Digital noise removal methods and systems for picture quality improvement on next generation high quality set-top-box and digital TV SOCs is disclosed with particular to a de-blocking method and system that is effective on on-grid and off-grid blocky artifacts generated by lossy video compression standards. Blocky artifacts are filtered by extracting motions vectors for a current pixel block, calculating off-grid positions based on the extracted motion vectors, and applying de-blocking filtering along the calculated off-grid positions. The methods and systems can further skip filtering on-grid blocky artifacts to be filtered by an on-grid de-blocking filter known in the art.