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Time and spatial ε-filter is proposed in order to improve the image quality of video compressed by DCT motion compensated coding. The ε-filter is a nonlinear digital filter proposed by authors before in order to remove small-amplitude random noise such as block noise and mosquito noise caused by DCT coding on images. Authors also proposed before motion compensated ε-filter which can efficiently remove such noise from video coded by motion compensated coding. In this paper, the extension of this motion compensated ε-filter to time domain is proposed, that is time and spatial ε-filter. It is shown that the noise is more powerfully removed from video than the previous method, while the complexity of the system is kept low. Moreover, the performance of this filter is shown to be improved by adaptive control of the parameter of the ε-filter.