TY - JOUR
T1 - Deconvolution of Point Sources
T2 - A Sampling Theorem and Robustness Guarantees
AU - Bernstein, Brett
AU - Fernandez-Granda, Carlos
PY - 2019/6
Y1 - 2019/6
N2 - 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 ℓ 1 -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.
AB - 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 ℓ 1 -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.
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U2 - 10.1002/cpa.21805
DO - 10.1002/cpa.21805
M3 - Article
AN - SCOPUS:85057874337
VL - 72
SP - 1152
EP - 1230
JO - Communications on Pure and Applied Mathematics
JF - Communications on Pure and Applied Mathematics
SN - 0010-3640
IS - 6
ER -