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

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 [Formula: see text]. Based on the new f...

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Detalles Bibliográficos
Autores principales: Xin, Gangtao, Fan, Pingyi, Letaief, Khaled B.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9857653/
https://www.ncbi.nlm.nih.gov/pubmed/36673189
http://dx.doi.org/10.3390/e25010048
Descripción
Sumario: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 [Formula: see text]. 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 [Formula: see text] 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.