Fast and Robust Reconstruction for Fluorescence Molecular Tomography via L_1-2 Regularization.

Area of Science:

• Biomedical Imaging
• Medical Physics
• Computational Imaging

Background:

• Sparse reconstruction is crucial for fluorescence molecular tomography (FMT).
• High coherence in FMT system matrices limits the effectiveness of standard L1 minimization for accurate reconstruction.
• Existing methods struggle with sparsity when system matrices are highly coherent.

Purpose of the Study:

• To develop a novel sparse reconstruction method for FMT that overcomes limitations of L1 minimization with coherent system matrices.
• To introduce an L1-L2 norm minimization approach for improved FMT reconstruction.
• To present an efficient algorithm for solving the proposed L1-L2 minimization problem.

Main Methods:

• Proposed a novel reconstruction method minimizing the difference between L1 and L2 norms (L1-L2 minimization).
• Developed an iterative Difference of Convex Algorithm (DCA) to solve the non-convex L1-L2 minimization problem.
• Employed the alternating direction method of multipliers (ADMM) with an adaptive penalty to solve L1 minimization subproblems within each DCA iteration.

Main Results:

• The proposed L1-L2 minimization method, solved via DCA, demonstrated superior performance compared to L1, L2, L1/2, and L0 minimization.
• Outperformance was particularly evident when dealing with highly coherent system matrices common in FMT.
• Validation was performed using both simulated and in vivo experimental FMT data.

Conclusions:

• The DCA-based L1-L2 minimization offers a robust and effective solution for sparse reconstruction in FMT, especially under challenging conditions of high system matrix coherence.
• This novel approach enhances reconstruction accuracy and sparsity compared to conventional methods.
• The findings suggest a significant advancement in FMT reconstruction algorithms for biomedical applications.