TY - JOUR
T1 - Multiplierless lifting-based fast X transforms derived from fast Hartley transform factorization
AU - Suzuki, Taizo
AU - Kyochi, Seisuke
AU - Tanaka, Yuichi
AU - Ikehara, Masaaki
N1 - Funding Information:
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.
Publisher Copyright:
© 2016, Springer Science+Business Media New York.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - This paper presents M-channel (M= 2 N, N∈ N, N≥ 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.
AB - This paper presents M-channel (M= 2 N, N∈ N, N≥ 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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U2 - 10.1007/s11045-016-0457-5
DO - 10.1007/s11045-016-0457-5
M3 - Article
AN - SCOPUS:84991384219
SN - 0923-6082
VL - 29
SP - 99
EP - 118
JO - Multidimensional Systems and Signal Processing
JF - Multidimensional Systems and Signal Processing
IS - 1
ER -