论文标题
扩展的投影指导方法，并应用于传输层析成像
Scaled Projected-Directions Methods with Application to Transmission Tomography
论文作者
论文摘要
X射线计算机断层扫描中的统计图像重建产生了与非阴性边界的大规模正则线性最小二乘问题，其中操作员的内存足迹是一个令人担忧的问题。在圆柱坐标中离散图像会导致大量的内存节省，并允许无需直接计算操作员的并行操作矢量产品，而无需降低图像质量。但是，它会恶化操作员的调理。我们通过块循环缩放量操作员改善了HESSIAN条件，并提出了一种策略，以在投影指导方法的上下文中处理非对抗缩放，以解决约束问题。我们使用两种算法来描述我们对缩放策略的实现：TRON，一种具有精确第二个衍生物的信任区域方法，以及L-BFGS-B，是具有有限的记忆Quasi-Newton Hessian近似值的LinesEarch方法。我们将我们的方法与问题变化的方法进行比较。在两个重建问题上，我们的方法收敛的速度比可变方法的变化更快，并且在最佳残留方面比一阶方法更高的精度。
Statistical image reconstruction in X-Ray computed tomography yields large-scale regularized linear least-squares problems with nonnegativity bounds, where the memory footprint of the operator is a concern. Discretizing images in cylindrical coordinates results in significant memory savings, and allows parallel operator-vector products without on-the-fly computation of the operator, without necessarily decreasing image quality. However, it deteriorates the conditioning of the operator. We improve the Hessian conditioning by way of a block-circulant scaling operator and we propose a strategy to handle nondiagonal scaling in the context of projected-directions methods for bound-constrained problems. We describe our implementation of the scaling strategy using two algorithms: TRON, a trust-region method with exact second derivatives, and L-BFGS-B, a linesearch method with a limited-memory quasi-Newton Hessian approximation. We compare our approach with one where a change of variable is made in the problem. On two reconstruction problems, our approach converges faster than the change of variable approach, and achieves much tighter accuracy in terms of optimality residual than a first-order method.
