Shearlet-based total variation diffusion for denoising

Authors:
Glenn R. Easley;Demetrio Labate;Flavia Colonna
Affiliations:
System Planning Corporation, Arlington, VA;Department of Mathematics, North Carolina State University, Raleigh, NC;Department of Mathematical Sciences, George Mason University, Fairfax, VA
Venue:
IEEE Transactions on Image Processing
Year:
2009

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Abstract

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.