Contourlets: A directional multiresolution image representation

We propose a new scheme, named contourlet, that provides a flexible multiresolution, local and directional image expansion. The contourlet transform is realized efficiently via a double iterated filter bank structure. Furthermore, it can be designed to satisfy the anisotropy scaling relation for curves, and thus offers a fast and structured curvelet-like decomposition. As a result, the contourlet transform provides a sparse representation for two-dimensional piecewise smooth signals resembling images. Finally, we show some numerical experiments demonstrating the potential of contourlets in several image processing tasks.