Recursive estimation of 2-dimensional signal using arma model

Abstract

The estimation of 2-dimensional data from the noisy observation is studied. The study covers both the filtering and the model identification. A 2-dimensional recursive filtering algorithm, based on the non-symmetric half-plane model, is described for the problem of minimum-mean-square error estimation. The optimum filtering problem is solved by formulating the nonsymmetric half-plane ARMA (autoregressive-moving average) model and utilizing the truncation properties of the ARMA model. The identification of the model which is needed for the recursive filtering, is also studied. For the on-line processing applications, the sequential parameter identification methods are introduced. In the parameter identification the truncation property is also utilized. The convergence of the sequential parameter identification algorithm is proved. Experiments are performed for real image data, combining the proposed parameter identification and the filtering algorithms. The results show that this method can give considerable improvement in SNR.