Linear filter theory based on Wiener filtering is well understood and used widely in many fields of image and signal processing. However, the use of linear filters is generally associated with implicit approximations. Therefore, in this work a series of non-linear filters is developed based on the concepts of Volterra series and these are applied to image interpolation problems. More explicitly, the aim is to interpolate one field of a frame of a television picture to form an estimate of the second field. This is known as de-interlacing and is useful in many areas of video processing, for example standards conversion. Conventional de-interlacing systems use a fixed linear combination of the pixels in the aperture. In this paper we consider the extension of these methods to allow estimators based on non-linear combinations of pixel values.