Xin Gangtao, Fan Pingyi, Letaief Khaled B
Department of Electronic Engineering, Tsinghua University, Beijing 100084, China.
Beijing National Research Center for Information Science and Technology, Tsinghua University, Beijing 100084, China.
Entropy (Basel). 2022 Dec 27;25(1):48. doi: 10.3390/e25010048.
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/logt). 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/logt) 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.
本文聚焦于图像压缩的极限理论。证明了对于一个图像源，存在一种具有形状的编码方法，在编码器/解码器中形状与像素比为O(1/logt)的特定条件下能够达到熵率。基于这一新发现，提出了一种具有形状的图像编码框架，并证明其对于平稳遍历过程是渐近最优的。此外，在图像数据库MNIST中已证实了编码器/解码器中形状与像素比的O(1/logt)条件，这表明基于形状编码的软压缩是图像无损压缩的一种近似最优方案。
