This paper focuses on the ultimate limit theory of image compression. It proves that for an image source, there exists a coding method with shapes that can achieve the entropy rate under a certain condition where the shape-pixel ratio in the encoder/decoder is $O({1 \over {\log t}})$. Based on the new finding, an image coding framework with shapes is proposed and proved to be asymptotically optimal for stationary and ergodic processes. Moreover, the condition $O({1 \over {\log t}})$ of shape-pixel ratio in the encoder/decoder has been confirmed in the image database MNIST, which illustrates the soft compression with shape coding is a near-optimal scheme for lossless compression of images.
翻译：本文侧重于图像压缩的最终限值理论 。 它证明对于图像源来说, 存在一种有形状的编码方法, 在一定条件下, 在编码器/ 解码器中的形状像素比率为$O( { 1\ over ~ log t ⁇ ) 的情况下, 可以实现 entropy 率 。 根据新发现, 提出了一个带有形状的图像编码框架, 并证明它对于固定和 ergodic 进程来说是无损压缩图像的近乎最佳的图案 。 此外, 编码器/ 解码器中的形状像素比率 $O( { 1\ over ~ log t ⁇ ) 条件已经在图像数据库中被确认为$O( $o) / delcixel 比率 。 MNIST 显示形状编码的软压缩是无损压缩图像的近乎最佳方案 。
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