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Multiplierless lifting-based fast X transforms derived from fast Hartley transform factorization

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Abstract

This paper presents M-channel (\(M=2^{N}\), \(N\in \mathbb {N}\), \(N\ge 1\)) multiplierless lifting-based (ML-) fast X transforms (FXTs), where X \(=\) F (Fourier), C (cosine), S (sine), and H (Hartley), i.e., FFT, FCT, FST, and FHT, derived from FHT factorization as way of lowering the cost of signal (image) processing. The basic forms of ML-FXTs are described. Then, they are customized for efficient image processing. The customized ML-FFT has a real-valued calculation followed by a complex-valued one. The ML-FCT customization for a block size of 8, which is a typical size for image coding, further reduces computational costs. We produce two customized ML-FCTs for lossy and lossless image coding. Numerical simulations show that ML-FFT and ML-FCTs perform comparably to the conventional methods in spite of having fewer operations.

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Notes

  1. Although it can be simply achieved by 3, 4, and 7 right shifters, we do not use it to avoid generating more rounding error.

  2. In the same way as Liang and Tran (2001) did, we used the floating-point coefficients of the scaling factors, which are always combined with the quantization steps and rounded to integers in practical implementations.

  3. The experiments in this paper show almost same results even if any image.

  4. More than 8 bit word length coefficients show almost same PSNRs.

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Acknowledgments

The authors would like to thank the anonymous reviewers, Dr. H. Aso, and Dr. K. Sugimoto for providing many constructive suggestions that significantly improve the presentation of this paper. This work was supported by a JSPS Grant-in-Aid for Young Scientists (B), Grant Number 16K18100.

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Authors and Affiliations

  1. Faculty of Engineering, Information and Systems, University of Tsukuba, Tsukuba, Ibaraki, Japan

    Taizo Suzuki

  2. Department of Information and Media Engineering, The University of Kitakyushu, Kitakyushu, Fukuoka, Japan

    Seisuke Kyochi

  3. Graduate School of BASE, Tokyo University of Agriculture and Technology, Koganei, Tokyo, Japan

    Yuichi Tanaka

  4. Department of Electronics and Electrical Engineering, Keio University, Yokohama, Kanagawa, Japan

    Masaaki Ikehara

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  1. Taizo Suzuki
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  2. Seisuke Kyochi
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  3. Yuichi Tanaka
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  4. Masaaki Ikehara
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Correspondence to Taizo Suzuki.

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Suzuki, T., Kyochi, S., Tanaka, Y. et al. Multiplierless lifting-based fast X transforms derived from fast Hartley transform factorization. Multidim Syst Sign Process 29, 99–118 (2018). https://doi.org/10.1007/s11045-016-0457-5

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  • DOI: https://doi.org/10.1007/s11045-016-0457-5

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