Performance Analysis of DCT, Hadamard, and PCA in Block-Based Image Compression

TL;DR

This paper compares DCT, Hadamard, and PCA transforms in block-based image compression, showing DCT's robustness at standard sizes and PCA's advantage only at larger block dimensions.

Contribution

The study provides an experimental analysis of classical and data-driven transforms, clarifying their performance across block sizes and compression rates.

Findings

PCA outperforms fixed transforms at large block sizes.

DCT remains near optimal for standard block sizes like 8x8.

DCT's robustness explains its widespread use in practical codecs.

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.