We consider the image
recovery problem where the observed image is simultaneously corrupted by blur
and impulse noise. Due to the edge preserving property of the total variation,
and the property of providing good sparse approximation to piecewise smooth functions
of the wavelet frames, we propose a Framelet-based hybrid regularization model
to significantly lessen staircase artifacts while well preserving the valuable
edge information of the image. We take advantage of an alternating direction
method of multiplier to efficiently find a solution of this model. Because of
the convex of our model, the convergence of our method can be guaranteed.
Experimental results are finally presented to show the efficiency of our method
in terms of the peak-signal-to-noise ratio, structure similarity index measure
and the relative error.
Mathematics Subject Classification: 65T60; 90C90
Keywords: total variation, impulse noise, alternating direction method of multiplier, Framelet.