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Active constrained truncated Newton method for simple-bound optical tomography
1Department of Chemical Engineering, Texas A&M University, College Station 77843, USA.
Summary
Constrained optimization significantly reduces computational time and storage for large-scale optical imaging reconstructions. This approach offers a more efficient alternative to traditional unconstrained methods using Tikhonov regularization.
Area of Science:
- Biomedical Optics
- Computational Imaging
- Inverse Problems
Background:
- Nonlinear unconstrained optimization, often using Newton-Raphson, is standard for optical imaging.
- Tikhonov regularization in unconstrained methods leads to high computational costs and storage demands for large-scale problems.
Purpose of the Study:
- To compare computational time and storage requirements between constrained and unconstrained optimization for optical imaging.
- To demonstrate the advantages of constrained minimization in large-scale optical imaging reconstructions.
Main Methods:
- Formulated the inverse optical imaging problem using both simple-bound constrained and unconstrained minimization.
- Employed a forward simulator with Galerkin finite-element formulation for excitation and fluorescence.
- Utilized a truncated Newton method with trust regions and automatic reverse differentiation for optimization.
Main Results:
- Constrained image reconstructions showed reduced computational time and storage needs.
- The inverse algorithm successfully identified spatial distributions of absorption and lifetime.
- Optimization was accelerated using truncated Newton and automatic reverse differentiation.
Conclusions:
- Physically based, constrained minimization offers a more logical and efficient approach for large-scale optical imaging.
- Constrained methods overcome the storage and computational limitations of unconstrained regularization techniques.