论文标题
快速近端梯度方法用于层析成像图像重建的非平滑凸优化
Fast Proximal Gradient Methods for Nonsmooth Convex Optimization for Tomographic Image Reconstruction
论文作者
论文摘要
引入并应用于层析成像图像重建，并应用于最小化非平滑凸功能的快速近视梯度方法（FPGM）和单调FPGM（MFPGM）。目标函数值序列的收敛属性得出了，包括$ o \ left（1/k^{2} \ right）$ non-Asymptotic bound。所提出的理论扩大了当前的知识，并解释了某些已知呈现良好实践表现的某些方法的收敛行为。涉及计算机断层扫描图像重建的数值实验显示了在实际情况下具有竞争力的方法。与代数重建技术进行了实验比较，以发现某些加速近端梯度算法的某些行为，这些行为显然尚未在将这些算法应用于层析成像图像重建时注意到。
The Fast Proximal Gradient Method (FPGM) and the Monotone FPGM (MFPGM) for minimization of nonsmooth convex functions are introduced and applied to tomographic image reconstruction. Convergence properties of the sequence of objective function values are derived, including a $O\left(1/k^{2}\right)$ non-asymptotic bound. The presented theory broadens current knowledge and explains the convergence behavior of certain methods that are known to present good practical performance. Numerical experimentation involving computerized tomography image reconstruction shows the methods to be competitive in practical scenarios. Experimental comparison with Algebraic Reconstruction Techniques are performed uncovering certain behaviors of accelerated Proximal Gradient algorithms that apparently have not yet been noticed when these are applied to tomographic image reconstruction.
