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3-D discrete analytical ridgelet transform.

David Helbert1, Philippe Carré, Eric Andres

  • 1Signal, Image, and Communication Laboratory, University of Poitiers, BP 30179, F-86962 Futuroscope-Chasseneuil, France. helbert@sic.sp2mi.univ-poitiers.fr

IEEE Transactions on Image Processing : a Publication of the IEEE Signal Processing Society
|December 13, 2006
PubMed
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We introduce the 3-D discrete analytical Ridgelet transform (3-D DART) for efficient image and video denoising. Simple thresholding of 3-D DART coefficients effectively removes noise from 3-D images and color videos.

Area of Science:

  • Digital Signal Processing
  • Image Analysis
  • Computer Vision

Background:

  • The Ridgelet transform is a powerful tool for analyzing directional features in data.
  • Existing 3-D transforms often face computational challenges or lack flexibility.
  • There is a need for efficient and adaptable 3-D transforms in image and video processing.

Purpose of the Study:

  • To propose and implement the 3-D discrete analytical Ridgelet transform (3-D DART).
  • To adapt the 3-D DART for applications such as 3-D image and color video denoising.
  • To demonstrate the efficiency and effectiveness of the 3-D DART in noise reduction.

Main Methods:

  • The 3-D DART is implemented using a Fourier strategy for the 3-D discrete Radon transform computation.

Related Experiment Videos

  • Discrete analytical geometry is employed to construct 3-D discrete analytical lines in the Fourier domain.
  • Two types of discrete lines are proposed: radial lines and planes, featuring an 'arithmetical thickness' parameter.

    • Main Results:

    • The 3-D DART offers a flexible, non-orthogonal representation with controllable redundancy.
    • A simple forward/inverse algorithm allows for exact reconstruction without iterative methods.
    • Experimental results show that simple thresholding of 3-D DART coefficients is effective for denoising 3-D images and color videos.

    Conclusions:

    • The 3-D DART is a novel and efficient discrete transform for multi-dimensional data analysis.
    • The transform's adaptability and simple implementation make it suitable for practical applications like denoising.
    • The proposed method demonstrates significant potential for noise reduction in 3-D imaging and video processing.