Image Deblurring in the Presence of Impulsive Noise
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24-05-2010, 11:56 AM

Presented By:
Nir Sochen*
Leah Bar
Nahum Kiryati
School of Electrical Engineering
Dept. of Applied Mathematics
Tel Aviv University

Consider the problem of image deblurring in the presence of impulsive noise. Stan- dard image deconvolution methods rely on the Gaussian noise model and do not per- form 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 ap- proaches are inadequate, because at high noise levels they induce nonlinear distortion that hampers the deblurring process. Distinguishing outliers from edge elements is dicult in current gradient-based edge-preserving restoration methods. The suggested approach integrates and extends the robust statistics, line process (half quadratic) and anisotropic diusion points of view. We present a unied variational approach to image deblurring and impulse noise removal. The objective functional consists of a delity term and a regularizer. Data delity is quantied using the robust modied 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 re- ects spatial organization properties of the image edges, that do not appear in the common line process or anisotropic diusion. This allows to distinguish outliers from edges and leads to superior experimental results.

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