24 August 2017 Convex relaxations of spectral sparsity for robust super-resolution and line spectrum estimation
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Abstract
We consider recovering the amplitudes and locations of spikes in a point source signal from its low-pass spectrum that may suffer from missing data and arbitrary outliers. We first review and provide a unified view of several recently proposed convex relaxations that characterize and capitalize the spectral sparsity of the point source signal without discretization under the framework of atomic norms. Next we propose a new algorithm when the spikes are known a priori to be positive, motivated by applications such as neural spike sorting and fluorescence microscopy imaging. Numerical experiments are provided to demonstrate the effectiveness of the proposed approach.
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Yuejie Chi, Yuejie Chi, } "Convex relaxations of spectral sparsity for robust super-resolution and line spectrum estimation", Proc. SPIE 10394, Wavelets and Sparsity XVII, 103941G (24 August 2017); doi: 10.1117/12.2270060; https://doi.org/10.1117/12.2270060
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