The Curvelet Transform
IEEE Signal Processing MagazinePublished 1 March 2010
Jianwei Ma, Gerlind Plonka
Citations438
SJR quartileQ1
SJR score2.69
SNIP3.97
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TL;DR
A review on the curvelet transform, including its history beginning from wavelets, its logical relationship to other multiresolution multidirectional methods like contourlets and shearlets, and its basic theory and discrete algorithm is presented.
Abstract
Multiresolution methods are deeply related to image processing, biological and computer vision, and scientific computing. The curvelet transform is a multiscale directional transform that allows an almost optimal nonadaptive sparse representation of objects with edges. It has generated increasing interest in the community of applied mathematics and signal processing over the years. In this article, we present a review on the curvelet transform, including its history beginning from wavelets, its logical relationship to other multiresolution multidirectional methods like contourlets and shearlets, its basic theory and discrete algorithm. Further, we consider recent applications in image/video processing, seismic exploration, fluid mechanics, simulation of partial different equations, and compressed sensing.
Keywords
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