Tikhonov-regularized bispectral variational method for optical signal reconstruction

  • Authors:

  • N. G. Iroshnikov;A. V. Larichev;A. A. Potyagalova;A. V. Razgulin

  • Affiliations:

  • Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia;Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia;Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia;Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

  • Venue:
  • Computational Mathematics and Modeling
  • Year:
  • 2013

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Abstract

A Tikhonov-regularized bispectral variational method is proposed for image restoration in the presence of strong phase distortions. This method combines a number of advantages of the bispectral approach, such as preservation and restoration of phase information, invariance to random shifts of the original signal, and no requirement of high-accuracy prior information about statistical properties of observed signals. In combination with the Tikhonov-regularized variational method, which is adapted to stable processing of large images, we obtain a fairly efficient image restoration method. Test results in the presence of atmospheric and underwater phase distortions reported in this article establish the advantages of the proposed method relative to the traditional recursive bispectral method.