提出快速准确的多色断层扫描重建算法，解决真实物理噪声问题。
Accurate, provable and fast polychromatic tomographic reconstruction: A variational inequality approach
- 基于变分不等式构建迭代算法，求解非线性衰减模型下的图像重建。
- 在少视角、低强度下仍保持高质量重建，计算效率优于现有方法。
- 适用于医学成像等需高精度、低辐射场景，适合研究者和工程师使用。
针对包含指数信号衰减、多波长X射线源、一般测量噪声（如泊松噪声）及多波段观测的计算机断层扫描（CT）信号重建问题，本文提出一种简单迭代算法EXACT（用于断层扫描的外梯度算法），将估计值建模为单调变分不等式的不动点。在对测量过程的合理假设下，证明了EXACT在统计性能与计算效率上的保证。同时考虑一种近期提出的高斯测量模型变体，给出了样本复杂度与迭代复杂度的界，优于现有算法。将EXACT应用于CT幻影图像恢复任务，结果显示其常以更少的射线视角、更低的源强度和更短的计算时间达到与现有方法相当的重建质量。代码已开源：https://github.com/voilalab/exact。
原文摘要 · Abstract (English)
We consider the problem of signal reconstruction for computed tomography (CT) under a nonlinear forward model that accounts for exponential signal attenuation, a polychromatic X-ray source, general measurement noise (e.g., Poisson shot noise), and observations acquired over multiple wavelength windows. We develop a simple iterative algorithm for single-material reconstruction, which we call EXACT (EXtragradient Algorithm for Computed Tomography), based on formulating our estimate as the fixed point of a monotone variational inequality. We prove guarantees on the statistical and computational performance of EXACT under realistic assumptions on the measurement process. We also consider a recently introduced variant of this model with Gaussian measurements and present sample and iteration complexity bounds for EXACT that improve upon those of existing algorithms. We apply our EXACT algorithm to a CT phantom image recovery task and show that it often requires fewer X-ray views, lower source intensity, and less computation time to achieve reconstruction quality similar to existing methods. Code is available at https://github.com/voilalab/exact.
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