Models, Numerics, and Optimization
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Focusing on optical imaging problems, applications, and theory, this book describes progress in optical tomography. The text consists of several self-contained chapters with references written by pioneers and experts in the theoretical aspects of optical tomography and nonlinear imaging in general. The first chapter introduces the theoretical problem of optical tomography as it is relevant to applications in biomedical imaging. Each subsequent chapter addresses a particular technique that has been applied to tackle the problem of instability in optical tomography. The last three chapters summarize the state of the art and address the future of the field.
Table of Contents
Introduction to Optical Tomography, Arridge et al.
Function Spaces and Abstract Formulation, Khan et al.
Transport Equation Formulation, Dom et al.
Transport Equation with Spatially Varying Refractive Index, Thomas et al.
Level Set Methods in Transport Optical Tomography
Tikhonov Regularization in Diffuse Optical Tomography, Renaut, Smimova, et al.
Bayesian Approach in Diffuse Optical Tomography, Kaipio et al.
Optimal Source in Diffuse Optical Tomography, Jacob et al.
Sparsity Constrained Regularization in Diffuse Optical Tomography, Maass et al.
State of Transport Optical Tomography, Natterer, Dom et al.
State of Diffuse Optical Tomography, Arridge, Khan et al.
Conclusions and Future Directions, Arridge, Khan et al.
T. Khan is with the Department of Mathematical Sciences at Clemson University, South Carolina.