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A Finite Element Method For Deblurring Images

In: Integral Methods in Science and Engineering

Author

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  • P. J. Harris

    (University of Brighton)

  • K. Chen

    (University of Liverpool)

Abstract

Much of the existing work on removing noise and blurring from digital images has concentrated on using the finite difference method to solve to governing integral and differential equations due to the ease with which the method can be applied to gridded data on a rectangular domain. However, it is much more difficult to use if the domain of the image is no longer rectangular, such as when a circular mask is applied to the image. In such cases it is advantageous to use the finite element method as it can be used to solve problems with curved boundaries with very little (if any) addition work being required. In this paper, we present a selection of finite element methods which can be used to reduce both the noise and blurring in digital images. The finite element method is applied to the governing equations, which may include first-kind integral operators and non-linear regularization operators, to yield a system of algebraic equations which can be solved using an iterative scheme based on Newton’s method. Different regularization operators are considered and compared in terms of their computational complexity and overall accuracy. The paper will present numerical results for analyzing typical examples images.

Suggested Citation

  • P. J. Harris & K. Chen, 2015. "A Finite Element Method For Deblurring Images," Springer Books, in: Christian Constanda & Andreas Kirsch (ed.), Integral Methods in Science and Engineering, edition 1, chapter 0, pages 291-299, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-16727-5_24
    DOI: 10.1007/978-3-319-16727-5_24
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