Sidky Emil Y, Chartrand Rick, Boone John M, Pan Xiaochuan
Department of Radiology, University of Chicago, Chicago, IL 60637, USA.
Theoretical Division T-5, Los Alamos National Laboratory, Los Alamos, NM 87545, USA.
IEEE J Transl Eng Health Med. 2014 Jun 30;2. doi: 10.1109/JTEHM.2014.2300862.
Exploiting sparsity in the image gradient magnitude has proved to be an effective means for reducing the sampling rate in the projection view angle in computed tomography (CT). Most of the image reconstruction algorithms, developed for this purpose, solve a nonsmooth convex optimization problem involving the image total variation (TV). The TV seminorm is the norm of the image gradient magnitude, and reducing the norm is known to encourage sparsity in its argument. Recently, there has been interest in employing nonconvex quasinorms with 0<<1 for sparsity exploiting image reconstruction, which is potentially more effective than because nonconvex is closer to -a direct measure of sparsity. This paper develops algorithms for constrained minimization of the total -variation (TV), of the image gradient. Use of the algorithms is illustrated in the context of breast CT-an imaging modality that is still in the research phase and for which constraints on X-ray dose are extremely tight. The TV-based image reconstruction algorithms are demonstrated on computer simulated data for exploiting gradient magnitude sparsity to reduce the projection view angle sampling. The proposed algorithms are applied to projection data from a realistic breast CT simulation, where the total X-ray dose is equivalent to two-view digital mammography. Following the simulation survey, the algorithms are then demonstrated on a clinical breast CT data set.
利用图像梯度幅度的稀疏性已被证明是降低计算机断层扫描（CT）投影视角采样率的有效方法。为此目的开发的大多数图像重建算法都解决了一个涉及图像总变差（TV）的非光滑凸优化问题。TV半范数是图像梯度幅度的范数，已知减小该范数会促使其自变量具有稀疏性。最近，人们对采用0 < p < 1的非凸拟范数进行利用稀疏性的图像重建产生了兴趣，这可能比TV更有效，因为非凸p - 范数更接近 - 稀疏性的直接度量。本文开发了用于图像梯度的总变差（TV）的p - 范数约束最小化的算法。在乳腺CT的背景下说明了这些算法的使用 - 乳腺CT是一种仍处于研究阶段且对X射线剂量限制极其严格的成像模态。基于TV的图像重建算法在计算机模拟数据上进行了演示，以利用梯度幅度稀疏性来减少投影视角采样。所提出的算法应用于来自真实乳腺CT模拟的投影数据，其中总X射线剂量相当于双视角数字乳腺摄影。在模拟研究之后，然后在临床乳腺CT数据集上演示了这些算法。
