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Recursive Kalman filters are often used for noise reduction in image data. These linear filters are based on the second-order statistics of image and noise. The noise is effectively reduced by the filtering operation, but the edges in the image are blurred and image contrast is reduced as well. These effects decrease the subjective quality of the image. A simple and computationally fast scan-ordered one-dimensional Kalman filter is derived, which is then provided with additional structural information about the edges in the noisy image. This filter behaves like the original noise-smoothing Kalman filter if no edges are present but has a greatly improved step response. In this way the edge-blurring phenomenon is effectively reduced. Results of several experiments are presented to demonstrate the feasibility of our approach.