Limited-angle tomography of an interior volume is a challenging, highly ill-posed problem with practical implications in medical and biological imaging, manufacturing, automation, and environmental and food security. Regularizing priors are necessary to reduce artifacts by improving the condition of such problems. Recently, it was shown that one effective way to learn the priors for strongly scattering yet highly structured 3D objects, e.g. layered and Manhattan, is by a static neural network [Goy et al. Proc. Natl. Acad. Sci. 116, 19848–19856 (2019)]. Here, we present a radically different approach where the collection of raw images from multiple angles is viewed analogously to a dynamical system driven by the object-dependent forward scattering operator. The sequence index in the angle of illumination plays the role of discrete time in the dynamical system analogy. Thus, the imaging problem turns into a problem of nonlinear system identification, which also suggests dynamical learning as a better fit to regularize the reconstructions. We devised a Recurrent Neural Network (RNN) architecture with a novel Separable-Convolution Gated Recurrent Unit (SC-GRU) as the fundamental building block. Through a comprehensive comparison of several quantitative metrics, we show that the dynamic method is suitable for a generic interior-volumetric reconstruction under a limited-angle scheme. We show that this approach accurately reconstructs volume interiors under two conditions: weak scattering, when the Radon transform approximation is applicable and the forward operator well defined; and strong scattering, which is nonlinear with respect to the 3D refractive index distribution and includes uncertainty in the forward operator.

内部体积的有限角度断层扫描是一个具有挑战性的、高度不适定的问题，在医学和生物成像、制造、自动化以及环境和食品安全方面具有实际意义。规范先验对于通过改善此类问题的状况来减少伪影是必要的。最近，研究表明，学习强散射但高度结构化的 3D 对象（例如分层对象和曼哈顿对象）的先验的一种有效方法是通过静态神经网络 [Goy 等人，2017]。过程。国家。阿卡德。科学。 116, 19848–19856 (2019)]。在这里，我们提出了一种完全不同的方法，其中从多个角度收集原始图像类似于由依赖于对象的前向散射算子驱动的动态系统。照明角度中的序列索引在动力系统类比中起着离散时间的作用。因此，成像问题变成了非线性系统识别问题，这也表明动态学习更适合正则化重建。我们设计了一种循环神经网络 (RNN) 架构，以新颖的可分离卷积门控循环单元 (SC-GRU) 作为基本构建块。通过对几个定量指标的综合比较，我们表明动态方法适用于有限角度方案下的通用内部体积重建。我们证明这种方法在两种条件下可以准确地重建体积内部：弱散射，当 Radon 变换近似适用并且前向算子定义明确时；强散射，相对于 3D 折射率分布而言是非线性的，并且包括前向算子的不确定性。