Robust transformed l1 metric for fluorescence molecular tomography

Yating Yuan; Huangjian Yi; Dizhen Kang; Jingjing Yu; Hongbo Guo; Xuelei He; Xiaowei He

doi:10.1016/j.cmpb.2023.107503

Robust transformed l₁ metric for fluorescence molecular tomography

Comput Methods Programs Biomed. 2023 Jun:234:107503. doi: 10.1016/j.cmpb.2023.107503. Epub 2023 Mar 22.

Authors

Yating Yuan¹, Huangjian Yi¹, Dizhen Kang¹, Jingjing Yu², Hongbo Guo¹, Xuelei He¹, Xiaowei He³

Affiliations

¹ The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China; School of Information Sciences and Technology, Northwest University, Xi'an, 710127, China.
² School of Physics and Information Technology, Shaanxi Normal University, Xi'an, 710119, China.
³ The Xi'an Key Laboratory of Radiomics and Intelligent Perception, Xi'an, China; School of Information Sciences and Technology, Northwest University, Xi'an, 710127, China. Electronic address: hexw@nwu.edu.cn.

PMID: 37015182
DOI: 10.1016/j.cmpb.2023.107503

Abstract

Background and objective: Fluorescence molecular tomography (FMT) is a non-invasive molecular imaging modality that can be used to observe the three-dimensional distribution of fluorescent probes in vivo. FMT is a promising imaging technique in clinical and preclinical research that has attracted significant attention. Numerous regularization based reconstruction algorithms have been proposed. However, traditional algorithms that use the squared l₂-norm distance usually exaggerate the influence of noise and measurement and calculation errors, and their robustness cannot be guaranteed.

Methods: In this study, we propose a novel robust transformed l₁ (TL1) metric that interpolates l₀ and l₁ norms through a nonnegative parameter α∈(0,+∞). The TL1 metric looks like the l_p-norm with p∈(0,1). These are markedly different because TL1 metric has two properties, boundedness and Lipschitz-continuity, which make the TL1 criterion suitable distance metric, particularly for robustness, owing to its stronger noise suppression. Subsequently, we apply the proposed metric to FMT and build a robust model to reduce the influence of noise. The nonconvexity of the proposed model made direct optimization difficult, and a continuous optimization method was developed to solve the model. The problem was converted into a difference in convex programming problem for the TL1 metric (DCATL1), and the corresponding algorithm converged linearly.

Results: Various numerical simulations and in vivo bead-implanted mouse experiments were conducted to verify the performance of the proposed method. The experimental results show that the DCATL1 algorithm is more robust than the state-of-the-art approaches and achieves better source localization and morphology recovery.

Conclusions: The in vivo experiments showed that DCATL1 can be used to visualize the distribution of fluorescent probes inside biological tissues and promote preclinical application in small animals, demonstrating the feasibility and effectiveness of the proposed method.

Keywords: Distance metric; Fluorescence molecular tomography; Iterative algorithm; Reconstruction; Robustness.

MeSH terms

Algorithms
Animals
Fluorescence
Fluorescent Dyes*
Image Processing, Computer-Assisted / methods
Mice
Phantoms, Imaging
Tomography* / methods

Substances

Fluorescent Dyes