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Blind image deconvolution using a banded matrix method

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Abstract

In this paper we study the blind image deconvolution problem in the presence of noise and measurement errors. We use a stable banded matrix based approach in order to robustly compute the greatest common divisor of two univariate polynomials and we introduce the notion of approximate greatest common divisor to encapsulate the above approach, for blind image restoration. Our method is analyzed concerning its stability and complexity resulting to useful conclusions. It is proved that our approach has better complexity than the other known greatest common divisor based blind image deconvolution techniques. Examples illustrating our procedures are given.

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Authors and Affiliations

  1. Department of Informatics & Telecommunications, University of Athens, Athens, Greece

    Antonios Danelakis

  2. Department of Mathematics, University of Athens, Panepistemiopolis, 15784, Athens, Greece

    Marilena Mitrouli

  3. Section of Mathematics & Engineering Sciences, Department of Military Sciences, Hellenic Army Academy, Vari, Greece

    Dimitrios Triantafyllou

Authors
  1. Antonios Danelakis
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  2. Marilena Mitrouli
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  3. Dimitrios Triantafyllou
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Corresponding author

Correspondence to Marilena Mitrouli.

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Danelakis, A., Mitrouli, M. & Triantafyllou, D. Blind image deconvolution using a banded matrix method. Numer Algor 64, 43–72 (2013). https://doi.org/10.1007/s11075-012-9654-y

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  • DOI: https://doi.org/10.1007/s11075-012-9654-y

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