Low-complexity 8-point DCT Approximation Based on Angle Similarity for Image and Video Coding
This work addresses energy and computing constraints in image and video coding, offering an incremental improvement over existing DCT approximations.
The paper tackled the problem of high computational cost in data decorrelation for real-time applications by proposing a low-complexity 8-point DCT approximation based on angle similarity, which outperforms competitors in matrix error and coding capabilities and can exceed the exact DCT in image encoding at certain compression ratios.
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.