000190925 001__ 190925
000190925 005__ 20190617200712.0
000190925 0247_ $$2doi$$a10.1137/120864143
000190925 022__ $$a1936-4954
000190925 02470 $$2ISI$$a000326033500009
000190925 037__ $$aARTICLE
000190925 245__ $$aDecay Properties of Riesz Transforms and Steerable Wavelets
000190925 260__ $$bSiam Publications$$c2013$$aPhiladelphia
000190925 269__ $$a2013
000190925 300__ $$a15
000190925 336__ $$aJournal Articles
000190925 520__ $$aThe Riesz transform is a natural multidimensional extension of the Hilbert transform, and it has been the object of study for many years due to its nice mathematical properties. More recently, the Riesz transform and its variants have been used to construct complex wavelets and steerable wavelet frames in higher dimensions. The flip side of this approach, however, is that the Riesz transform of a wavelet often has slow decay. One can nevertheless overcome this problem by requiring the original wavelet to have sufficient smoothness, decay, and vanishing moments. In this paper, we derive necessary conditions in terms of these three properties that guarantee the decay of the Riesz transform and its variants, and, as an application, we show how the decay of the popular Simoncelli wavelets can be improved by appropriately modifying their Fourier transforms. By applying the Riesz transform to these new wavelets, we obtain steerable frames with rapid decay.
000190925 6531_ $$aRiesz transform
000190925 6531_ $$asteerable wavelets
000190925 6531_ $$asingular integrals
000190925 700__ $$0245475$$g213487$$uEcole Polytech Fed Lausanne, Biomed Imaging Grp, CH-1015 Lausanne, Switzerland$$aWard, John Paul
000190925 700__ $$aChaudhury, Kunal Narayan
000190925 700__ $$uEcole Polytech Fed Lausanne, Biomed Imaging Grp, CH-1015 Lausanne, Switzerland$$aUnser, Michael$$g115227$$0240182
000190925 773__ $$j6$$tSiam Journal On Imaging Sciences$$k2$$q984-998
000190925 8564_ $$uhttp://bigwww.epfl.ch/publications/ward1301.html$$zURL
000190925 8564_ $$uhttp://bigwww.epfl.ch/publications/ward1301.pdf$$zURL
000190925 8564_ $$uhttp://bigwww.epfl.ch/publications/ward1301.ps$$zURL
000190925 909C0 $$xU10347$$0252054$$pLIB
000190925 909CO $$ooai:infoscience.tind.io:190925$$qGLOBAL_SET$$pSTI$$particle
000190925 917Z8 $$x115226
000190925 937__ $$aEPFL-ARTICLE-190925
000190925 970__ $$award1301/LIB
000190925 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000190925 980__ $$aARTICLE