Block effect reduction by the 1-D gray polynomial interpolation

In this paper, the one-dimensional gray polynomial interpolation (1-D GPI) developed for image enlargement in Hsieh et al. (2007) [27] is applied to reduce the block effect in the block discrete cosine transform (BDCT) image/video coders. Note that the block effect in the BDCT coders results from insufficient bits for transform coefficients. An interpolation approach is proposed to relieve the block effect problem. The proposed approach consists of three stages. First, the input image/frame is down sampled by the direct down sampling (DDS) scheme to reduce the amount of data. Second, the down sampled image/frame is put into a BDCT coder, such as the JPEG and the MPEG-2. Finally, the 1-D GPI is applied to enlarge the decoded image. When the JPEG and the MPEG-2 are used as BDCT coders, the coding systems are called the JPEG-GPI and the MPEG-GPI, respectively. The proposed JPEG-GPI and MPEG-GPI are verified through examples. Simulation results indicate that both the JPEG-GPI and the MPEG-GPI are able to effectively reduce the block effect significantly and therefore the subjective visual quality improved in the given examples. Note that (i) the down sampling scheme in the first stage can be any down sampling scheme other than the DDS, and (ii) the interpolation approach in the third stage may be different from the 1-D GPI. Thus, various down sampling schemes, the nearest neighbor down sampling (NNDS), the bilinear down sampling (BLDS), and the bicubic down sampling (BCDS) schemes are under consideration. These down sampling schemes are used to replace the DDS in the JPEG-GPI and the MPEG-GPI to investigate the effect on the coding performance. The simulation results show that the DDS always gives the highest PSNR for all cases under same condition. Moreover, the 1-GPI is substituted by popular 2-D interpolation approaches, the nearest neighbor interpolation (NNI), the bilinear interpolation (BLI), and the bicubic interpolation (BCI). With the DDS scheme, the simulation results indicate that the JPEG-BLI has a little bit better PSNR than the JPEG-GPI for all cases while similar visual quality of reconstructed image is found. When compared with the MPEG-GPI, the MPEG-BCI has higher PSNR when the DDS is employed. And the reconstructed frames from the MPEG-GPI and the MPEG-BCI have similar visual quality. In summary, by the simulation results the proposed coding system, as expected, is able to significantly reduce the block effect happened in the cases of the low bit rate coding or high compression ratio.