scholarly journals Computational approaches for parametric imaging of dynamic PET data

2019 ◽  
Author(s):  
S Crisci ◽  
M Piana ◽  
V Ruggiero ◽  
M Scussolini
Keyword(s):  
Numerical Optimization ◽  
Trust Region Method ◽  
Trust Region ◽  
Nonlinear Least Squares ◽  
Affine Scaling ◽  
Parametric Imaging ◽  
Simulation Framework ◽  
Functional Images ◽  
Ill Posed ◽  
Newton Scheme

AbstractParametric imaging of nuclear medicine data exploits dynamic functional images in order to reconstruct maps of kinetic parameters related to the metabolism of a specific tracer injected in the biological tissue. From a computational viewpoint, the realization of parametric images requires the pixel-wise numerical solution of compartmental inverse problems that are typically ill-posed and nonlinear. In the present paper we introduce a fast numerical optimization scheme for parametric imaging relying on a regularized version of the standard affine-scaling Trust Region method. The validation of this approach is realized in a simulation framework for brain imaging and comparison of performances is made with respect to a regularized Gauss-Newton scheme and a standard nonlinear least-squares algorithm.

A Regularized Affine-Scaling Trust-Region Method for Parametric Imaging of Dynamic PET Data

2021 ◽  
Vol 14 (1) ◽  
pp. 418-439
Author(s):  
S. Crisci ◽  
M. Piana ◽  
V. Ruggiero ◽  
M. Scussolini
Keyword(s):  
Trust Region Method ◽  
Trust Region ◽  
Affine Scaling ◽  
Parametric Imaging ◽  
Dynamic Pet ◽  
Region Method

Nonmonotone conic trust region method with line search technique for bound constrained optimization

2019 ◽  
Vol 53 (3) ◽  
pp. 787-805
Author(s):  
Lijuan Zhao
Keyword(s):  
Constrained Optimization ◽  
Line Search ◽  
Optimization Problems ◽  
Trust Region Method ◽  
Trust Region ◽  
Affine Scaling ◽  
Search Technique ◽  
Region Method ◽  
Bound Constrained Optimization ◽  
Line Search Technique

In this paper, we propose a nonmonotone trust region method for bound constrained optimization problems, where the bounds are dealt with by affine scaling technique. Differing from the traditional trust region methods, the subproblem in our algorithm is based on a conic model. Moreover, when the trial point isn’t acceptable by the usual trust region criterion, a line search technique is used to find an acceptable point. This procedure avoids resolving the trust region subproblem, which may reduce the total computational cost. The global convergence and Q-superlinear convergence of the algorithm are established under some mild conditions. Numerical results on a series of standard test problems are reported to show the effectiveness of the new method.

A trust region method based on a new affine scaling technique for simple bounded optimization

2013 ◽  
Vol 28 (4) ◽  
pp. 871-888 ◽  
Author(s):  
Xiao Wang ◽  
Ya-Xiang Yuan
Keyword(s):  
Trust Region Method ◽  
Trust Region ◽  
Affine Scaling ◽  
Scaling Technique ◽  
Region Method

Constrained inversion of gravity fields for complex 3-D structures

Geophysics ◽  
2001 ◽  
Vol 66 (2) ◽  
pp. 501-510 ◽  
Author(s):  
Roberto A. V. Moraes ◽  
R. O. Hansen
Keyword(s):  
Degrees Of Freedom ◽  
Trust Region Method ◽  
Trust Region ◽  
Petroleum Exploration ◽  
Magnetic Data ◽  
Matrix Formulation ◽  
Ill Posed ◽  
System Equations ◽  
Complex Structural ◽  
Gravity Interpretation

As part of a research program to develop gravity interpretation tools that can be merged with seismic techniques, a full 3-D complex structural inversion scheme for (possibly multibody) polyhedral models has been developed. The forward modeling algorithm was adopted from previous work. Because the inverse problem is generally very ill posed, several methods of regularizing the inversion were investigated and a combination of the most useful was adopted. The combination includes (i) a structured matrix formulation for the system equations, (ii) an analytical expression for the Jacobian calculation, (iii) first‐derivative damping, (iv) a choice of damping parameter based on a variation of the trust region method, (v) a weighted scheme for parameter correction, and (vi) complete freezing of degrees of freedom found not to influence the gravity field significantly. This combination yields a robust inversion which was successfully demonstrated on data over the Galveston Island salt dome, offshore Texas. Variations of the technique should be applicable to magnetic data, which would make the method useful for mining problems and petroleum exploration settings involving volcanic structures.

On an Elliptical Trust-Region Procedure for Ill-Posed Nonlinear Least-Squares Problems

2018 ◽  
Vol 178 (3) ◽  
pp. 824-859 ◽  
Author(s):  
Stefania Bellavia ◽  
Elisa Riccietti
Keyword(s):  
Least Squares ◽  
Trust Region ◽  
Nonlinear Least Squares ◽  
Least Squares Problems ◽  
Ill Posed
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