Deconvolution of Point Sources: A Sampling Theorem and Robustness Guarantees
Deconvolution of Point Sources: A Sampling Theorem and Robustness Guarantees
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点源的反卷积：采样定理和鲁棒性保证
DOI：
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发表时间：
2017
影响因子：
3
通讯作者：
C. Fernandez‐Granda
中科院分区：
文献类型：
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作者：
B. Bernstein;C. Fernandez‐Granda
在这项工作中，我们分析了一种凸规划方法，用于从与已知核卷积的非均匀样本中估计点源或尖峰的叠加。我们考虑一个一维模型，其中内核是高斯函数或Ricker小波，灵感来自于电子物理学和成像中的应用。我们的分析表明，最小化一个连续的对应的1-范数实现了原始尖峰的精确恢复，只要（1）信号支持满足最小分离条件和（2）有至少两个样本接近每个尖峰。此外，我们推导出理论保证的方法的鲁棒性，密集和稀疏的加性噪声。© 2018威利期刊股份有限公司
In this work we analyze a convex‐programming method for estimating superpositions of point sources or spikes from nonuniform samples of their convolution with a known kernel. We consider a one‐dimensional model where the kernel is either a Gaussian function or a Ricker wavelet, inspired by applications in geophysics and imaging. Our analysis establishes that minimizing a continuous counterpart of the ℓ1‐norm achieves exact recovery of the original spikes as long as (1) the signal support satisfies a minimum‐separation condition and (2) there are at least two samples close to every spike. In addition, we derive theoretical guarantees on the robustness of the approach to both dense and sparse additive noise. © 2018 Wiley Periodicals, Inc.
影响因子：
2.5
作者：
Vogelstein, Joshua T.;Packer, Adam M.;Paninski, Liam
通讯作者：
Paninski, Liam
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