论文标题
非负超分辨率的双重方法：扰动分析
The dual approach to non-negative super-resolution: perturbation analysis
论文作者
论文摘要
我们研究了超分辨率的问题，在该问题中，我们可以从高斯内核中的一些卷积样本中恢复非负点源的位置和权重。已经表明，通过最大程度地降低了度量的总变异规范，可以实现精确的恢复，而实现这一目标的实际方法是解决双重问题。在本文中，我们研究了解决方案双重问题的溶液的稳定性，无论是在精确的测量中还是在用添加噪声测量的情况下进行测量。特别是，我们建立了双重变量中的扰动与优化器周围原始变量中的扰动之间的关系，以及优化器周围双变量中的扰动与测量中添加噪声的大小之间的相似关系。我们的分析基于隐式函数定理的定量版本。
We study the problem of super-resolution, where we recover the locations and weights of non-negative point sources from a few samples of their convolution with a Gaussian kernel. It has been shown that exact recovery is possible by minimising the total variation norm of the measure, and a practical way of achieve this is by solving the dual problem. In this paper, we study the stability of solutions with respect to the solutions dual problem, both in the case of exact measurements and in the case of measurements with additive noise. In particular, we establish a relationship between perturbations in the dual variable and perturbations in the primal variable around the optimiser and a similar relationship between perturbations in the dual variable around the optimiser and the magnitude of the additive noise in the measurements. Our analysis is based on a quantitative version of the implicit function theorem.
