TY - GEN
T1 - Hyperbolic shearlets
AU - Easley, Glenn R.
AU - Labate, Demetrio
AU - Patel, Vishal M.
PY - 2012
Y1 - 2012
N2 - Wavelets with composite dilations extend the traditional wavelet approach by allowing for the construction of waveforms defined not only at various scales and locations but also according to various orthogonal transformations. The shearlets, which yield optimally sparse representations for a large class of 2D and 3D data is the most widely known example of wavelets with composite dilations. However, many other useful constructions are obtained within this framework. In this paper, we examine the hyperbolic shearlets, a variant of the shearlet construction obtained as a system of well localized waveforms defined at various scales, locations and orientations, where the directionality is controlled by orthogonal transformations producing a sort of shearing along hyperbolic curves. The effectiveness of this new representation is illustrated by applications to image denoising. Our results compare favorably against similar denoising algorithms based on wavelets, curvelets and other sophisticated multiscale representations.
AB - Wavelets with composite dilations extend the traditional wavelet approach by allowing for the construction of waveforms defined not only at various scales and locations but also according to various orthogonal transformations. The shearlets, which yield optimally sparse representations for a large class of 2D and 3D data is the most widely known example of wavelets with composite dilations. However, many other useful constructions are obtained within this framework. In this paper, we examine the hyperbolic shearlets, a variant of the shearlet construction obtained as a system of well localized waveforms defined at various scales, locations and orientations, where the directionality is controlled by orthogonal transformations producing a sort of shearing along hyperbolic curves. The effectiveness of this new representation is illustrated by applications to image denoising. Our results compare favorably against similar denoising algorithms based on wavelets, curvelets and other sophisticated multiscale representations.
KW - Wavelets with composite dilations
KW - contourlets
KW - directional wavelets
KW - multiresolution analysis
KW - shearlets
UR - http://www.scopus.com/inward/record.url?scp=84875866650&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84875866650&partnerID=8YFLogxK
U2 - 10.1109/ICIP.2012.6467393
DO - 10.1109/ICIP.2012.6467393
M3 - Conference contribution
AN - SCOPUS:84875866650
SN - 9781467325332
T3 - Proceedings - International Conference on Image Processing, ICIP
SP - 2449
EP - 2452
BT - 2012 IEEE International Conference on Image Processing, ICIP 2012 - Proceedings
T2 - 2012 19th IEEE International Conference on Image Processing, ICIP 2012
Y2 - 30 September 2012 through 3 October 2012
ER -