Regular Hybrid Wavelets and Directional Filter Banks: Extensions and Applications

In a previous work, we proposed a new family of nonredundant geometrical image transforms using hybrid wavelets and directional filter banks (HWD). In this paper we further develop and examine the proposed family and provide an efficient realization utilizing regular filters. Furthermore, we extend and employ the new proposed HWD transforms in two key image processing applications, coding and denoising, and demonstrate their promising results. For coding, an SPIHT-like algorithm is developed for HWD; and for denoising, a translation-invariant HWD (TIHWD) transform is constructed. Our simulations illustrate significant improvements under the proposed transforms when compared with other transform variations.