比较三种图像压缩变换，发现DCT在常用尺寸下仍最高效。
Performance Analysis of DCT, Hadamard, and PCA in Block-Based Image Compression
- 实验对比DCT、Hadamard和PCA在不同块大小下的性能
- 当块维度大时PCA更优，但8×8等标准尺寸下DCT接近最优
- 解释了为何实际编码器仍广泛使用DCT
基于块的图像压缩依赖变换编码将信号能量集中到少量系数中。尽管传统编码器使用固定变换如离散余弦变换（DCT），数据驱动方法如主成分分析（PCA）理论上在去相关性上最优。本文通过率失真分析与能量集中度评估，对DCT、Hadamard和PCA在多种块尺寸和压缩率下进行实验比较。结果表明，仅当块维数足够大时PCA才优于固定变换；而在标准块尺寸（如$8\times8$）及低比特率下，DCT仍接近最优。这些发现解释了DCT在实际编码器中的鲁棒性，并揭示了逐块学习变换的局限性。
原文摘要 · Abstract (English)
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.
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