1. An image processing apparatus, comprising: expansion means for expanding an input image by interpolation using peripheral pixel values; positioning means for carrying out positioning of an expanded image obtained by expansion of the input image and an output image obtained in an immediately preceding operation cycle; separation means for separating the output image into low frequency components and high frequency components; and mixture-addition means for mixing the low frequency components with the expanded image and adding the high frequency components to the image obtained by the mixture to produce a new output image.