scholarly journals Improving the Convergence Rate in Affine Registration of PET and SPECT Brain Images Using Histogram Equalization

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
D. Salas-Gonzalez ◽  
J. M. Górriz ◽  
J. Ramírez ◽  
P. Padilla ◽  
I. A. Illán
Keyword(s):  
Convergence Rate ◽  
Optimization Algorithm ◽  
Histogram Equalization ◽  
Brain Images ◽  
Affine Registration ◽  
Registration Algorithm ◽  
Affine Model ◽  
The Cost ◽  
General Affine ◽  
Brain Template

A procedure to improve the convergence rate for affine registration methods of medical brain images when the images differ greatly from the template is presented. The methodology is based on a histogram matching of the source images with respect to the reference brain template before proceeding with the affine registration. The preprocessed source brain images are spatially normalized to a template using a general affine model with 12 parameters. A sum of squared differences between the source images and the template is considered as objective function, and a Gauss-Newton optimization algorithm is used to find the minimum of the cost function. Using histogram equalization as a preprocessing step improves the convergence rate in the affine registration algorithm of brain images as we show in this work using SPECT and PET brain images.

scholarly journals ON THE CONVERGENCE RATE OF POTENTIALS OF BRENIER MAPS

2021 ◽  
pp. 1-37
Author(s):  
Florian F. Gunsilius
Keyword(s):  
Convergence Rate ◽  
Poincaré Inequality ◽  
Optimal Transportation ◽  
Matching Theory ◽  
Economic Research ◽  
Poincare Inequality ◽  
Optimal Transportation Problem ◽  
Minimax Rate ◽  
The Cost ◽  
Kantorovich Problem

The theory of optimal transportation has experienced a sharp increase in interest in many areas of economic research such as optimal matching theory and econometric identification. A particularly valuable tool, due to its convenient representation as the gradient of a convex function, has been the Brenier map: the matching obtained as the optimizer of the Monge–Kantorovich optimal transportation problem with the euclidean distance as the cost function. Despite its popularity, the statistical properties of the Brenier map have yet to be fully established, which impedes its practical use for estimation and inference. This article takes a first step in this direction by deriving a convergence rate for the simple plug-in estimator of the potential of the Brenier map via the semi-dual Monge–Kantorovich problem. Relying on classical results for the convergence of smoothed empirical processes, it is shown that this plug-in estimator converges in standard deviation to its population counterpart under the minimax rate of convergence of kernel density estimators if one of the probability measures satisfies the Poincaré inequality. Under a normalization of the potential, the result extends to convergence in the $L^2$ norm, while the Poincaré inequality is automatically satisfied. The main mathematical contribution of this article is an analysis of the second variation of the semi-dual Monge–Kantorovich problem, which is of independent interest.

A Determinant Elimination Method for Bottleneck Assignment and Generalized Assignment Problems

2012 ◽  
Vol 239-240 ◽  
pp. 1522-1527
Author(s):  
Wen Bo Wu ◽  
Yu Fu Jia ◽  
Hong Xing Sun
Keyword(s):  
Computational Complexity ◽  
Optimization Algorithm ◽  
Assignment Problem ◽  
Numerical Experiments ◽  
High Efficiency ◽  
Synthesis Method ◽  
Assignment Problems ◽  
Generalized Assignment ◽  
The Cost ◽  
Time And Space Complexity

The bottleneck assignment (BA) and the generalized assignment (GA) problems and their exact solutions are explored in this paper. Firstly, a determinant elimination (DE) method is proposed based on the discussion of the time and space complexity of the enumeration method for both BA and GA problems. The optimization algorithm to the pre-assignment problem is then discussed and the adjusting and transformation to the cost matrix is adopted to reduce the computational complexity of the DE method. Finally, a synthesis method for both BA and GA problems is presented. The numerical experiments are carried out and the results indicate that the proposed method is feasible and of high efficiency.

Improved Gauss-Newton optimisation methods in affine registration of SPECT brain images

2008 ◽  
Vol 44 (22) ◽  
pp. 1291 ◽  
Author(s):  
D. Salas-Gonzalez ◽  
J.M. Górriz ◽  
J. Ramírez ◽  
A. Lass ◽  
C.G. Puntonet
Keyword(s):  
Brain Images ◽  
Affine Registration ◽  
Optimisation Methods

A decision-making method based on Bayesian optimization algorithm for small modular reactor

Kerntechnik ◽  
2020 ◽  
Vol 85 (2) ◽  
pp. 109-121 ◽  
Author(s):  
B. Zhang ◽  
M. Peng ◽  
S. Cheng ◽  
L. Sun
Keyword(s):  
Decision Making ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Optimal Operation ◽  
Bayesian Optimization ◽  
Operating Personnel ◽  
Bayesian Optimization Algorithm ◽  
Autonomous Operation ◽  
Small Modular Reactor ◽  
The Cost

Abstract Small modular reactors (SMRs) are suitable for deployment in isolated underdeveloped areas to support highly localized microgrids. In order to achieve almost autonomous operation for reducing the cost of operating personnel, an autonomous control system with decision-making capability is needed. In this paper, a decision-making method based on Bayesian optimization algorithm (BOA) is proposed to explore the optimal operation scheme under fault conditions. BOA is used to adjust exploration strategy of operation scheme according to observations (operation schemes previously explored). To measure the feasibility of each operation scheme, an objective function that considers security and economy is established. BOA attempts to obtain the optimal operation scheme with maximum of the objective function in as few iterations as possible. To verify the proposed method, all main pump powered off fault is simulated by RELAP5 code. The optimal operation scheme of the fault is applied, the transient result shows that all key parameters are within safe limits and SMR is maintained at relatively high power, which means that BOA has the decision-making capability to get an optimal operation scheme on fault conditions.

Cluster Based Medical Image Registration Using Optimized Neural Network

2017 ◽  
pp. 1437-1467
Author(s):  
Joydev Hazra ◽  
Aditi Roy Chowdhury ◽  
Paramartha Dutta
Keyword(s):  
Neural Network ◽  
Genetic Algorithm ◽  
Image Registration ◽  
Convergence Rate ◽  
Optimization Algorithm ◽  
Clustering Algorithms ◽  
Data Sets ◽  
Learning Method ◽  
Local Minima ◽  
The Neural Network

Registration of medical images like CT-MR, MR-MR etc. are challenging area for researchers. This chapter introduces a new cluster based registration technique with help of the supervised optimized neural network. Features are extracted from different cluster of an image obtained from clustering algorithms. To overcome the drawback regarding convergence rate of neural network, an optimized neural network is proposed in this chapter. The weights are optimized to increase the convergence rate as well as to avoid stuck in local minima. Different clustering algorithms are explored to minimize the clustering error of an image and extract features from suitable one. The supervised learning method applied to train the neural network. During this training process an optimization algorithm named Genetic Algorithm (GA) is used to update the weights of a neural network. To demonstrate the effectiveness of the proposed method, investigation is carried out on MR T1, T2 data sets. The proposed method shows convincing results in comparison with other existing techniques.

scholarly journals Inverse Strategies for Identifying the Parameters of Constitutive Laws of Metal Sheets

2016 ◽  
Vol 2016 ◽  
pp. 1-18 ◽  
Author(s):  
P. A. Prates ◽  
A. F. G. Pereira ◽  
N. A. Sakharova ◽  
M. C. Oliveira ◽  
J. V. Fernandes
Keyword(s):  
Finite Element ◽  
Cost Function ◽  
Optimization Algorithm ◽  
Yield Criterion ◽  
Kinematic Hardening ◽  
Constitutive Laws ◽  
Constitutive Law ◽  
Identification Procedure ◽  
Metal Sheets ◽  
The Cost

This article is a review regarding recently developed inverse strategies coupled with finite element simulations for the identification of the parameters of constitutive laws that describe the plastic behaviour of metal sheets. It highlights that the identification procedure is dictated by the loading conditions, the geometry of the sample, the type of experimental results selected for the analysis, the cost function, and optimization algorithm used. Also, the type of constitutive law (isotropic and/or kinematic hardening laws and/or anisotropic yield criterion), whose parameters are intended to be identified, affects the whole identification procedure.

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