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Shearlet-Based Total Variation Diffusion for Denoising

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3 Author(s)
Glenn R. Easley ; Syst. Planning Corp., Arlington, VA ; Demetrio Labate ; Flavia Colonna

We propose a shearlet formulation of the total variation (TV) method for denoising images. Shearlets have been mathematically proven to represent distributed discontinuities such as edges better than traditional wavelets and are a suitable tool for edge characterization. Common approaches in combining wavelet-like representations such as curvelets with TV or diffusion methods aim at reducing Gibbs-type artifacts after obtaining a nearly optimal estimate. We show that it is possible to obtain much better estimates from a shearlet representation by constraining the residual coefficients using a projected adaptive total variation scheme in the shearlet domain. We also analyze the performance of a shearlet-based diffusion method. Numerical examples demonstrate that these schemes are highly effective at denoising complex images and outperform a related method based on the use of the curvelet transform. Furthermore, the shearlet-TV scheme requires far fewer iterations than similar competitors.

Published in:

IEEE Transactions on Image Processing  (Volume:18 ,  Issue: 2 )