Non-linear quantization for arbitrary distributions and applications to Medical Image Processing

We report the development of a scalar quantization approach that helps build tables of decision and reconstruction levels for any probability density function (pdf). Several example pdf's are used for illustration: Uniform, Gaussian, Laplace, one-sided Rayleigh, and Gamma (One sided and double-sided symmetrical). The main applications of the methodology are principally aimed at Multiresolution Image compression where generally the Stretched Exponential pdf is encountered. Specialising to this important case, we perform quantization and information entropy calculations from selected medical MRI (Magnetic Resonance Imaging) pictures of the human brain. The image histograms are fitted to a Stretched exponential model and the corresponding entropies are compared.