Adaptive Bayesian augmented Lagrangian algorithm for fluorescence molecular tomography.

Area of Science:

• Biomedical Imaging
• Computational Imaging
• Medical Physics

Background:

• Fluorescence molecular tomography (FMT) enables 3D in vivo fluorescent probe imaging.
• FMT reconstruction faces challenges from light scattering and ill-posed inverse problems, limiting accuracy and reliability.
• Existing methods struggle with computational efficiency and robustness to noise.

Purpose of the Study:

• To introduce the adaptive Bayesian augmented Lagrangian (ABAL) algorithm for improved FMT reconstruction.
• To enhance the accuracy, robustness, and computational efficiency of FMT.
• To address the challenges of sparsity promotion and noise in FMT.

Main Methods:

• Developed the ABAL algorithm integrating sparse Bayesian learning (SBL) with the augmented Lagrangian (AL) framework.
• Reformulated the inverse problem as weighted L₁ minimization with adaptive regularization.
• Employed the AL method to solve the minimization problem, improving efficiency and mitigating local minima.

Main Results:

• The ABAL method demonstrated accurate reconstruction performance in simulations and experiments.
• Achieved an average minimum localization error (LE) of 0.358 mm.
• Obtained an average Dice coefficient of 0.775, indicating high shape recovery and accuracy.

Conclusions:

• The ABAL algorithm significantly improves stability and reconstruction accuracy in FMT.
• The method shows high localization accuracy, shape recovery, and robustness.
• ABAL holds potential for practical applications in fluorescence molecular tomography.