A Theory for Multiresolution Signal Decomposition: The Wavelet Representation
IEEE Transactions on Pattern Analysis and Machine Intelligence
JPEG 2000: Image Compression Fundamentals, Standards and Practice
JPEG 2000: Image Compression Fundamentals, Standards and Practice
Estimation of the information by an adaptive partitioning of the observation space
IEEE Transactions on Information Theory
Image compression via joint statistical characterization in the wavelet domain
IEEE Transactions on Image Processing
IEEE Transactions on Image Processing
Sparse geometric image representations with bandelets
IEEE Transactions on Image Processing
Directional multiscale modeling of images using the contourlet transform
IEEE Transactions on Image Processing
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This paper reports an information-theoretic analysis of the dependencies that exist between curvelet coefficients. We show that strong dependencies exist in local intra-band micro-neighborhoods, and that the shape of these neighborhoods is highly anisotropic. With this respect, it is found that the two immediately adjacent neighbors that lie in a direction orthogonal to the orientation of the subband convey the most information about the coefficient. Moreover, taking into account a larger local neighborhood set than this brings only mild gains with respect to intra-band mutual information estimations. Furthermore, we point out that linear predictors do not represent sufficient statistics, if applied to the entire intra-band neighborhood of a coefficient. We conclude that intra-band dependencies are clearly the strongest, followed by their inter-orientation and inter-scale counterparts; in this respect, the more complex intra-band/inter-scale or intra-band/inter-orientation models bring only mild improvements over intra-band models. Finally, we exploit the coefficient dependencies in a curvelet-based image coding application and show that the scheme is comparable and in some cases even outperforms JPEG2000.