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.

翻译：JPEG算法是图像压缩的事实标准。我们研究能否利用自适应网格细化来优化压缩比，并提出了一种新的自适应图像压缩算法。我们证明，在给定误差范数下，该算法能以高概率生成准最优的细分网格。这种细分网格的存储开销极小，因而可实现高效的压缩算法。实验表明，相较于标准JPEG压缩，新算法能在许多图像上以无可见质量损失的方式获得更优的压缩比。本工作的数学核心在于证明：当假设图像像素存在微小加性高斯噪声时，Binev最优树逼近算法能以高概率适用于图像压缩。