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Rotational image deblurring with sparse matrices

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Abstract

We describe iterative deblurring algorithms that can handle blur caused by a rotation along an arbitrary axis (including the common case of pure rotation). Our algorithms use a sparse-matrix representation of the blurring operation, which allows us to easily handle several different boundary conditions. We also include robust stopping rules for the iterations. The performance of our algorithms is illustrated with examples.

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Acknowledgments

We thank Henrik Aanæs for his invaluable help with the geometric aspects, and John Bardsley for his help with the implementation of the randomized GCV method.

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Authors and Affiliations

  1. Department of Applied Mathematics and Computer Science, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark

    Per Christian Hansen

  2. Department of Mathematics and Computer Science, Emory University, Atlanta, GA, 30322, USA

    James G. Nagy

  3. Fraunhofer Institute for Integrated Circuits, Am Wolfsmantel 33, 91058 , Erlangen, Germany

    Konstantinos Tigkos

Authors
  1. Per Christian Hansen
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  2. James G. Nagy
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  3. Konstantinos Tigkos
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Corresponding author

Correspondence to Per Christian Hansen.

Additional information

Communicated by Rosemary Renaut.

This work was supported by Grant No. 274-07-0065 from the Danish Research Council for Technology and Production Sciences, Grant No. DMS-1115627 from the US National Science Foundation, and Grant No. AF9550-12-1-0084 from the US Air Force Office of Scientific Research.

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Hansen, P.C., Nagy, J.G. & Tigkos, K. Rotational image deblurring with sparse matrices. Bit Numer Math 54, 649–671 (2014). https://doi.org/10.1007/s10543-013-0464-y

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