Abstract: The ill-posedness inherent in the bandlimited signal extrapolation problem can be treated by means of regularization parameters. In this paper, a regularized closed form of the 2-D extrapolation matrix, which is tolerant to noise, is formed by utilizing regularization parameters. Also the realization of the architecture of a two dimensional digital extrapolator is presented. A 2-D recursive Kalman filtering extrapolation algorithm is proposed.