Extensions on Low-complexity DCT Approximations for Larger Blocklengths Based on Minimal Angle Similarity

TL;DR

This paper introduces new low-complexity DCT approximations for larger block sizes (16, 32, 64) based on minimal angle similarity, demonstrating improved performance and efficient algorithms for image encoding.

Contribution

It presents novel low-complexity DCT approximations for larger block sizes using minimal angle similarity, outperforming existing methods in accuracy and computational efficiency.

Findings

Proposed transforms outperform existing approximations in classical metrics.

Fast algorithms developed for the new transforms.

Practical image encoding tests show improved results.

Abstract

The discrete cosine transform (DCT) is a central tool for image and video coding because it can be related to the Karhunen-Lo\`eve transform (KLT), which is the optimal transform in terms of retained transform coefficients and data decorrelation. In this paper, we introduce 16-, 32-, and 64-point low-complexity DCT approximations by minimizing individually the angle between the rows of the exact DCT matrix and the matrix induced by the approximate transforms. According to some classical figures of merit, the proposed transforms outperformed the approximations for the DCT already known in the literature. Fast algorithms were also developed for the low-complexity transforms, asserting a good balance between the performance and its computational cost. Practical applications in image encoding showed the relevance of the transforms in this context. In fact, the experiments showed that the proposed transforms had better results than the known approximations in the literature for the cases of 16, 32, and 64 blocklength.