An M-channel directional filter bank compatible with the contourlet and shearlet frequency tiling

In this work, we present new methods for creating M-channel directional filters to construct multiresolution and multidirectional orthogonal/ biorthogonal transforms. A key feature of these methods is the ability to solve the polynomial Bezout equation in higher dimensions by taking advantage of solutions that have been proposed for solving a related equation known as the analytic Bezout equation. These new techniques are capable of creating directional filters that yield spatial-frequency tilings equivalent to those of the contourlet and the shearlet transforms. Such directional filter banks can create sparse representations for a large class of images and can be used for various restoration problems, compression schemes, and image enhancements.