论文标题
Cosharp：用于单发断层形状传感的凸面程序
CoShaRP: A Convex Program for Single-shot Tomographic Shape Sensing
论文作者
论文摘要
我们介绍了单发X射线断层扫描，旨在从单个锥形梁投影测量中估算目标图像。由于测量值少于未知数的数量，因此该线性逆问题非常确定。此外，它比传统的层析成像更具挑战性，在传统断层扫描中，足够大量的投影角形成了测量值，从而实现了简单的反转过程。但是，如果目标图像仅由已知形状组成，则单发断层扫描将变得不那么严重。因此，形状的先验将线性不足的图像估计问题转化为估计形状旋转式翻译的非线性问题。在本文中，我们通过使用形状的可能的旋转式翻译字典来规避非线性。我们提出了一个凸面程序Cosharp，以成功地恢复字典词。 Cosharp依赖于单纯型约束，可以使用原始偶算法快速解决。数值实验表明，Cosharp从中等嘈杂的测量值中恢复了稳定的形状。
We introduce single-shot X-ray tomography that aims to estimate the target image from a single cone-beam projection measurement. This linear inverse problem is extremely under-determined since the measurements are far fewer than the number of unknowns. Moreover, it is more challenging than conventional tomography where a sufficiently large number of projection angles forms the measurements, allowing for a simple inversion process. However, single-shot tomography becomes less severe if the target image is only composed of known shapes. Hence, the shape prior transforms a linear ill-posed image estimation problem to a non-linear problem of estimating the roto-translations of the shapes. In this paper, we circumvent the non-linearity by using a dictionary of possible roto-translations of the shapes. We propose a convex program CoShaRP to recover the dictionary-coefficients successfully. CoShaRP relies on simplex-type constraint and can be solved quickly using a primal-dual algorithm. The numerical experiments show that CoShaRP recovers shapes stably from moderately noisy measurements.
