AbstractThe authors investigated construction of an extended‐order statistic filter to remove non‐Gaussian white noise added to image signal. First, they devised a differential‐order statistic filter using signal‐differential ordering instead of a signal‐value ordering and estimated its noise reduction performance. Next, they proposed an extended‐order statistic filter which unifies the three‐order information of time, signal value, and signal differences obtained from a signal within the filter window.Preparing the 3‐dimensionalized filter coefficient space and using filter coefficients chosen sequentially in the three different orders among them allow effective noise reduction performance to be obtained. In addition, as a method for resolving a problem on the design method of filter coefficients, investigation was made using a synthesized training sequence. Extracting parameters necessary to a linear AR model from an objective signal, it is shown that the filter design using a training sequence synthesized from it gives noise reduction performance similar to the one at the optimal design.