Mixture Estimation From Multichannel Image Data

Abstract

The following problem arises in Computer vision, diagnostic medical imaging, and remote sensing: At each pixel in an image a vector of observations is measured, and the distribution of these measurements is approximated by a mixture model. The goal is to estimate the mixing proportions of the classes by pixel in the image together with any unknown parameters in the latent distributions. In many problems of this type, it is appropriate to incorporate constraints on mixing proportions. This article deals with spatial smoothness constraints, which have been found useful in analyzing sequences of emission tomography images. An estimation methodology using penalized likelihood with multiple smoothing parameters is proposed. Numerical methods for implementing this methodology are developed. This includes an importance sampling technique for approximating the effective degrees of freedom of the solution. The methodology is illustrated with an application to the analysis of a dynamic emission tomography study using a C ₁₁-labeled thymidine tracer. Some simulations motivated by this example are also presented.

KEY WORDS:

• EM algorithm
• Multidimensional smoothing
• Positron emission tomography