Image identification and estimation using the maximum entropy principle

Abstract Image identification and estimation using a reduced update Kalman filter (RUKF) requires that a model for the generating process is available. In (Kaufman, H.,Woods, J.W., Dravida, S., Tekalp, A.M., 1983. IEEE Trans. Automat. Control AC-28 (7)), a RUKF was used for image pixel density estimation using a 2D autoregressive model (AR) and for blurred image restoration (Koch, S., Kaufman, H., Biemond, J., 1995. IEEE Trans. Image Process. 4 (4), 520–523). However, in (Kaufman et al., 1983) , the AR model order and the measurement noise covariance were assumed to be known a priori. Recently, in (Kadaba, S.R., Gelfand, S.B., Kashyap, R.L., 1998. IEEE Trans. Image Process. 7 (10), 1439–1452) the authors proposed a recursive estimation algorithm for images using non-gaussian AR models. They supposed, like in (Kaufman et al., 1983) , that the measurement noise covariance and the model order were a priori known. Also, the process noise density, which may be non-gaussian, is assumed to be known. In the present work, image identification and estimation using a RUKF is reconsidered. No a priori information concerning the model order, the measurement noise covariance is needed. They are determined according to the maximum entropy principle (MEP) using an exhaustive search algorithm. It is shown that the estimation error with maximum entropy corresponds to the minimum mean squared error (MSE) giving the true model order and for the true noise covariance. Experimental results on simulated and real images are given to illustrate the performance of the proposed approach.