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 Image processing using directionlets

  • Standard wavelet transform (WT) is widely used in image processing (including JPEG-2000) because of:
    • Sparse representation of general images
    • Separable filtering and subsampling
    • Simple (one-dimensional) filter design
    • Low computational complexity
  • Several transforms with different orientations have been proposed to address this inefficiency of the WT, like curvelets (Donoho et al.), contourlets (Do et al.), wedgelets (Donoho, Baraniuk), bandelets (Mallat et al.), etc.
  • However, some of them require non-separable (two-dimensional) operations, oversampling, high computational complexity, or fail to satisfy perfect reconstruction.
  • Directionlets retain the basic properties of the WT:
    • Critical sampling
    • Separability and simple filter design
    • Low computational complexity
  • Application of directionlets in image compression is straightforward because of critical sampling. Lagrange-based optimization can be used to determine the optimal choice of transform directions and tiling.