Statistical Models for Images:
Compression, Restoration and Synthesis

Eero P Simoncelli

Published in:
Proc. 31st Asilomar Conference on Signals, Systems and Computers
Pacific Grove, CA. November 2-5, 1997.
doi: 10.1109/ACSSC.1997.680530
© IEEE Signal Processing Society.

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.
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More recent publications on these topics:
  • Statistical Modeling: Statistical modeling of photographic images. E P Simoncelli. Chapter 4.7 in Handbook of Image and Video Processing, 2nd Edition, ed. Alan Bovik, Academic Press, 2005.    Abstract and reprint
    Random Cascades on Wavelet Trees and Their Use in Modeling and Analyzing Natural Imagery. M J Wainwright and E P Simoncelli and A S Willsky. Applied and Computational Harmonic Analysis, 11(1), 2001.    Abstract and reprint,
  • Compression: Image Compression via Joint Statistical Characterization in the Wavelet Domain. R W Buccigrossi and E P Simoncelli. IEEE Trans Image Processing, 8(12):1688-1701, Dec 1999.    Abstract
  • Denoising: Image denoising using scale mixtures of Gaussians in the wavelet domain J Portilla, V Strela, M Wainwright and E P Simoncelli. IEEE Trans Image Processing, 12(11): 1338-1351, Nov 2003. Abstract
  • Texture Modeling: A parametric texture model based on joint statistics of complex wavelet coefficients. J Portilla and E P Simoncelli. Int'l Journal of Computer Vision 40(1):49-71, October, 2000.    Abstract