Harnessing Sparsity Over the Continuum: Atomic norm minimization for superresolution

At the core of many sensing and imaging applications, the signal of interest can be modeled as a linear superposition of translated or modulated versions of some template [e.g., a point spread function (PSF) or a Green's function] and the fundamental problem is to estimate the translation or modulation parameters (e.g., delays, locations, or Dopplers) from noisy measurements. This problem is centrally important to not only target localization in radar and sonar, channel estimation in wireless communications, and direction-of-arrival estimation in array signal processing, but also modern imaging modalities such as superresolution single-molecule fluorescence microscopy, nuclear magnetic resonance imaging, and spike localization in neural recordings, among others.