Geometrical priors in a Bayesian approach to improve wavelet threshold procedures

Maarten Jansen; Adhemar Bultheel

doi:10.1117/12.366813

26 October 1999 Geometrical priors in a Bayesian approach to improve wavelet threshold procedures

Maarten Jansen, Adhemar Bultheel

Proceedings Volume 3813, Wavelet Applications in Signal and Image Processing VII; (1999) https://doi.org/10.1117/12.366813
Event: SPIE's International Symposium on Optical Science, Engineering, and Instrumentation, 1999, Denver, CO, United States

Abstract

Wavelet threshold algorithms replace wavelet coefficients with small magnitude by zero and keep or shrink the other coefficients. This is basically a local procedure, since wavelet coefficients characterize the local regularity of a function. Although a wavelet transform has decorrelating properties, structures in images, like edges, are never decorrelated completely, and these structures appear in the wavelet coefficients. We therefore introduce geometrical prior model for configurations of large wavelet coefficients and combine this with the local characterization of a classical threshold procedure into a Bayesian framework. The threshold procedure selects the large coefficients in the actual image. This observed configuration enters the prior model, which, by itself, only describes configurations, not coefficient values. In this way, we can compute for each coefficient the probability of being `sufficiently clean'.

Citation Download Citation

Maarten Jansen and Adhemar Bultheel "Geometrical priors in a Bayesian approach to improve wavelet threshold procedures", Proc. SPIE 3813, Wavelet Applications in Signal and Image Processing VII, (26 October 1999); https://doi.org/10.1117/12.366813

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