Image Coding With Data-Driven Fast Transforms Based on Approximate Givens Factorizations
Dilshan Morawaliyadda, Pradeepa Yahampath · IEEE Access · 2025
In image compression, adaptive transform coding with optimal linear transforms computed from data being coded has been shown to outperform the widely used two-dimensional discrete cosine transform (2D-DCT). However, unlike the 2D-DCT for which fast computation algorithms exist, data-driven transforms are random matrices with no particular structure that can be exploited for fast computations. We present an approach to low-complexity data-driven image coding using structured orthonormal transform matrices constructed from approximate Givens factorizations optimized for transform coding. These Givens factorization-based fast transforms (GFFTs) are optimized by a tree-search algorithm on the orthonormal matrix manifold to minimize the mean square error of high-rate transform coding. Experimental results obtained with an adaptation of the baseline JPEG algorithm are presented which show that, for many images, the GFFTs outperform the 2D-DCT at comparable or lower computational complexity, with peak signal-to-noise ratio (PSNR) improvements as high as 6 dB in some cases.