Image coding using dual-tree discrete wavelet transform

Jingyu Yang, Yao Wang, Wenli Xu, Qionghai Dai

Research output: Contribution to journalArticlepeer-review


In this paper, we explore the application of 2-D dual-tree discrete wavelet transform (DDWT), which is a directional and redundant transform, for image coding. Three methods for sparsifying DDWT coefficients, i.e., matching pursuit, basis pursuit, and noise shaping, are compared. We found that noise shaping achieves the best nonlinear approximation efficiency with the lowest computational complexity. The interscale, intersubband, and intrasubband dependency among the DDWT coefficients are analyzed. Three subband coding methods, i.e., SPIHT, EBCOT, and TCE, are evaluated for coding DDWT coefficients. Experimental results show that TCE has the best performance. In spite of the redundancy of the transform, our DDWT_TCE scheme outperforms JPEG2000 up to 0.70 dB at low bit rates and is comparable to JPEG2000 at high bit rates. The DDWT_TCE scheme also outperforms two other image coders that are based on directional filter banks. To further improve coding efficiency, we extend the DDWT to an anisotropic dual-tree discrete wavelet packets (ADDWP), which incorporates adaptive and anisotropic decomposition into DDWT. The ADDWP subbands are coded with TCE coder. Experimental results show that ADDWP_TCE provides up to 1.47 dB improvement over the DDWT_TCE scheme, outperforming JPEG2000 up to 2.00 dB. Reconstructed images of our coding schemes are visually more appealing compared with DWT-based coding schemes thanks to the directionality of wavelets.

Original languageEnglish (US)
Pages (from-to)1555-1569
Number of pages15
JournalIEEE Transactions on Image Processing
Issue number9
StatePublished - 2008


  • Anisotropic decomposition
  • Image coding
  • Redundant transform
  • Sparse representation
  • Wavelet transform

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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