Comparative assessment of linear least-squares, nonlinear least-squares, and Patlak graphical method for regional and local quantitative tracer kinetic modeling in cerebral dynamic18F-FDG PET

2019 ◽  
Vol 46 (3) ◽  
pp. 1260-1271 ◽  
Author(s):  
Fayçal Ben Bouallègue ◽  
Fabien Vauchot ◽  
Denis Mariano-Goulart
Keyword(s):  
Least Squares ◽  
Kinetic Modeling ◽  
Fdg Pet ◽  
Graphical Method ◽  
Nonlinear Least Squares ◽  
Comparative Assessment ◽  
Linear Least Squares ◽  
Tracer Kinetic Modeling ◽  
Tracer Kinetic

scholarly journals Quantification of 18F-JNJ-42259152, a Novel Phosphodiesterase 10A PET Tracer: Kinetic Modeling and Test-Retest Study in Human Brain

2013 ◽  
Vol 54 (8) ◽  
pp. 1285-1293 ◽  
Author(s):  
K. Van Laere ◽  
R. U. Ahmad ◽  
H. Hudyana ◽  
K. Dubois ◽  
M. E. Schmidt ◽  
...  
Keyword(s):  
Human Brain ◽  
Kinetic Modeling ◽  
Tracer Kinetic Modeling ◽  
Pet Tracer ◽  
Tracer Kinetic ◽  
Phosphodiesterase 10A

Quantitative retinal blood flow mapping from fluorescein videoangiography using tracer kinetic modeling

2015 ◽  
Vol 40 (10) ◽  
pp. 2169 ◽  
Author(s):  
Kenneth M. Tichauer ◽  
Micah Guthrie ◽  
Logan Hones ◽  
Lagnojita Sinha ◽  
Keith St. Lawrence ◽  
...  
Keyword(s):  
Blood Flow ◽  
Kinetic Modeling ◽  
Retinal Blood Flow ◽  
Flow Mapping ◽  
Tracer Kinetic Modeling ◽  
Tracer Kinetic

Tracer Kinetic Modeling of the 5-HT1AReceptor Ligand [carbonyl-11C]WAY-100635 for PET

NeuroImage ◽  
1998 ◽  
Vol 8 (4) ◽  
pp. 426-440 ◽  
Author(s):  
Roger N. Gunn ◽  
Peter A. Sargent ◽  
Christopher J. Bench ◽  
Eugenii A. Rabiner ◽  
Safiye Osman ◽  
...  
Keyword(s):  
Kinetic Modeling ◽  
Tracer Kinetic Modeling ◽  
Way 100635 ◽  
Tracer Kinetic

Linear least squares method in nonlinear parametric inverse problems

2020 ◽  
Vol 28 (2) ◽  
pp. 307-312
Author(s):  
Leonid L. Frumin
Keyword(s):  
Inverse Problems ◽  
Least Squares ◽  
Least Squares Method ◽  
Nonlinear Least Squares ◽  
Linear Least Squares ◽  
Estimation Of Parameters ◽  
Discrete Approximations ◽  
Operator Equations ◽  
Transcendental Functions ◽  
Nonlinear Least Squares Method

AbstractA generalization of the linear least squares method to a wide class of parametric nonlinear inverse problems is presented. The approach is based on the consideration of the operator equations, with the selected function of parameters as the solution. The generalization is based on the two mandatory conditions: the operator equations are linear for the estimated parameters and the operators have discrete approximations. Not requiring use of iterations, this approach is well suited for hardware implementation and also for constructing the first approximation for the nonlinear least squares method. The examples of parametric problems, including the problem of estimation of parameters of some higher transcendental functions, are presented.

Tracer Kinetic Modeling in PET

PET Clinics ◽  
2007 ◽  
Vol 2 (2) ◽  
pp. 267-277 ◽  
Author(s):  
M'hamed Bentourkia ◽  
Habib Zaidi
Keyword(s):  
Kinetic Modeling ◽  
Tracer Kinetic Modeling ◽  
Tracer Kinetic

scholarly journals Hybrid Levenberg–Marquardt and weak-constraint ensemble Kalman smoother method

2016 ◽  
Vol 23 (2) ◽  
pp. 59-73 ◽  
Author(s):  
J. Mandel ◽  
E. Bergou ◽  
S. Gürol ◽  
S. Gratton ◽  
I. Kasanický
Keyword(s):  
Least Squares ◽  
Newton Method ◽  
Nonlinear Least Squares ◽  
Additional Observation ◽  
Linear Least Squares ◽  
Regularization Term ◽  
Marquardt Method ◽  
Kalman Smoother ◽  
Levenberg Marquardt ◽  
Adjoint Operators

Abstract. The ensemble Kalman smoother (EnKS) is used as a linear least-squares solver in the Gauss–Newton method for the large nonlinear least-squares system in incremental 4DVAR. The ensemble approach is naturally parallel over the ensemble members and no tangent or adjoint operators are needed. Furthermore, adding a regularization term results in replacing the Gauss–Newton method, which may diverge, by the Levenberg–Marquardt method, which is known to be convergent. The regularization is implemented efficiently as an additional observation in the EnKS. The method is illustrated on the Lorenz 63 model and a two-level quasi-geostrophic model.

Sign in / Sign up

Export Citation Format

Share Document