Video encoding method and apparatus, a video decoding method and apparatus, these programs and the recording medium

When decoding the encoded data of the video, each frame constituting the image is divided into a plurality of regions, when performing predictive decoding on each of the areas, temporary decoded image obtained by decoding if the image from the low-resolution prediction residual generate, to produce a final decoded image by updating the decoded value. Further, divides each frame constituting the image into a plurality of regions, when performing predictive coding for each of the areas, if the down-sampling the high-resolution prediction residual to generate a low-resolution prediction residual, the It generates sub-sampling prediction residual by sub-sampling process for sampling only some of the pixels of the high resolution prediction residual, and the low-resolution prediction residual them.