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.
翻译：----
基于邻近法的点源定位方法
本文摘要：
点源定位通常模拟为基于测量的 Lasso 问题。然而，在非希尔伯特空间（如 Radon 测度空间）中的优化方法比在希尔伯特空间中的要差得多。大多数点源定位的数值算法基于 Frank-Wolfe 条件梯度方法，而对于其收敛性的理论则是 ad hoc。本文对邻近法在测度空间中的扩展进行了研究，包括正反传拆分及其惯性版本以及原始-对偶邻近拆分。这些方法的收敛证明遵循标准模式。我们展示了它们的数值有效性。
相关内容
微信扫码咨询专知VIP会员