The method of hierarchical multi-neighbor predictors and residual orthogonal transforms and its application to image compression (with K. Ashizawa and K. Yamatani), Transactions of the Japan Society for Industrial and Applied Mathematics, vol.17, no.3, pp.239-257, 2007 (in Japanese).
We propose new image algorithms by predicting each block using an improved
gradient estimation at the block boundary followed by applying an orthogonal
transformation to the prediction error. Compared to the previously proposed
polyharmonic local cosine transform where the DC components of adjacent blocks
were used for the gradient estiation, our new methods directly use multiple
combinations of the neighboring pixel values to estimate the gradients at
block boundary more accurately. Hence, we can improve the prediction of
each block using such gradient information. Consequently, we can improve
image reconstruction quality and reduce the blocking artifact and aliasing noise.
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