Qiao Zhiwei, Redler Gage, Epel Boris, Halpern Howard
School of Computer and Information Technology, Shanxi University, Taiyuan, Shanxi, China.
Department of Radiation Oncology, Moffitt Cancer Center, Tampa, FL, USA.
J Xray Sci Technol. 2024;32(6):1481-1504. doi: 10.3233/XST-240029.
Optimization based image reconstruction algorithm is an advanced algorithm in medical imaging. However, the corresponding solving algorithm is challenging because the model is usually large-scale and non-smooth. This work aims to devise a simple and convergent solver for optimization model.
The alternating direction method of multipliers (ADMM) algorithm is a simple and effective solver of the optimization model. However, there always exists a sub-problem that has not close-form solution. One may use gradient descent algorithm to solve this sub-problem, but the step-size selection via line search is time-consuming. Or, one may use fast Fourier transform (FFT) to get a close-form solution if the sparse transform matrix is of special structure. In this work, we propose a fully linearized ADMM (FL-ADMM) algorithm that avoids line search to determine step-size and applies to sparse transform of any structure.
We derive the FL-ADMM algorithm instances for three total variation (TV) models in 2D computed tomography (CT). Further, we validate and evaluate one FL-ADMM algorithm and explore how two important factors impact convergence rate. These studies show that the FL-ADMM algorithm may accurately solve the optimization model.
The FL-ADMM algorithm is a simple, effective, convergent and universal solver of optimization model in image reconstruction. Compared to the standard ADMM algorithm, the new algorithm does not need time-consuming step-size line-search or special demand to sparse transform. It is a rapid prototyping tool for optimization based image reconstruction.
基于优化的图像重建算法是医学成像中的一种先进算法。然而，由于模型通常规模较大且不光滑，相应的求解算法具有挑战性。这项工作旨在为优化模型设计一种简单且收敛的求解器。
乘子交替方向法（ADMM）算法是优化模型的一种简单有效的求解器。然而，总是存在一个没有闭式解的子问题。可以使用梯度下降算法来解决这个子问题，但通过线搜索选择步长很耗时。或者，如果稀疏变换矩阵具有特殊结构，可以使用快速傅里叶变换（FFT）来获得闭式解。在这项工作中，我们提出了一种完全线性化的ADMM（FL-ADMM）算法，该算法避免了线搜索来确定步长，并且适用于任何结构的稀疏变换。
我们推导了二维计算机断层扫描（CT）中三种总变分（TV）模型的FL-ADMM算法实例。此外，我们验证并评估了一种FL-ADMM算法，并探讨了两个重要因素如何影响收敛速度。这些研究表明，FL-ADMM算法可以准确地求解优化模型。
FL-ADMM算法是图像重建中优化模型的一种简单、有效、收敛且通用的求解器。与标准ADMM算法相比，新算法不需要耗时的步长线搜索，也不需要对稀疏变换有特殊要求。它是基于优化的图像重建的快速原型工具。
