on the sequences of parameters. As an application, we extend our main results to solve the convex minimization problem. Moreover, the numerical experiments are presented to support the feasibility and efficiency of the proposed method.

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Combined Energy Minimization for Image Reconstruction from Few Views

Mathematical Problems in Engineering ◽

10.1155/2012/154630 ◽

2012 ◽

Vol 2012 ◽

pp. 1-15 ◽

Cited By ~ 36

Author(s):

Wei Wei ◽

Xiao-Lin Yang ◽

Bin Zhou ◽

Jun Feng ◽

Pei-Yi Shen

Keyword(s):

Image Reconstruction ◽

Conjugate Gradient ◽

Gradient Method ◽

Energy Minimization ◽

Numerical Experiments ◽

Applied Mathematics ◽

Image Features ◽

Density Region ◽

Nonlinear Conjugate Gradient Method ◽

Nonlinear Conjugate Gradient

Reconstruction from few views is an important problem in medical imaging and applied mathematics. In this paper, a combined energy minimization is proposed for image reconstruction.l2energy of the image gradient is introduced in the lower density region, and it can accelerate the reconstruction speed and improve the results. Total variation of the image is introduced in the higher density region, and the image features can be preserved well. Nonlinear conjugate gradient method is introduced to solve the problem. The efficiency and accuracy of our method are shown in several numerical experiments.

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DG approach to large bending plate deformations with isometry constraint

Mathematical Models and Methods in Applied Sciences ◽

10.1142/s0218202521500044 ◽

2021 ◽

pp. 1-43

Author(s):

Andrea Bonito ◽

Ricardo H. Nochetto ◽

Dimitrios Ntogkas

Keyword(s):

Discontinuous Galerkin ◽

Minimization Problem ◽

Numerical Experiments ◽

Gradient Flow ◽

Kirchhoff Plate ◽

Geometrically Nonlinear ◽

Plate Model ◽

Global Minimizers ◽

Dg Method ◽

Kirchhoff Plate Model

We propose a new discontinuous Galerkin (dG) method for a geometrically nonlinear Kirchhoff plate model for large isometric bending deformations. The minimization problem is nonconvex due to the isometry constraint. We present a practical discrete gradient flow that decreases the energy and computes discrete minimizers that satisfy a prescribed discrete isometry defect. We prove [Formula: see text]-convergence of the discrete energies and discrete global minimizers. We document the flexibility and accuracy of the dG method with several numerical experiments.

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An accelerated majorization-minimization algorithm with convergence guarantee for non-Lipschitz wavelet synthesis model *

Inverse Problems ◽

10.1088/1361-6420/ac38b8 ◽

2021 ◽

Vol 38 (1) ◽

pp. 015001

Author(s):

Yanan Zhao ◽

Chunlin Wu ◽

Qiaoli Dong ◽

Yufei Zhao

Keyword(s):

Minimization Problem ◽

Stationary Point ◽

Numerical Experiments ◽

Complete Convergence ◽

Convergence Result ◽

Image Process ◽

Minimization Algorithm ◽

Computationally Efficient ◽

Special Case ◽

Reconstruction Model

Abstract We consider a wavelet based image reconstruction model with the ℓ p (0 < p < 1) quasi-norm regularization, which is a non-convex and non-Lipschitz minimization problem. For solving this model, Figueiredo et al (2007 IEEE Trans. Image Process. 16 2980–2991) utilized the classical majorization-minimization framework and proposed the so-called Isoft algorithm. This algorithm is computationally efficient, but whether it converges or not has not been concluded yet. In this paper, we propose a new algorithm to accelerate the Isoft algorithm, which is based on Nesterov’s extrapolation technique. Furthermore, a complete convergence analysis for the new algorithm is established. We prove that the whole sequence generated by this algorithm converges to a stationary point of the objective function. This convergence result contains the convergence of Isoft algorithm as a special case. Numerical experiments demonstrate good performance of our new algorithm.

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