We present a deep learning-based algorithm to jointly solve a reconstruction problem and a wavefront set extraction problem in tomographic imaging. The algorithm is based on a recently developed digital wavefront set extractor as well as the well-known microlocal canonical relation for the Radon transform. We use the wavefront set information about x-ray data to improve the reconstruction by requiring that the underlying neural networks simultaneously extract the correct ground truth wavefront set and ground truth image. As a necessary theoretical step, we identify the digital microlocal canonical relations for deep convolutional residual neural networks. We find strong numerical evidence for the effectiveness of this approach.

翻译：我们提出了一个深层次的基于学习的算法,以共同解决重建问题和摄影成像中的波形提取问题。算法的基础是最近开发的数码波浪波谱提取器,以及众所周知的Radon变形的微本地光学关系。我们利用波波谱X射线数据信息来改善重建,方法是要求基础神经网络同时提取正确的地面真相波谱和地面真相图像。作为一个必要的理论步骤,我们为深相波谱残余神经网络确定数字微观局部线系关系。我们为这一方法的有效性找到强有力的数字证据。