Overlapping block discrete cosine transform coding and its fast algorithm

The discrete cosine transform (DCT) method is well known for a highly efficient coding for still images. A problem in this method is that the block distortion is observed in low‐rate coding. The overlapping block transform (OBT) has recently been proposed, aiming at the reduction of the block distortion. OBT is derived as a frequency analyzer/synthesizer with the origin of the spatial coordinate at the mid‐point between the sampling points and the main processing operation results in a DCT of unordinary type. This increases the computational complexity compared to the ordinary DCT. From such a viewpoint, this paper first derives the overlapping block DCT (OBDCT) with the same main processing as that of the ordinary DCT, by placing the origin of the spatial coordinate at the sampling point. OBDCT has the same coding efficiency as that of the traditional OBT, and OBDCT with the transform length 8 has the same coding efficiency as that of DCT with the transform length 16. A fast OBDCT algorithm is derived by integrating and simplifying the proposed OBDCT and the transform processing. Finally, it is shown that the fast OBDCT with the forementioned transform length can be executed by 55 percent of multiplications of the fast OBT and 67 percent of the fast DCT.