Estimation of the Number of True Gray Levels, Their Values, and Relative Frequencies in a Noisy Image

Abstract

In some applications information is presented as a two-dimensional image corrupted by random noise. Due to the precision of the equipment that forms the image, we can typically have a large number, v, of observed gray levels. But in many situations we know that the number of true gray levels, p, corresponding to, for example, the number of tissue types in a brain slice, is much less than v. In this article we propose a method based on the kernel density estimator for estimating the p underlying true gray levels and their relative frequencies. The strong convergence rates for estimators of these quantities are established. The method is successfully applied to artificial and magnetic resonance images.

Key Words:

• Kernel density estimation
• Magnetic resonance image
• Simulation study
• Strong convergence rate