A characterization of the Non-Degenerate Source Condition in super-resolution
A characterization of the Non-Degenerate Source Condition in super-resolution
复制标题
超分辨率中非简并源条件的表征
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
V. Duval
中科院分区：
文献类型：
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作者：
V. Duval
在最近的一篇文章中，Schiebinger等人提供了一个由M狄拉克质量组成的信号的无噪声恢复的充分条件，给出了2 M + 1个观测结果，例如，它与高斯滤波器的卷积，使用基追踪测量。在目前的工作中，我们表明，他们的标准的一个变体提供了一个必要和充分条件的非退化源条件（NDSC），这是由Duval和Peyr{\'e}，以确保支持在超分辨率的稳定性。我们提供了充分的条件，例如，无条件地举行的拉普拉斯内核提供一个至少有2 M的测量。对于高斯滤波器，我们表明，这些条件是满足两个非常不同的配置：样本近似均匀勒贝格措施，或更令人惊讶的是，样本都局限在一个足够小的间隔。
In a recent article, Schiebinger et al. provided sufficient conditions for the noiseless recovery of a signal made of M Dirac masses given 2M + 1 observations of, e.g. , its convolution with a Gaussian filter, using the Basis Pursuit for measures. In the present work, we show that a variant of their criterion provides a necessary and sufficient condition for the Non-Degenerate Source Condition (NDSC) which was introduced by Duval and Peyr{\'e} to ensure support stability in super-resolution. We provide sufficient conditions which, for instance, hold unconditionally for the Laplace kernel provided one has at least 2M measurements. For the Gaussian filter, we show that those conditions are fulfilled in two very different configurations: samples which approximate the uniform Lebesgue measure or, more surprisingly, samples which are all confined in a sufficiently small interval.
原子线谱估计的近似支持恢复：分辨率和精度的故事
影响因子：
2.5
作者：
Li, Qiuwei;Tang, Gongguo
通讯作者：
Tang, Gongguo