Flexible Aluminum Tubes and a Least Square Multi-objective Non-linear Optimization Scheme

2004 ◽  
Author(s):  
Benny Endelt
Keyword(s):  
Linear Optimization ◽  
Least Square ◽  
Optimization Scheme ◽  
Multi Objective ◽  
Non Linear ◽  
Aluminum Tubes

Non-linear Optimization Scheme Applied to EIT Medical Images Based on the Gauss-Newton Method With Iterative Conductivity Update and Total Variation Regularization

2021 ◽  
Author(s):  
Bruno Miguel Gil Rosa ◽  
Guang-Zhong Yang
Keyword(s):  
Inverse Problem ◽  
Total Variation ◽  
Linear Optimization ◽  
Linear Method ◽  
The Body ◽  
Total Variation Regularization ◽  
Back Projection ◽  
Distribution Map ◽  
Optimization Scheme ◽  
Non Linear

Abstract Medical imaging modalities are vast and include the well-established techniques of Computerized Tomography (CT), Magnetic Resonance Imaging (MRI) or Ultrasounds. Though the underlying physics differs amongst modalities, a similar Inverse Mapping is shared: the recovery of the internal physical property under analysis from measurements obtained at the exterior of the body. In the lesser common technique of Electrical Impedance Tomography (EIT), measurement of the voltage levels around a body part are used to retrieve the internal distribution map for conductivity. The complexity of the Inverse Problem in EIT surpasses that found for the Forward Problem (or Mapping), both in terms of mathematical formulation and computational overload. The ill-posed nature of the Inverse Problem further contributes to that intricacy, and solutions to tackle it will be presented in this paper by means of a non-linear optimization scheme involving the iterative Gauss-Newton (GN) method with Total Variation (TV) regularization, applied to two-dimensional (2D) body domains only. The proposed scheme is also compared to other traditional reconstruction algorithms like 2D back-projection and the sensitivity approximation to the Jacobian matrix of the system of equations governing EIT. Results from conductivity map reconstructions in anatomical phantoms have shown an improvement in signal-to-noise ratio (SNR) and distribution map error (DME) of 36% and 11% for the proposed non-linear method relative to the back-projection and single-step GN method with sensitivity approximation.

Modeling of Non-Linear Relations Among Different Design Evaluation Measures for Multi-Objective Design Optimization

2005 ◽  
Author(s):  
H. Yang ◽  
D. Xue ◽  
Y. L. Tu
Keyword(s):  
Design Optimization ◽  
Comparison Method ◽  
Least Square ◽  
Design Evaluation ◽  
Linear Relations ◽  
Evaluation Measures ◽  
Multi Objective ◽  
Fitting Method ◽  
Non Linear ◽  
Curve Fitting Method

This research introduces a new approach to model the non-linear relations among different design evaluation measures and to achieve the optimal design considering these different design evaluation measures through multi-objective optimization. In this approach, different design evaluation measures are mapped to comparable design evaluation indices. The non-linear relation between a design evaluation measure and its design evaluation index is identified based on the least-square curve-fitting method. The weighting factors for different design evaluation indices, representing the importance measures of these indices in the multi-objective design optimization, are achieved using the pair-wise comparison method. A case study example of automobile caliper disc brake design considering 4 different design evaluation measures is given to illustrate the effectiveness of the introduced approach.

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