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# Why Shape Coding? Asymptotic Analysis of the Entropy Rate for Digital Images

Apr 2022

This paper focuses on the ultimate limit theory of image compression. Itproves that for an image source, there exists a coding method with shapes thatcan achieve the entropy rate under a certain condition where the shape-pixelratio in the encoder/decoder is $O({1 \over {\log t}})$. Based on the newfinding, an image coding framework with shapes is proposed and proved to beasymptotically optimal for stationary and ergodic processes.

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