International Journal of Computer Vision

, Volume 70, Issue 3, pp 279–298

Image Deblurring in the Presence of Impulsive Noise


  • Leah Bar
    • School of Electrical EngineeringTel Aviv University
  • Nahum Kiryati
    • School of Electrical EngineeringTel Aviv University
  • Nir Sochen
    • Dept. of Applied MathematicsTel Aviv University

DOI: 10.1007/s11263-006-6468-1

Cite this article as:
Bar, L., Kiryati, N. & Sochen, N. Int J Comput Vision (2006) 70: 279. doi:10.1007/s11263-006-6468-1


Consider the problem of image deblurring in the presence of impulsive noise. Standard image deconvolution methods rely on the Gaussian noise model and do not perform well with impulsive noise. The main challenge is to deblur the image, recover its discontinuities and at the same time remove the impulse noise. Median-based approaches are inadequate, because at high noise levels they induce nonlinear distortion that hampers the deblurring process. Distinguishing outliers from edge elements is difficult in current gradient-based edge-preserving restoration methods. The suggested approach integrates and extends the robust statistics, line process (half quadratic) and anisotropic diffusion points of view. We present a unified variational approach to image deblurring and impulse noise removal. The objective functional consists of a fidelity term and a regularizer. Data fidelity is quantified using the robust modified L1 norm, and elements from the Mumford-Shah functional are used for regularization. We show that the Mumford-Shah regularizer can be viewed as an extended line process. It reflects spatial organization properties of the image edges, that do not appear in the common line process or anisotropic diffusion. This allows to distinguish outliers from edges and leads to superior experimental results.


image deblurringrestorationimpulse noisesalt and pepper noisevariational methods

Copyright information

© Springer Science + Business Media, LLC 2006