Optimization algorithms for Medical Image Processing, Biomedical Engineering, and Proton Radiation Therapy.

Talks and presentations

Accelerated Primal-Dual Fixed Point Method

September 19, 2025

Plenary Talk, Union of Mathematical Imaging (UMI), Enshi, Hubei, China

This work proposes an Accelerated Primal–Dual Fixed-Point (APDFP) method that employs Nesterov type acceleration to solve composite problems of the form \(\min_x\, f(x)+g\circ B(x)\), where \(g\) is nonsmooth and \(B\) is a linear operator. The APDFP features fully decoupled iterations and can be regarded as a generalization of Nesterov’s accelerated gradient the setting where the \(B\) can be non identity matrix.Theoretically, we improve the convergence rate of the partial primal-dual gap with respect to the Lipschitz constant of gradient of \(f\) from \(\mathcal{O}(\frac{1}{k})\) to \(\mathcal{O}(\frac{1}{k^2})\). Numerical experiments on graph-guided logistic regression and CT image reconstruction are conducted to validate the correctness and demonstrate the efficiency of the proposed method.

A ridge-filter-based and group-sparsity-regularized energy layer reduction method for IMPT

August 10, 2024

Oral Presentation, 66th ASTRO Annual Meeting, Washington DC, USA

Rapid IMPT delivery is essential for improving proton therapy efficiency, allowing more patients to be treated, enhancing dynamic target motion management, and reducing uncertainties to improve treatment quality. It also enables more breath-hold treatments while minimizing normal tissue damage by reducing target margins. This work focuses on reducing energy switching time—a key factor in IMPT delivery speed—without compromising plan quality. By introducing a novel Ridge-Filter-based and Group-Sparsity-regularized (RFGS) method, we significantly decrease the number of required energy layers, making treatment faster and more efficient.

Improving dose conformality for proton LATTICE via proton ARC therapy

June 07, 2024

Oral Presentation, 62nd Particle Therapy Co-Operative Group (PTCOG), Singapore

LATTICE therapy is a three-dimensional spatially fractionated radiotherapy (SFRT) technique that delivers a spatially modulated dose distribution characterized by high-dose peaks and low-dose valleys within the target volume. When integrated with intensity-modulated proton therapy (IMPT), LATTICE therapy benefits from the superior dose conformality of proton Bragg peaks, enabling more precise dose sculpting. However, the clinical implementation of LATTICE therapy using IMPT has been limited by challenges such as suboptimal target coverage and increased dose deposition in adjacent organs-at-risk (OARs). This study introduces a novel proton arc therapy approach to enhance dose coverage while improving OAR sparing, thereby optimizing the delivery of Proton LATTICE therapy.

Stochastic and accelerated primal dual fixed point methods

July 16, 2023

Presentation, Young Research Forum, Chinese Society for Industrial and Applied Mathematic, Nanjing, Jiangsu, China

Many important problems in data science and medical imaging—such as graphical lasso and computed tomography (CT) reconstruction—can be formulated as composite optimization problems. Although first-order primal-dual methods are widely adopted for their simplicity and low per-iteration cost, their performance often becomes unsatisfactory when applied to large-scale problems, which are increasingly common in practice. In this talk, we present three algorithmic extensions of the primal-dual fixed point (PDFP) method: the inertial PDFP (iPDFP), the stochastic PDFP (SPDFP), and the stochastic variance-reduced PDFP (SVRG-PDFP). These methods are specifically designed to address the computational challenges inherent in large-scale optimization tasks in data science and medical sciences. We provide convergence analyses for each algorithm and demonstrate their practical effectiveness through extensive numerical experiments.

An orthogonal matching pursuit optimization method for proton IMPT, ARC and FLASH with large-minimum-MU constraints

June 13, 2023

Oral Presentation, 61st Particle Therapy Co-Operative Group (PTCOG), Madrid, Spain

In proton radiation therapy (RT), the intensity of each deliverable proton spot—measured in monitor units (MU)—must either be zero or meet a minimum-MU (MMU) threshold. This constraint creates a nonconvex optimization problem. Higher-dose-rate treatments, such as efficient intensity-modulated proton therapy (IMPT), ARC proton therapy, and FLASH therapy, require solving this MMU problem with even larger MMU thresholds. However, increasing the MMU threshold makes the problem even more challenging to solve. This work aims to develop a more effective optimization method based on orthogonal matching pursuit (OMP) to address the MMU problem with large MMU thresholds. The proposed method demonstrated superior performance compared to the state-of-the-art methods, including the alternating direction method of multipliers (ADMM), proximal gradient descent (PGD), and stochastic coordinate descent (SCD).