Geometrical priors for noisefree wavelet coefficient configurations in image denoising

Wavelet threshold algorithms replace 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 inimages, like edges, are never decorrelated completely, and these structures appear in the wavelet coefficients. We therefore introduce a 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 coefficients values. In this way, we can compute for each coefficient the probability of being ``sufficiently clean''.Lecture notes in statistics, vol 141status: publishe