The Nonsubsampled Contourlet Transform: Theory, Design, and Applications

  • Authors:
  • A. L. da Cunha;Jianping Zhou;M. N. Do

  • Affiliations:
  • Dept. of Electr. & Comput. Eng., Illinois Univ., Urbana, IL;-;-

  • Venue:
  • IEEE Transactions on Image Processing
  • Year:
  • 2006

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Abstract

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 a 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