Wavelet thresholding via MDL for natural images

We study the application of Rissanen's Principle of Minimum Description Len gth (MDL) to the problem of wavelet denoising and compression for natural i mages. After making a connection between thresholding and model selection, we derive an MDL criterion based on a Laplacian model for noiseless wavelet coefficients. We find that this approach leads to an adaptive thresholding rule. While achieving mean-squared -error performance comparable with othe r popular thresholding schemes, the MDL procedure tends to keep far fewer c oefficients. From this property, we demonstrate that our method is an excel lent toot for simultaneous denoising and compression. We make this claim pr ecise by analyzing MDL thresholding in two optimality frameworks; one in wh ich we measure rate and distortion based on quantized coefficients and one in which we do not quantize, but instead record rate simply as the number o f nonzero coefficients.