论文标题
点源定位的近端方法
Proximal methods for point source localisation
论文作者
论文摘要
点源定位通常被建模为措施上的套索类型问题。然而，非希尔伯特空间中的优化方法（例如ra量度量的空间）的发达远不如希尔伯特空间。用于点源定位的大多数数值算法都是基于Frank-Wolfe条件梯度方法，为此开发了临时收敛理论。我们将近端型方法扩展到度量空间。这包括前向后的分裂，其惯性版本和原始的偶近近端分裂。他们的收敛证明遵循标准模式。我们证明了它们的数值功效。
Point source localisation is generally modelled as a Lasso-type problem on measures. However, optimisation methods in non-Hilbert spaces, such as the space of Radon measures, are much less developed than in Hilbert spaces. Most numerical algorithms for point source localisation are based on the Frank-Wolfe conditional gradient method, for which ad hoc convergence theory is developed. We develop extensions of proximal-type methods to spaces of measures. This includes forward-backward splitting, its inertial version, and primal-dual proximal splitting. Their convergence proofs follow standard patterns. We demonstrate their numerical efficacy.
