- Kevin R. Vixie
- T-7 Mathematical Modeling and Analysis
- .
- Vixie’s research is clustered around Inverse Problems, Image Analysis, High Dimensional Analysis, Networks, and the supporting mathematical and computational methods. In particular, he is interested in, PDE/variational/geometric measure theory approaches to image analysis and fluid/materials modeling, and Application of geometric and analytic insights to high dimensional data analysis.
-
- He is just getting interested in the above problems where there is some implicit or explicit network structure.
- Vixie is currently part of a team at LANL working on sparse tomography of fast events. The team is looking at this multifaceted problem in order to improve the quality of the current image reconstructions from data collected with proton radiography. Potentially, the methods and techniques being developed have much wider applicability since any method that enables one to reduce the number of radiographs and still retain accurate reconstructions is applicable in any other application where tomography is used.
- Vixie started and continues to organize a cross-division interdisciplinary group meeting once a week to discuss a wide range of research issues, which relate to radiography and image analysis. The Radiographic Analysis Study Group
- meetings each have tutorials and discussion sections and are approximately two to three hours long.
- Tutorials range from geometric measure theory and functional analysis to wavelet methods to discussion of experimental data and accelerator design.
- .
- Image Analysis
- Vixie is working on several projects related to the analysis of image data including the application of PDE-based image analysis tools to radiographic images, development of a nonlinear PCA toolbox for face-recognition, and the development of physics based metrics for the comparison of radiographic image data to simulations.
- In general, he is doing what he can to promote the development of an advanced and broadly based image analysis research capability at Los Alamos.
- Before coming to LANL, Vixie worked on a NASA funded project with Andy Fraser and Richard Smith on the modeling of time series that have their origin in geophysical systems. He used vector auto regressive hidden Markov models to do this.
- His dissertation "Geometry and Dynamics of Data Driven Modeling" was made up of four papers written in collaboration with other researchers.
- The first two papers deal with the problem of aliasing in signals, the third one addresses the solution of the radiographic problem in which the radiographs are taken sequentially in time, and the fourth one looks at a particular measure for model performance in the case that the model tries to capture the behavior of a dynamical system. His adviser was A. M. Fraser.
- Vixie’s expertise includes:
- •Nonlinear Functional Analysis
- •Partial Differential Equations
- •Geometric Measure Theory
- •Variational Analysis
- •Dynamical Systems
- •Geometric Methods
- .
- Vixie’s Publications include:
- - Andy Fraser, Nick Hengartner, Kevin Vixie and Brendt Wohlberg, "Classification modulo invariance, with application to face recognition", Journal of Computational and Graphical Statistics, vol. 12, no. 4, pp. 829--852, Dec 2003 LA-UR-03-3409
- - Andy Fraser, Nick Hengartner, Kevin Vixie and Brendt Wohlberg, "Incorporating invariants in Mahalanobis distance based classifiers: Application to Face Recognition", in International Joint Conference on Neural Networks (IJCNN), (Portland, OR, USA), 2003 LA-UR-03-3426
- - T. Asaki and K. Vixie, "SVD Analysis for Radiographic Object Reconstruction II: Null Space Enhancements", 2002 LA-UR-03-5937
- - T. Asaki and K. Vixie, "SVD Analysis for Radiographic Object Reconstruction I: Initial Results", 2002 LA-UR-01-6534
-
- - T. Asaki and K. Vixie, "Standard 2D Test Objects for Radiographic Inversion Studies", 2002 LA-UR-02-3978
- Kevin Vixie, Signals and Hidden Information, PhD thesis, Portland State University, 2001 LA-UR-13881-t
-
|
