A new family of nonredundant transforms using hybrid wavelets and directional filter banks

We propose a new family of nonredundant geometrical image transforms that are based on wavelets and directional filter banks. We convert the wavelet basis functions in the finest scales to a flexible and rich set of directional basis elements by employing directional filter banks, where we form a nonredundant transform family, which exhibits both directional and nondirectional basis functions. We demonstrate the potential of the proposed transforms using nonlinear approximation. In addition, we employ the proposed family in two key image processing applications, image coding and denoising, and show its efficiency for these applications.