Directional Filter Banks with Directional Vanishing Moments: A Brief Review

Contourlet transform is an efficient directional multiscale decomposition of images that combines the Laplacian pyramid (LP) with directional filter banks (DFBs). The LP decomposes the input image into multiple scales, whereas the DFBs applied on bandpass images of the pyramid yields directional localization. Similar to wavelets in 1-D, the key feature of contourlets is that they can quickly “feel” the edges of images. This is attributed to their ability to annihilate directional smoothness. One way to achieve this annihilating property is to impose the so-called directional vanishing moments (DVMs) on the design of DFBs. This report is a review of two-channel filter banks with DVMs, the building blocks for DFBs, with contourlet transform as context. The construction of contourlet transform is briefly discussed together with basics of 2-D multirate signal processing. The design of biorthogonal perfect reconstruction filter banks with DVMs is the main topic of this report.