06-11-2012, 11:57 AM
Deblurring of Color Images Corrupted by Impulsive Noise
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Abstract
We consider the problem of restoring a multichannel image corrupted by blur and impulsive noise (e.g. saltand-
pepper noise). Using the variational framework, we consider the L1 fidelity term and several possible regularizers.
In particular, we use generalizations of the Mumford-Shah functional to color images and ¡-convergence
approximations to unify deblurring and denoising. Experimental comparisons show that the Mumford-Shah
stabilizer yields better results with respect to Beltrami and Total Variation regularizers. Color edge detection
is a beneficial by-product of our methods.
INTRODUCTION
In this work we consider the problem of restoring a color image degraded by blur and high impulsive
noise level. Deblurring and denoising are probably two of the most studied problems in image processing. But
while most of the literature on deblurring and denoising either considers these problems separately, or deals
with deblurring at very low noise level, in the specific problem we deal with here, both tasks are performed
simultaneously.
The deconvolution problem (also referred to as deblurring or more generally as restoration) has a long and rich
history, which can be traced by an interested reader with the help of reviews by Demoment [1], Biemond et
al. [2], Banham and Katsaggelos [3], and Puetter et al. [4]. The overwhelming majority of the works on
deblurring consider the case of blurred gray-level images with a small amount of additive Gaussian noise [5],
[6], [7], [8], [9], [10]. A promising and efficient method to solve this problem even in the presence of high
noise level was proposed by Neelamani et al. [11], where hybrid Fourier-wavelet regularization was used in the
deconvolution process. Nikolova et al. [12] incorporated the piecewise Gaussian Markov random field model in
the regularization term. This formulation can be viewed as half-quadratic regularization [9], [10], which leads
to a truncated quadratic function of the image gradients.