An image data compression method using extrapolative prediction‐discrete sine transform; in the case of two‐dimensional coding

This paper considers the highly efficient coding of the gray‐level image. The extrapolative prediction‐discrete sine transform scheme, which was previously proposed by the authors for the case of one‐dimensional coding, is extended to the case of two‐dimensional coding. In the proposed method, the image is partitioned into square blocks. The correlations among blocks are eliminated by applying the two‐dimensional extrapolative prediction for each block from the restored boundary pixel. The correla‐in the block is eliminated by applying the orthogonal transformation to the prediction errors. In this paper, the correlation function of the image is assumed as the isotropic exponential function, and a two‐dimensional extrapolative prediction method is derived, which can be realized as a simple manipulation. The transformation of the prediction errors is performed by the variable‐separation type two‐dimensional extrapolative prediction‐discrete sine transform, where the one‐dimensional extrapolative prediction‐discrete sine transform is applied to rows and columns. Then the rate‐distortion characteristic is calculated, indicating that the proposed method is useful. It is shown that the proposed method with 4 × 4 block size has almost the same coding efficiency as the discrete cosine transform coding with 16 × 16 block size. A computer simulation was made for the actual image, leading to a result validating the theoretical estimation. The proposed method requires less computation per pixel, compared with the discrete cosine transform coding. The method is especially useful from the viewpoint of hardware implementation, since the block size is as small as 1/16.