SIAM Journal on Imaging Sciences, Volume 13, Issue 4, Page 1754-1780, January 2020.
This work studies the problem of estimating a two-dimensional superposition of point sources or spikes from samples of their convolution with a Gaussian kernel. Our results show that minimizing a continuous counterpart of the $\ell_1$-norm exactly recovers the true spikes if they are sufficiently separated, and the samples are sufficiently dense. In addition, we provide numerical evidence that our results extend to non-Gaussian kernels relevant to microscopy and telescopy.

中文翻译：

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二维反卷积的采样定理

SIAM影像科学杂志，第13卷，第4期，第1754-1780页，2020年1月。
这项工作研究了估计点源或峰值的二维叠加问题，这些点源或峰值来自高斯核卷积样本。我们的结果表明，如果充分分离了真实的峰值并且样本足够密集，则使\\ ell_1 $范数的连续对应项最小化可以准确地恢复真实峰值。此外，我们提供了数值证据，表明我们的结果扩展到了与显微镜和望远镜相关的非高斯核。