A recursive estimation technique is applied to the noisy image which is represented by a hyperbolic partial differential equation (PDE). Approximating a PDE model by a finite-difference approximation leads to an autoregressive (AR) model representation which Jain pointed out. In this paper, we use a new PDE model for the image representation. To apply a recursive estimation scheme to the image which is degraded by white noise, we propose the transformation of the.AR model into a state-space representation. To this representation, we apply a Kalman strip processor to reduce the order of the computation and storage, and the strip smoother (the optimal fixed-interval smoother) is also applied to obtain a better estimated imago. Three numerical examples are illustrated to show the effectiveness of the proposed algorithm.