The problem solved in this paper is formulated as: given an observation of an noisy image against the background and given the statistics of the image and the noise, find an estimate of the image such that the computer-time and storage requirements of the estimator are modest. Two-dimensional line scanning image model is applied to get the reasonable state space equation. The resulting image restoration is performed by the scalar Kalman filter, smoother. Vector processing is also posslble to process simultaneously all rows of the image matrix.