This paper presents a new algorithmic framework for computing sparse solutions to large-scale linear discrete ill-posed problems. The approach is motivated by recent perspectives on iteratively reweighted norm schemes, viewed through the lens of iterative refinement. This framework leverages the efficiency and fast convergence of flexible Krylov methods while achieving higher accuracy through suitable restarts. Additionally, we demonstrate that the proposed methods outperform other flexible Krylov approaches in memory-limited scenarios. Relevant convergence theory is discussed, and the performance of the proposed algorithms is illustrated through a range of numerical examples, including image deblurring and computed tomography.

翻译：本文提出了一种新的算法框架，用于计算大规模线性离散不适定问题的稀疏解。该方法受到近期关于迭代重加权范数方案的新视角启发，并通过迭代优化的视角进行审视。该框架充分利用了灵活Krylov方法的高效性和快速收敛性，同时通过适当的重启策略实现更高精度。此外，我们证明了所提方法在内存受限场景下优于其他灵活Krylov方法。文中讨论了相关的收敛理论，并通过包括图像去模糊和计算机断层扫描在内的一系列数值算例，展示了所提算法的性能。