报告人介绍：

陈冲，中国科学院数学与系统科学研究院研究员，研究兴趣包括：医学成像反问题、图像处理、计算几何以及人工智能等，担任计算数学、CT理论与应用研究、Int. J. Comput. Math.、J. Math. Imaging Vis.等国内外期刊编委，研究工作获国家自然科学基金委优秀青年科学基金资助。

报告简介：

Motivated by a class of nonlinear imaging inverse problems, for instance, multispectral computed tomography (MSCT), we study the convergence theory of the nonlinear Kaczmarz method (NKM) for solving the system of nonlinear equations with componentwise convex mapping, namely, the function corresponding to each equation being convex. Such kind of nonlinear mapping may not satisfy the commonly used componentwise tangential cone condition (TCC). For this purpose, we propose a novel condition named relative gradient discrepancy condition (RGDC), and make use of it to prove the convergence of the NKM with several general index selection strategies, where these strategies include the cyclic strategy and the maximum residual strategy. Particularly, we investigate the application of the NKM for solving nonlinear systems in MSCT image reconstruction. We prove that the nonlinear mappings in this context fulfill the proposed RGDC rather than the componentwise TCC, and provide a global convergence of the NKM based on the previously obtained results. Numerical experiments further illustrate the numerical convergence of the NKM for MSCT image reconstruction.