Rayleigh-Rice mixture parameter estimation via EM algorithm for change detection in multispectral images

The problem of estimating the parameters of a Rayleigh-Rice mixture density is often encountered in image analysis (e.g., remote sensing and medical image processing). In this paper we address this general problem in the framework of change detection (CD) in multitemporal and multispectral images. One widely used approach to change detection in multispectral images is based on Change Vector Analysis (CVA). Here, the distribution of the magnitude of the difference image can be theoretically modeled by a Rayleigh-Rice mixture density. However, given the complexity of this model, in applications a Gaussian-mixture approximation is often considered, which may affect the change detection results. In this paper we present a novel technique for parameter estimation of the Rayleigh-Rice density that is based on a specific definition of the Expectation-Maximization (EM) algorithm. The proposed technique, which is characterized by good theoretical properties, iteratively updates the parameters and does not depend on specific optimization routines. Several numerical experiments on synthetic data demonstrate the effectiveness of the method which is general and can be applied to any image processing problem involving the Rayleigh-Rice mixture density. In the change detection context, the Rayleigh-Rice model (which is theoretically derived) outperforms other empirical models. Experiments on real multitemporal and multispectral remote sensing images confirm the validity of the model by returning significantly higher change detection accuracies than those obtained by using state-of-the-art approaches.