Regularisation methods of inverse problems: theory and computation

这个项目的目的是研究反问题的正则化方法，这些反问题在某种意义上是病态的，其解不连续地依赖于数据。当只有噪声数据可用时，正则化方法通过将原始反问题替换为由所谓的正则化参数监控的一族适定的相邻问题来定义稳定的近似解。该项目预计将开发纯粹由数据驱动的规则，以选择正规化参数，并展示它们在理论和实践中是如何运作的。它还将开发凸框架、加速策略以及预处理和分裂思想，以设计高效的正则化解算器。

This project aims to investigate regularisation methods for inverse problems which are ill-posed in the sense that their solutions depend discontinuously on the data. When only noisy data is available, regularisation methods define stable approximate solutions by replacing the original inverse problem with a family of well-posed neighbouring problems monitored by a so-called regularisation parameter. The project expects to develop purely data-driven rules to choose the regularisation parameter and show how they work in theory, and in practice. It will also develop convex framework, acceleration strategies as well as preconditioning and splitting ideas to design efficient regularisation solvers.