title: Shearlet-based total variation diffusion for denoising.
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.
authors.affiliation: System Planning Corporation, Arlington, VA 22209, USA.geasley@sysplan.com
authors.forename: Glenn R
authors.initials: GR
authors.lastname: Easley
authors.forename: Demetrio
authors.initials: D
authors.lastname: Labate
authors.forename: Flavia
authors.initials: F
authors.lastname: Colonna
mesh_terms: D000465:Algorithms; D016477:Artifacts; D007089:Image Enhancement / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D015203:Reproducibility of Results; D012680:Sensitivity and Specificity