Harnessing Sparsity over the Continuum: Atomic Norm Minimization for Super Resolution

Abstract

Convex optimization recently emerges as a compelling framework for performing super resolution, garnering significant attention from multiple communities spanning signal processing, applied mathematics, and optimization. This article offers a friendly exposition to atomic norm minimization as a canonical convex approach to solve super resolution problems. The mathematical foundations and performances guarantees of this approach are presented, and its application in super resolution image reconstruction for single-molecule fluorescence microscopy are highlighted.

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• Timely and Painless Breakups: Off-the-grid Blind Message Recovery and Users' Demixing
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• Random Pulse Sequences for Qubit Noise Spectroscopy
• A Coordinate Descent Approach to Atomic Norm Denoising
• On the Stable Resolution Limit of Total Variation Regularization for Spike Deconvolution
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