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

Taizo Suzuki, Seisuke Kyochi, Yuichi Tanaka, Masaaki Ikehara

Research output: Contribution to journalArticle

Abstract

This paper presents M-channel ((Formula presented.), (Formula presented.), (Formula presented.)) multiplierless lifting-based (ML-) fast X transforms (FXTs), where X (Formula presented.) 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.

Original languageEnglish
Pages (from-to)1-20
Number of pages20
JournalMultidimensional Systems and Signal Processing
DOIs
Publication statusAccepted/In press - 2016 Sep 24

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Factorization
Fast Fourier transforms
Transform
Image coding
Image processing
Image Coding
Costs
Image Processing
Computer simulation
Customization
Fuzzy Set Theory
Signal Processing
Computational Cost
Numerical Simulation

ASJC Scopus subject areas

  • Software
  • Signal Processing
  • Information Systems
  • Hardware and Architecture
  • Computer Science Applications
  • Artificial Intelligence
  • Applied Mathematics

Cite this

Multiplierless lifting-based fast X transforms derived from fast Hartley transform factorization. / Suzuki, Taizo; Kyochi, Seisuke; Tanaka, Yuichi; Ikehara, Masaaki.

In: Multidimensional Systems and Signal Processing, 24.09.2016, p. 1-20.

Research output: Contribution to journalArticle

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