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

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.

Corrected typo in formula for the coding gain. 16 pages, 12 figures, 10 tables

References in corpus (3)

• DCT-like Transform for Image Compression Requires 14 Additions Only
• An Integer Approximation Method for Discrete Sinusoidal Transforms
• A Digital Hardware Fast Algorithm and FPGA-based Prototype for a Novel 16-point Approximate DCT for Image Compression Applications

Cited by in corpus (7)

• A Class of Low-complexity DCT-like Transforms for Image and Video Coding
• A Multiparametric Class of Low-complexity Transforms for Image and Video Coding
• Low-complexity Scaling Methods for DCT-II Approximations
• Low-complexity Rounded KLT Approximation for Image Compression
• Extensions on Low-complexity DCT Approximations for Larger Blocklengths Based on Minimal Angle Similarity
• Data-independent Low-complexity KLT Approximations for Image and Video Coding
• Fast Data-independent KLT Approximations Based on Integer Functions