2018
DOI: 10.1002/cpa.21805
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Deconvolution of Point Sources: A Sampling Theorem and Robustness Guarantees

Abstract: 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`1-norm achieves exact recovery of the original spikes as long as (1) the signal support satisfies a minimum-sep… Show more

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Cited by 20 publications
(32 citation statements)
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“…As a result, different sparse combinations of features may yield essentially the same data. For a detailed analysis of this issue in the context of super-resolution and deconvolution of point sources we refer the reader to Section 3.2 in [13] (see also [59] and [78]) and Section 2.1 in [3], respectively.…”
Section: Beyond Sparsity and Randomness: Separation And Correlation Dmentioning
confidence: 99%
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“…As a result, different sparse combinations of features may yield essentially the same data. For a detailed analysis of this issue in the context of super-resolution and deconvolution of point sources we refer the reader to Section 3.2 in [13] (see also [59] and [78]) and Section 2.1 in [3], respectively.…”
Section: Beyond Sparsity and Randomness: Separation And Correlation Dmentioning
confidence: 99%
“…where ξ > 0 is a parameter that must be tuned according to the noise level. Previous works have established robustness guarantees for TV-norm minimization applied to specific SNL problems such as super-resolution [14,34] and deconvolution [3] at small noise levels. These proofs are based on dual certificates.…”
Section: Robustness To Noisementioning
confidence: 99%
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