A two-dimensional recursive estimation algorithm based on the asymmetric half-plane model is described for the problem of MMSE (minimum mean-square error) filtering. The optimum filtering problem is solved by formulating the asymmetric half-plane ARMA (autoregressive moving average) model for two-dimensional data. The sequential parameter identification from the noisy two-dimensional data is also discussed, utilizing the stochastic approximation. Experiments were performed for real image data, combining the proposed parameter identification and estimation algorithms. The results show that this method gives considerable improvement in SNR.