Abstract
This paper analyzed the implementational aspects of the contourlet filter bank (or the pyramidal directional filter bank (PDFB)), and considered its application in image coding. First, details of the binary tree-structured directional filter bank (DFB) are presented, including a modification to minimize the phase delay factor and necessary steps for handling rectangular images. The PDFB is viewed as an overcomplete filter bank, and the directional filters are expressed in terms of polyphase components of the pyramidal filter bank and the conventional DFB. The aliasing effect of the conventional DFB and the Laplacian pyramid to the directional filters is then considered, and the conditions for reducing this effect are presented. The new filters obtained by redesigning the PDFBs satisfying these requirements have much better frequency responses. A hybrid multiscale filter bank consisting of the PDFB at higher scales and the traditional maximally decimated wavelet filter bank at lower scales is constructed to provide a sparse image representation. A novel embedded image coding system based on the image decomposition and a morphological dilation algorithm is then presented. The coding algorithm efficiently clusters the significant coefficients using progressive morphological operations. Context models for arithmetic coding are designed to exploit the intraband dependency and the correlation existing among the neighboring directional subbands. Experimental results show that the proposed coding algorithm outperforms the current state-of-the-art wavelet-based coders, such as JPEG2000, for images with directional features.
Highlights
Wavelet and filter bank (FB) have been one of major research topics in signal processing for the last two decades [1]
The paper discusses the pyramidal directional filter bank (PDFB) for the contourlet transform as an overcomplete FB and shows that the equivalent directional filters of the PDFB suffer from the aliasing effects due to its implementation structure
The equivalent directional filters of the PDFB have excellent passband and stopband characteristics, which is the key requirement for the contourlet to attain its asymptotic approximation power of smooth signal having discontinuities around C2 curve
Summary
Wavelet and filter bank (FB) have been one of major research topics in signal processing for the last two decades [1]. The PDFB or contourlet FB is a combination of EURASIP Journal on Advances in Signal Processing the Laplacian pyramid [6] and the conventional directional filter bank (DFB) [7]. It unites the advantages of both systems, which are multiresolution and multidirection. Because of its effectiveness in representing natural image, the PDFB has been used in image coding recently [13,14,15,16] These works, are based on the original implementation of the PDFB [5], which contains aliasing in the directional filters. Experimental results show that the proposed coding algorithm outperforms the current state-of-the-art waveletbased coders, such as JPEG2000, for images with directional features
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