A Sparsity-Constrained Preconditioned Kaczmarz Reconstruction Method for Fluorescence Molecular Tomography

Area of Science:

• Biomedical imaging
• Optical imaging
• Molecular imaging

Background:

• Fluorescence molecular tomography (FMT) enables molecular and cellular level biological process resolution.
• The inverse problem in FMT is ill-posed due to limited measurements, numerous unknowns, and photon diffusion in tissues.

Purpose of the Study:

• To propose a novel method for reconstructing fluorescent targets in FMT.
• To address the ill-posed nature of the FMT inverse problem.

Main Methods:

• Developed a sparsity-constrained preconditioned Kaczmarz (SCP-Kaczmarz) method.
• The SCP-Kaczmarz method incorporates preconditioning to reduce forward matrix row correlation and enforces sparsity in Kaczmarz iterations.
• Validated the method using numerical simulations, phantom experiments, and in vivo studies.

Main Results:

• The SCP-Kaczmarz method demonstrated improved convergence compared to the classical Kaczmarz method.
• Enhanced accuracy in fluorescent target reconstruction was observed with the proposed method.
• The method proved effective in numerical, phantom, and in vivo experimental settings.

Conclusions:

• The SCP-Kaczmarz method offers a significant advancement for FMT reconstruction.
• This technique provides better accuracy and faster convergence for molecular imaging applications.
• The findings support the utility of SCP-Kaczmarz for resolving biological processes with FMT.