Low-complexity 8-point DCT Approximation Based on Angle Similarity for Image and Video Coding

TL;DR

This paper introduces a low-complexity 8-point DCT approximation based on angle similarity, which is computationally efficient and can outperform the exact DCT in image and video coding under certain conditions.

Contribution

It proposes a novel angle-based approximation method for the DCT that reduces computational complexity while maintaining or improving coding performance.

Findings

Outperforms competitors in matrix error and coding capabilities

Can outperform exact DCT in image encoding at specific compression ratios

Successfully implemented as FPGA prototype circuits

Abstract

The principal component analysis (PCA) is widely used for data decorrelation and dimensionality reduction. However, the use of PCA may be impractical in real-time applications, or in situations were energy and computing constraints are severe. In this context, the discrete cosine transform (DCT) becomes a low-cost alternative to data decorrelation. This paper presents a method to derive computationally efficient approximations to the DCT. The proposed method aims at the minimization of the angle between the rows of the exact DCT matrix and the rows of the approximated transformation matrix. The resulting transformations matrices are orthogonal and have extremely low arithmetic complexity. Considering popular performance measures, one of the proposed transformation matrices outperforms the best competitors in both matrix error and coding capabilities. Practical applications in image and video coding demonstrate the relevance of the proposed transformation. In fact, we show that the proposed approximate DCT can outperform the exact DCT for image encoding under certain compression ratios. The proposed transform and its direct competitors are also physically realized as digital prototype circuits using FPGA technology.