Fast Data-independent KLT Approximations Based on Integer Functions

• Main Authors: Radünz, A. P, Coelho, D. F. G, Bayer, F. M, Cintra, R. J, Madanayake, A
• Format: Journal Article
• Language: English
• Published: 11-10-2024
• Subjects: Computer Science - Computer Vision and Pattern Recognition; Computer Science - Numerical Analysis; Mathematics - Numerical Analysis; Statistics - Methodology
• DOI: 10.48550/arxiv.2410.09227

Multimedia Tools and Applications, 83(26):67303--67325, January
2024 The Karhunen-Lo\`eve transform (KLT) stands as a well-established discrete
transform, demonstrating optimal characteristics in data decorrelation and
dimensionality reduction. Its ability to condense energy compression into a
select few main components has rendered it instrumental in various applications
within image compression frameworks. However, computing the KLT depends on the
covariance matrix of the input data, which makes it difficult to develop fast
algorithms for its implementation. Approximations for the KLT, utilizing
specific rounding functions, have been introduced to reduce its computational
complexity. Therefore, our paper introduces a category of low-complexity,
data-independent KLT approximations, employing a range of round-off functions.
The design methodology of the approximate transform is defined for any
block-length $N$, but emphasis is given to transforms of $N = 8$ due to its
wide use in image and video compression. The proposed transforms perform well
when compared to the exact KLT and approximations considering classical
performance measures. For particular scenarios, our proposed transforms
demonstrated superior performance when compared to KLT approximations
documented in the literature. We also developed fast algorithms for the
proposed transforms, further reducing the arithmetic cost associated with their
implementation. Evaluation of field programmable gate array (FPGA) hardware
implementation metrics was conducted. Practical applications in image encoding
showed the relevance of the proposed transforms. In fact, we showed that one of
the proposed transforms outperformed the exact KLT given certain compression
ratios.