通过优化网格细化实现自适应图像压缩

IF 1 4区 数学 Q3 MATHEMATICS, APPLIED Computational Methods in Applied Mathematics Pub Date : 2024-01-01 DOI:10.1515/cmam-2023-0097
Michael Feischl, Hubert Hackl
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引用次数: 0

摘要

JPEG 算法是图像压缩的事实标准。我们研究了自适应网格细化是否可用于优化压缩比,并提出了一种新的自适应图像压缩算法。我们证明,对于给定的误差规范,它能高概率地生成准最优细分网格。这种细分网格的存储开销极小,因此是一种高效的压缩算法。我们通过实验证明,新算法可以实现比标准 JPEG 压缩更好的压缩率,而且在许多图像上没有明显的质量损失。这项工作的数学核心表明,当我们假定图像像素上的加性高斯噪声很小时,Binev 的最优树近似算法适用于高概率图像压缩。
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Adaptive Image Compression via Optimal Mesh Refinement
The JPEG algorithm is a defacto standard for image compression. We investigate whether adaptive mesh refinement can be used to optimize the compression ratio and propose a new adaptive image compression algorithm. We prove that it produces a quasi-optimal subdivision grid for a given error norm with high probability. This subdivision can be stored with very little overhead and thus leads to an efficient compression algorithm. We demonstrate experimentally, that the new algorithm can achieve better compression ratios than standard JPEG compression with no visible loss of quality on many images. The mathematical core of this work shows that Binev’s optimal tree approximation algorithm is applicable to image compression with high probability, when we assume small additive Gaussian noise on the pixels of the image.
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来源期刊
CiteScore
2.40
自引率
7.70%
发文量
54
期刊介绍: The highly selective international mathematical journal Computational Methods in Applied Mathematics (CMAM) considers original mathematical contributions to computational methods and numerical analysis with applications mainly related to PDEs. CMAM seeks to be interdisciplinary while retaining the common thread of numerical analysis, it is intended to be readily readable and meant for a wide circle of researchers in applied mathematics. The journal is published by De Gruyter on behalf of the Institute of Mathematics of the National Academy of Science of Belarus.
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