Wavelet thresholding via MDL for natural images

We study the application of Rissanen's Principle of Minimum Description Length (MDL) to the problem of wavelet denoising and compression for natural images. After making a connection between thresholding and model selection, we derive an MDL criterion based on a Laplacian model for noiseless wavelet coe cients. We nd that this approach leads to an adaptive thresholding rule. While achieving mean squared error performance comparable with other popular thresholding schemes, the MDL procedure tends to keep far fewer coe cients. From this property, we demonstrate that our method is an excellent tool for simultaneous denoising and compression. We make this claim precise by analyzing MDL thresholding in two optimality frameworks; one in which we measure rate and distortion based on quantized coe cients and one in which we do not quantize, but instead record rate simply as the number of non-zero coe cients. Index Terms { Compression, denoising, Laplacian distribution, MDL, natural images, statistical estimation, wavelet thresholding. 1 Bell Laboratories, Murray Hill, NJ and 2 University of California at Berkeley, Berkeley, CA