The Shiftable Complex Directional Pyramid—Part II: Implementation and Applications

In Part I ["The shiftable complex directional pyramid-Part I: Theoretical Aspects," IEEE TRANSACTIONS on Signal Processing, vol. 56, no. 10, October 2008], we proposed a novel image decomposition called the shiftable complex directional pyramid. The shiftable, multiresolution and multidirectional image decomposition is constructed by the pyramidal dual-tree directional filter bank (PDTDFB). In this Part II, we consider the design and implementation issues of the PDTDFB and its applications in image processing. The PDTDFB is composed of a multiresolution filter bank (FB) and a pair of directional filter banks (DFB); the design of each FB is considered separately. The binary tree structure of the DFB is modified to minimize the phase delay factor in order to reduce the border artifact in case symmetric extension is used. The filters presented in this paper are designed in frequency domain, and approximated by finite-impulse-response (FIR) filters. Numerical experiments show that the filters from the dual branches approximate the Hilbert transform of those from the primal ones, and the resulting PDTDFB yields acceptable shiftability. The shiftable pyramid decomposition is then tested in image processing applications, including image denoising, texture retrieval and seismic image migration.