This paper presents an image, then a video, compression scheme based on a restoration process applied to a transform domain. Most of the method relies on the ability to suppress, then automatically restore some transformed coefficients in a coding scheme. We use a total variation (TV) minimization model in order to voluntarily predict canceled coefficients. Thus, the method can be assimilated to a new prediction step by inpainting of transformed coefficients. The method has successfully been tested in a DCT-based JPEG coder, but with results that do not overpass the actual state-of-the-art. The main contribution of our work stands in the fact that this method has been introduced into actual video coding standards based on a predicting step. In these standards, a residual error is coded to recover the initial signal. In this case we noticed that the residual error has much less energy than the original coefficients and therefore that the compression rate could significantly be improved by using the same cancellation/restoration method, as a new prediction step. This has been (efficiently) tested on the H.264/AVC standard.