A new image data compression method–extrapolative prediction–discrete sine transform coding (in the case of one–dimensional coding)

This paper proposes the extrapolative prediction‐discrete sine transform as a new highly efficient coding for the gray‐level image. In the proposed method, an extrapolative prediction is made from the immediately preceding pixel to the present pixel block, and the prediction error signal is encoded by the orthogonal transform. Assuming that the information source for the image is a stationary first‐order Markov process in the wide sense, it is shown that the orthogonal transform which decorrelates the prediction error signal can be approximated by a certain kind of sine transform. An algorithm is presented for the high‐speed execution of this data. The rate‐distortion characteristic is discussed for the case of one‐dimensional coding, and it is shown theoretically that the coding efficiency of the proposed method is nearly the same as those of the discrete 16‐pixel cosine transform with block length of 4 pixels and the 8‐pixel fast Karhunen‐Loéve transform. Comparing the coding complexities of those methods, the proposed method is shown to be especially advantageous in the hardware realization. Computer simulations were made for actual images using the fixed‐rate coding and variable‐rate coding (entropy coding), and the result supports the idea.