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Total variation reconstruction from quadratic measurements

Abstract

In this paper, we consider a problem of reconstructing an image from incomplete quadratic measurements by minimizing its total variation. The problem of reconstructing an object from incomplete nonlinear acquisitions arises in many applications, such as astronomical imaging or depth reconstruction. Placing ourselves in a discrete setting, we provide theoretical guarantees for stable and robust image recovery from incomplete noisy quadratic measurements.

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Correspondence to Anastasia Zakharova.

Additional information

This work is co-financed by the European Union with the European regional development fund (ERDF, NH0002137) and by the Normandie Regional Council via the M2NUM project.

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Zakharova, A. Total variation reconstruction from quadratic measurements. Numer Algor 75, 81–92 (2017). https://doi.org/10.1007/s11075-016-0197-5

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Keywords

  • Total variation
  • Phase retrieval
  • Image recovery