
R
E S E A R C H  D I R E C T I O N L E T S
Image processing using
directionlets
 Standard wavelet transform
(WT) is
widely used in image processing (including JPEG2000) because of:
 Sparse representation of general images
 Separable filtering and subsampling
 Simple (onedimensional) 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 nonseparable
(twodimensional) 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.
Lagrangebased optimization can be used to determine the optimal choice
of transform directions and tiling.
 Selected references:
 V. Velisavljevic, B.
BeferullLozano, M. Vetterli, Spacefrequency
quantization for image compression with directionlets, IEEE Trans.
on Image
Proc, to appear.
 V. Velisavljevic, B. BeferullLozano, M. Vetterli, P. L.
Dragotti, Lowrate reduced
complexity image
compression using directionlets, IEEE
Int. Conf. on Image Proc. (ICIP), Atlanta, GA, October 2006.
 V.
Velisavljevic, B. BeferullLozano, M. Vetterli, P. L. Dragotti, Directionlets: anisotropic
multidirectional representation with separable filtering, IEEE
Trans. on Image Proc., July
2006.
 V.
Velisavljevic, Directionlets:
anisotropic
multidirectional representation with separable filtering,
Ph.D. Thesis no. 3358(2005), LCAV, School of Computer and Communication
Sciences, EPFL, Lausanne, Switzerland, October 2005.
 V.
Velisavljevic, B. BeferullLozano, M. Vetterli, P. L. Dragotti, Approximation power of
directionlets, IEEE Int. Conf. on Image Proc.(ICIP), Genova, Italy,
September 2005.
