In this paper, we propose an object-based variational approach for the decoding of DV, M-JPEG, and MPEG1-2 video sequences. This new method improves the visual quality by considering simultaneously two kind of artifacts: artifacts due to compression, such as blocking effects and quantization noise, and other defects due to acquisition, transmission, or storage, such as dropouts and banding. Generally, methods improving the visual quality in video sequences consider these two kind of artifacts separately, and consist most of the time in post-processing techniques, applied to a single kind of artifact. The proposed method adopts a global approach for the decoding. It deals with the minimization of half-quadratic criteria, which allow the simultaneous estimation and restoration of backgrounds, on one side, and the moving objects detection on the other side. Each background and each object are processed separately, according to their spatial and temporal properties, to remove effectively blocking effects, quantization noise, and dropouts. Several experimental results are presented in this paper. They demonstrate the efficiency of the decoding method: blocking effects are largely removed and missing data are significantly reduced, compared to the standard decoding, resulting in a greater visual quality of the sequence.