Reversible transform coding of images

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Abstract
Though reversible predictive coding and reversible subband coding exist already as reversible coding of gray-level still images, reversible method has almost not been proposed against transform coding. Therefore, in this paper, we propose some reversible transform coding methods. In case that we use conventional transform coding as it is, we have to make the number of levels of the transform coefficient very large in order to reconstruct the input signal with no distortion. Therefore, we propose transform codings that have reversibility whereas the number of levels of the transform coefficient are not very large. We propose reversible coding methods that correspond to the discrete Walsh-Hadamard, Haar, and cosine transform. Furthermore, we propose a method that uses the difference of the n-th order, a method of which the number of levels of the transform coefficient is the same as that of the input signal, and a reversible overlap transform coding method. Simulation shows that the compression efficiency of the proposed method is almost the same as that of predictive coding.

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