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A note on Taylor boundary conditions for accurate image restoration

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Abstract

In recent years, several efforts were made in order to introduce boundary conditions for deblurring problems that allow to get accurate reconstructions. This resulted in the birth of Reflective, Anti-Reflective and Mean boundary conditions, which are all based on the idea of guaranteeing the continuity of the signal/image outside the boundary. Here we propose new boundary conditions that are obtained by suitably combining Taylor series and finite difference approximations. Moreover, we show that also Anti-Reflective and Mean boundary conditions can be attributed to the same framework. Numerical results show that, in case of low levels of noise and blurs able to perform a suitable smoothing effect on the original image (e.g. Gaussian blur), the proposed boundary conditions lead to a significant improvement of the restoration accuracy with respect to those available in the literature.

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Acknowledgments

This work is partly supported by MIUR PRIN 2012 N. 2012MTE38N and by grants of the group GNCS of INdAM.

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Authors and Affiliations

  1. Dipartimento di Ingegneria, Scienze Informatiche e Matematica, Università degli Studi dell’Aquila, Via Vetoio, Loc. Coppito, 67010, L’Aquila, Italy

    Pietro Dell’Acqua

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  1. Pietro Dell’Acqua
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Correspondence to Pietro Dell’Acqua.

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Communicated by: Lothar Reichel

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Dell’Acqua, P. A note on Taylor boundary conditions for accurate image restoration. Adv Comput Math 43, 1283–1304 (2017). https://doi.org/10.1007/s10444-017-9525-0

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  • DOI: https://doi.org/10.1007/s10444-017-9525-0

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