3D Discrete Shearlet Transform and Video Denoising

This paper introduces a numerical implementation of the 3D shearlet transform, a directional transform which is derived from the theory of shearlets. The shearlet approach belongs to a class of directional multiscale methods emerged during the last 10 years to overcome the limitations of traditional multiscale systems, which also include curvelets and contourlets. Unlike other methods, shearlets are derived from the theory of affine systems, which allows a very flexible mathematical structure and a natural transition from the continuous to the digital setting. Following the recent proof of the optimality of the 3D shearlet representation, in this paper we develop an algorithmic implementation of the 3D shearlet transform that follows closely the spatial-frequency pattern of the corresponding continuous transform. The performance of the algorithm is illustrated on problems of video denoising and successfully compared against other state-of-the-art multiscale techniques, including curvelets and surfacelets.