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Shift-invariant approximations of structured shift-variant blurring matrices

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Abstract

In this paper we analyze in a general and pure algebraic way imaging systems characterized by shift-variant integral kernels which hide some intrinsic shift-invariance, related to an appropriate coordinate change; we call as structured shift-variant these kinds of imaging systems. In this respect, we propose an algorithm for finding a coordinate transformation which allows a structured shift-variant PSF to become explicitly shift-invariant. The usage of the computed coordinate transformation will highly reduce the numerical complexity of the imaging system, providing a real time deblurring in some real applications. Some preliminary numerical results show the effectiveness of the proposal.

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Authors and Affiliations

  1. Dipartimento di Matematica, Via Dodecaneso 35, 16146, Genova, Italy

    Claudio Estatico & Fabio Di Benedetto

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  1. Claudio Estatico
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  2. Fabio Di Benedetto
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Correspondence to Fabio Di Benedetto.

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Estatico, C., Di Benedetto, F. Shift-invariant approximations of structured shift-variant blurring matrices. Numer Algor 62, 615–635 (2013). https://doi.org/10.1007/s11075-012-9686-3

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  • DOI: https://doi.org/10.1007/s11075-012-9686-3

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