Total variation regularization for nonlinear fluorescence tomography with an augmented Lagrangian splitting approach.

Area of Science:

• Biomedical imaging
• Optical imaging
• Image reconstruction

Background:

• Fluorescence tomography reconstructs fluorescent dye distribution in scattering samples using boundary light measurements.
• Standard L(2) regularization methods yield smooth reconstructions, limiting resolution.
• Improved resolution is crucial for accurate localization of fluorescent targets.

Purpose of the Study:

• Investigate the efficacy of total variation (TV) regularization for fluorescence tomography.
• Enhance the localization and resolution of reconstructed fluorescent inclusions.
• Compare TV regularization with traditional L(2) methods.

Main Methods:

• Employed total variation (TV) regularization for the inverse problem in fluorescence tomography.
• Utilized an augmented Lagrange method to efficiently solve the inverse problem.
• Separated Gauss-Newton minimization from TV minimization for computational efficiency.

Main Results:

• TV regularization significantly improved the localization of reconstructed inclusions.
• The half-width measure of reconstructed inclusions decreased by at least 25% compared to L(2) reconstructions.
• Reconstructions showed sharper and more defined boundaries of fluorescent targets.

Conclusions:

• Total variation (TV) regularization is a superior method for fluorescence tomography reconstruction.
• TV regularization overcomes the resolution limitations of L(2) methods.
• This approach offers enhanced accuracy for biomedical imaging applications.