Image reconstruction of fluorescent molecular tomography based on the tree structured Schur complement decomposition

Area of Science:

• Biomedical imaging
• Computational mathematics

Background:

• Fluorescent molecular tomography (FMT) inverse problems involve complex matrix operations, leading to computational errors and complexity.
• Existing methods struggle with the ill-posed nature of FMT reconstruction.

Purpose of the Study:

• To develop a novel strategy for accelerating FMT reconstruction.
• To reduce computational complexity and improve accuracy in FMT.
• To enhance the ill-posed inverse problem of FMT using adaptive regularization.

Main Methods:

• A tree structured Schur complement decomposition strategy was employed to decompose the global system.
• Subsystems were solved using the biconjugate gradient method.
• An adaptive regularization scheme was developed, considering spatial and objective function variations.

Main Results:

• The proposed tree structured Schur complement decomposition significantly outperformed conventional methods in reconstruction accuracy and speed.
• The adaptive regularization scheme effectively improved the ill-posedness of the inverse problem compared to Tikhonov regularization.

Conclusions:

• The developed methods substantially enhance reconstructed image quality in FMT.
• The proposed techniques accelerate the FMT reconstruction process.