Abstract
Block based image compression relies on transform coding to concentrate signal energy into a small number of coefficients. While classical codecs use fixed transforms such as the Discrete Cosine Transform (DCT), data driven methods such as Principal Component Analysis (PCA) are theoretically optimal for decorrelation. This paper presents an experimental comparison of DCT, Hadamard, and PCA across multiple block sizes and compression rates. Using rate distortion and energy compaction analysis, we show that PCA outperforms fixed transforms only when block dimensionality is sufficiently large, while DCT remains near optimal for standard block sizes such as $8\times8$ and at low bit rates. These results explain the robustness of DCT in practical codecs and highlight the limitations of block wise learned transforms.
Abstract (translated)
基于块的图像压缩依赖于变换编码，以将信号能量集中在少量系数上。虽然传统的编解码器使用固定的变换如离散余弦变换（DCT），但像主成分分析（PCA）这样的数据驱动方法理论上在去相关方面是最优的。本文对不同大小的块和不同的压缩率下，比较了DCT、Hadamard变换以及PCA的表现。通过率失真分析和能量紧缩分析，我们发现当块的维度足够大时，PCA才能优于固定的变换；而在标准尺寸如$8\times8$ 的块上，特别是在低比特率的情况下，DCT依然接近最优。 这些结果解释了为什么在实际的编解码器中DCT表现出强大的鲁棒性，并突出了基于块学习变换的局限性。
URL
https://arxiv.org/abs/2601.06273
