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Approximate super-resolution and truncated moment problems in all dimensions

Author

Listed:
  • Javier Hernan Garcia Sanchez
  • Camilo Hernandez
  • Mauricio Junca
  • Mauricio Velasco

Abstract

We study the problem of reconstructing a discrete measure on a compact set K subset Rn from a finite set of moments (possibly known only approximately) via convex optimization. We give new uniqueness results, new quantitative estimates for approximate recovery and a new sum-of-squares based hierarchy for approximate super-resolution on compact semi-algebraic sets.

Suggested Citation

  • Javier Hernan Garcia Sanchez & Camilo Hernandez & Mauricio Junca & Mauricio Velasco, 2018. "Approximate super-resolution and truncated moment problems in all dimensions," Documentos de Trabajo 17234, Quantil.
    • Handle: RePEc:col:000508:017234
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    Keywords

    CONVEX OPTIMIZATIONSUPER-RESOLUTIONTRUNCATED MOMENTS;

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other

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