论文标题
在二维中进行反卷积的抽样定理
A Sampling Theorem for Deconvolution in Two Dimensions
论文作者
论文摘要
这项工作研究了估计点源的二维叠加或用高斯内核卷积样品中的尖峰的问题。我们的结果表明，如果$ \ ell_1 $ norm的连续对应物最小化，则如果足够分开，则可以恢复真实的尖峰，并且样品足够致密。此外，我们提供了数值证据，表明我们的结果扩展到与显微镜和望远镜相关的非高斯内核。
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.
