Date: October 9, 2025
Publisher: College of Information Science and Technology

Editor: Li Weimiao

A research team led by Lin Yizun from the Department of Mathematics at Jinan University’s College of Information Science and Technology has achieved significant progress in optimization algorithms and medical image reconstruction. Their paper, titled “An accelerated preconditioned proximal gradient algorithm with a generalized Nesterov momentum for PET image reconstruction,” has been officially published in Inverse Problems, a leading international journal in mathematics.

The paper’s authors include Lin Yizun as the first author, He Yongxin—a master’s student enrolled in 2023 at the Department of Mathematics—as the second author, Prof. C. Ross Schmidtlein from Memorial Sloan Kettering Cancer Center in the U.S. as the third author, and Prof. Han Deren from Beihang University as the corresponding author and fourth author.

Inverse Problems is classified as a T1 journal in the Chinese Mathematical Society’s Grading Directory of High-Quality Sci-Tech Journals, representing an authoritative international publication at the intersection of applied mathematics, computational science, and engineering. The journal focuses on core theories and methodologies in inverse problems research, covering key areas such as mathematical modeling, inversion algorithms, regularization theory, and image reconstruction. It aims to advance techniques for reliably and efficiently reconstructing unknown parameters or physical fields from observational data. The journal’s contributions are widely applied in medical imaging, geophysical exploration, non-destructive testing, and environmental monitoring, and it is recognized for its rigorous peer review and emphasis on innovative research.

The study addresses the ill-posed nature of image reconstruction in positron emission tomography (PET). The researchers proposed a novel reconstruction model based on smoothed high-order isotropic total variation regularization and designed an accelerated preconditioned proximal gradient algorithm (APPGA) incorporating a generalized Nesterov momentum technique. The paper provides a rigorous theoretical proof of the algorithm’s convergence and establishes convergence rates ofo(1/k²ᵠ)for the objective function value ando(1/kᵠ)for successive iteration differences, whereω ∈ (0,1]is the momentum parameter. Numerical experiments demonstrate that the proposed algorithm outperforms existing methods, such as PKMA and PPGA, in convergence speed, while also exhibiting strong robustness and adaptability in non-smooth high-order total variation regularization models.

The APPGA algorithm introduced in this research is not only applicable to medical image reconstruction but can also be extended to large-scale ill-posed optimization problems in fields such as machine learning, showing considerable potential for broader applications.

Link to the paper:
https://iopscience.iop.org/article/10.1088/1361-6420/adbd6a/meta