The nonsubsampled contourlet transform: Theory, design, and applications

Arthur L. da Cunha, Jianping Zhou, Minh N. Do

Research output: Contribution to journalArticlepeer-review


In this paper, we develop the nonsubsampled contourlet transform (NSCT) and study its applications. The construction proposed in this paper is based on a nonsubsampled pyramid structure and nonsubsampled directional filter banks. The result is a flexible multiscale, multidirection, and shift-invariant image decomposition that can be efficiently implemented via the à trous algorithm. At the core of the proposed scheme is the nonseparable two-channel nonsubsampled filter bank (NSFB). We exploit the less stringent design condition of the NSFB to design filters that lead to a NSCT with better frequency selectivity and regularity when compared to the contourlet transform. We propose a design framework based on the mapping approach, that allows for a fast implementation based on a lifting or ladder structure, and only uses one-dimensional filtering in some cases. In addition, our design ensures that the corresponding frame elements are regular, symmetric, and the frame is close to a tight one. We assess the performance of the NSCT in image denoising and enhancement applications. In both applications the NSCT compares favorably to other existing methods in the literature.

Original languageEnglish (US)
Pages (from-to)3089-3101
Number of pages13
JournalIEEE Transactions on Image Processing
Issue number10
StatePublished - Oct 2006


  • Contourlet transform
  • Frames
  • Image denoising
  • Image enhancement
  • Multidimensional filter banks
  • Nonsubsampled filter banks

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Computer Graphics and Computer-Aided Design
  • Software
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Computer Vision and Pattern Recognition

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