This paper proposes a new two-step procedure for sparse-view tomographic image reconstruction. It is called RISING, since it combines an early-stopped Rapid Iterative Solver with a subsequent Iteration Network-based Gaining step. So far, regularized iterative methods have widely been used for X-ray computed tomography image reconstruction from low-sampled data, since they converge to a sparse solution in a suitable domain, as upheld by the Compressed Sensing theory. Unfortunately, their use is practically limited by their high computational cost which imposes to perform only a few iterations in the available time for clinical exams. Data-driven methods, using neural networks to post-process a coarse and noisy image obtained from geometrical algorithms, have been recently studied and appreciated for both their computational speed and accurate reconstructions. However, there is no evidence, neither theoretically nor numerically, that neural networks based algorithms solve the mathematical inverse problem modeling the tomographic reconstruction process. In our two-step approach, the first phase executes very few iterations of a regularized model-based algorithm whereas the second step completes the missing iterations by means of a neural network. The resulting hybrid deep-variational framework preserves the convergence properties of the iterative method and, at the same time, it exploits the computational speed and flexibility of a data-driven approach. Experiments performed on a simulated and a real data set confirm the numerical and visual accuracy of the reconstructed RISING images in short computational times.
Generalized Fourier Diffraction Theorem and Filtered Backpropagation for Tomographic Reconstruction
University of Vienna（维也纳大学）；Technical University Berlin（柏林工业大学）；Santa Anna IT Research Institute（圣安娜IT研究所）；Christian Doppler Laboratory for Mathematical Modeling and Simulation of Next-Generation Ultrasound Devices (MaMSi)（下一代超声设备数学建模与仿真克里斯蒂安·道普勒实验室）
Superiorization of Preconditioned Conjugate Gradient Algorithms for Tomographic Image Reconstruction
Institute of Mathematical Science and Computation, University of São Paulo（圣保罗大学数学科学与计算研究所）；Department of Computer Science, The Graduate Center, City University of New York（纽约市立大学研究生院计算机科学系）；School of Electrical Engineering, Southwest Jiaotong University（西南交通大学电气工程学院）；Program in Electrical and Computer Engineering, Federal University of Technology（联邦技术大学电气与计算机工程项目）
