Suzuki, Taizo; Kyochi, Seisuke; Tanaka, Yuichi; Ikehara, Masaaki Multiplierless lifting-based fast X transforms derived from fast Hartley transform factorization. (English) Zbl 1450.94023 Multidimensional Syst. Signal Process. 29, No. 1, 99-118 (2018). Summary: 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. MSC: 94A12 Signal theory (characterization, reconstruction, filtering, etc.) 65T50 Numerical methods for discrete and fast Fourier transforms Software:SIPI Image Database; binDCT PDFBibTeX XMLCite \textit{T. Suzuki} et al., Multidimensional Syst. Signal Process. 29, No. 1, 99--118 (2018; Zbl 1450.94023) Full Text: DOI References: [1] Ahmed, N., & Rao, K. R. (1975). Orthogonal transforms for digital signal processing. Berlin: Springer. · Zbl 0335.94001 [2] Beauchamp, K. (1984). Applications of Walsh and related functions. Cambridge: Academic Press. · Zbl 0326.42007 [3] Bracewel, R. N. (1983). Discrete Hartley transform. Journal of the Optical Society of America, 73(12), 1832-1835. [4] Chen, Y. J., Oraintara, S., Tran, T. D., Amaratunga, K., & Nguyen, T. Q. (2002). Multiplierless approximation of transforms with adder constraint. 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