Stochastic Model of Block Segmentation Based on Improper Quadtree and Optimal Code under the Bayes Criterion †

Yuta Nakahara*, Toshiyasu Matsushima

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Most previous studies on lossless image compression have focused on improving preprocessing functions to reduce the redundancy of pixel values in real images. However, we assumed stochastic generative models directly on pixel values and focused on achieving the theoretical limit of the assumed models. In this study, we proposed a stochastic model based on improper quadtrees. We theoretically derive the optimal code for the proposed model under the Bayes criterion. In general, Bayes-optimal codes require an exponential order of calculation with respect to the data lengths. However, we propose an algorithm that takes a polynomial order of calculation without losing optimality by assuming a novel prior distribution.

Original languageEnglish
Article number1152
JournalEntropy
Volume24
Issue number8
DOIs
Publication statusPublished - 2022 Aug

Keywords

  • Bayes code
  • lossless image compression
  • quadtree
  • stochastic generative model

ASJC Scopus subject areas

  • Information Systems
  • Mathematical Physics
  • Physics and Astronomy (miscellaneous)
  • Electrical and Electronic Engineering

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