Statistical Models for Images: Compression, Restoration and Synthesis

We present a parametric statistical model for visual images in the wavelet transform domain. We characterize the joint densities of coefficient magnitudes at adjacent spatial locations, adjacent orientations, and adjacent spatial scales. The model accounts for the statistics of a wide variety of visual images. As a demonstration of this, we’ve used the model to design a progressive image encoder with state-of-the-art rate-distortion performance. We also show promising examples of image restoration and texture synthesis. Vision is arguably our most important sensory system, judging from both the ubiquity of visual forms of communication, and the large proportion of the human brain devoted to visual processing. Nevertheless, it has proven difficult to establish a good mathematical definition (in the form of a statistical model) for visual images. Many applications i