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A Finite Element Formulation of the Total Variation Method for Denoising a Set of Data

In: Integral Methods in Science and Engineering

Author

Listed:
  • P. J. Harris

    (University of Brighton)

  • K. Chen

    (University of Liverpool)

Abstract

The problem of removing the noise from an image can be formulated as the solution of a nonlinear differential equation. In most work, the finite different method is used to approximate the differential equation and a fixed-point method is used to solve the resulting nonlinear algebraic equations. However, the differential equation is such that an alternative system of nonlinear equations can be obtained by using a Galerkin based finite element formulation. The equations which result from the finite element method can be solved using Newton’s method rather than a fixed point method. This paper will consider the Galerkin finite element formulation of this problem and investigate the convergence of Newton’s method for obtaining the solution to the nonlinear system of equations. The methods will be illustrated with a number of typical one- and two-dimensional examples.

Suggested Citation

  • P. J. Harris & K. Chen, 2013. "A Finite Element Formulation of the Total Variation Method for Denoising a Set of Data," Springer Books, in: Christian Constanda & Bardo E.J. Bodmann & Haroldo F. de Campos Velho (ed.), Integral Methods in Science and Engineering, edition 127, chapter 0, pages 175-182, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4614-7828-7_12
    DOI: 10.1007/978-1-4614-7828-7_12
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