Modeling of subband coefficients for clustering-based adaptive quantization with spatial constraints

Discrete wavelet transform provides an advantageous framework of multiresolution space-frequency representation with promising applications in image processing. An efficient modeling of the spatial and frequency characteristics of the wavelet transform coefficients has been recognized as a key to designing efficient quantization for wavelet-based image coding. We have proposed a Bayesian estimation framework to provide a unified, simultaneous modeling of both the spatial distribution and the intensity distribution of the wavelet transform coefficients [IEEE Trans. Circuit Syst. Video Technol. 7 (1997) 343], where the spatially localized characteristics of a given subband are modeled by Gibbs random fields (GRF). In this study, we investigate the modeling of individual cluster intensity distribution of the subband coefficients, within the context of a joint scene and signal modeling. This joint modeling decomposes the overall distribution of the coefficients into the superposition of individual cluster distributions. Among Gaussian, Laplacian, and generalized Gaussian distributions, we conclude that the composite of multiple generalized Gaussian distributions is most consistent with the over-all distribution of the coefficients for any given high frequency subband. Meanwhile, modeling by Laplacian distributions has its advantage in terms of low computational complexity. The joint modeling enables us to devise a novel scene adaptive and signal adaptive quantization that fully exploits the coding redundancies resulting from wavelet transform. The concept and the mechanism of the proposed Bayesian estimation framework are applicable and tunable to other wavelet-based image processing tasks.