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Low-complexity 8-point DCT approximation based on angle similarity for image and video coding

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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.

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Acknowledgements

The authors acknowldege the partial support from Brazilian funding agencies CNPq and FACEPE.

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Authors and Affiliations

  1. Programa de Pós-Graduação em Engenharia Elétrica, Universidade Federal de Pernambuco (UFPE), Recife, Brazil

    Raíza S. Oliveira

  2. Signal Processing Group, Departamento de Estatística, Universidade Federal de Pernambuco (UFPE), Recife, Brazil

    Raíza S. Oliveira, Renato J. Cintra & André Leite

  3. ECE, University of Calgary, Calgary, AB, Canada

    Renato J. Cintra

  4. Departamento de Estatística, Universidade Federal de Santa Maria, Santa Maria, Brazil

    Fábio M. Bayer

  5. Programa de Pós-Graduação em Computação, Universidade Federal do Rio Grande do Sul, Porto Alegre, Brazil

    Thiago L. T. da Silveira

  6. Department of Electrical and Computer Engineering, University of Akron, Akron, OH, USA

    Arjuna Madanayake

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  1. Raíza S. Oliveira
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Oliveira, R.S., Cintra, R.J., Bayer, F.M. et al. Low-complexity 8-point DCT approximation based on angle similarity for image and video coding. Multidim Syst Sign Process 30, 1363–1394 (2019). https://doi.org/10.1007/s11045-018-0601-5

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