Embodiments of this invention include computer-implemented mathematical methods to develop software and/or hardware implementations that use wavelet transforms (WT) to pre-process video frames that can then be compressed using a variety of codecs to produce compressed video frames. Such compressed video frames can then be transmitted, decompressed, post-processed using the post-processing methods disclosed in the invention and displayed in their original size and quality using software and/or hardware implementations of embodiments of the invention, thereby producing real-time high-quality reproduction of video sequences. Embodiments of devices that can implement the methods of this invention include mainframe computers, desktop computers, personal computers, laptop computers, tablet computers, wireless computers, television sets, set top boxes, cellular telephones, and computer readable media.