Solving inverse problems with Iterative regularisation and convex penalties

该项目旨在开发和研究新的计算程序，用于解决不具有传统正则化方法所需的通常平滑特性（或源条件）的逆问题。这类逆问题的例子非常普遍，包括图像恢复、光声断层成像和光谱学。预计这个项目将极大地扩展这些问题的方法工具箱，利用巴拿赫空间、凸分析、并行计算和优化的思想。该项目有望对更好地理解逆问题及其求解程序作出实质性贡献。

This project aims to develop and investigate new computational procedures for the solution of inverse problems which do not have the usual smoothness properties (or source conditions) required for the traditional regularisation methods. Examples of such inverse problems are very common and include image restoration, photo-acoustic tomography and spectroscopy. It is anticipated that this project will substantially extend the toolbox of methods for such problems utilising ideas from Banach spaces, convex analysis, parallel computing and optimisation. This project is expected to make a substantial contribution to a better understanding of inverse problems and their solution procedures.