000063053 001__ 63053
000063053 005__ 20181114181916.0
000063053 0247_ $$2doi$$a10.1109/78.709545
000063053 02470 $$2ISI$$a000075544300027
000063053 037__ $$aARTICLE
000063053 245__ $$aMultiresolution Approximation Using Shifted Splines
000063053 269__ $$a1998
000063053 260__ $$bIEEE$$c1998
000063053 336__ $$aJournal Articles
000063053 520__ $$9eng$$a We consider the construction of least squares pyramids using shifted polynomial spline basis functions. We derive the pre- and post-filters as a function of the degree n and the shift parameter Δ. We show that the underlying projection operator is entirely specified by two transfer functions acting on the even and odd signal samples, respectively. We introduce a measure of shift-invariance and show that the most favorable configuration is obtained when the knots of the splines are centered with respect to the grid points (i.e., Δ=1/2 when n is odd, and Δ=0 when n is even). The worst case corresponds to the standard multiresolution setting where the spline spaces are nested. 
000063053 6531_ $$aShifted Splines
000063053 700__ $$aMüller, F.
000063053 700__ $$aBrigger, P.
000063053 700__ $$aIllgner, K.
000063053 700__ $$0240182$$aUnser, M.$$g115227
000063053 773__ $$j46$$k9$$q2555–2558$$tIEEE Transactions on Signal Processing
000063053 8564_ $$uhttp://bigwww.epfl.ch/publications/mueller9801.ps$$zURL
000063053 8564_ $$uhttp://bigwww.epfl.ch/publications/mueller9801.html$$zURL
000063053 8564_ $$s161654$$uhttps://infoscience.epfl.ch/record/63053/files/mueller9801.pdf$$zn/a
000063053 909C0 $$0252054$$pLIB$$xU10347
000063053 909CO $$ooai:infoscience.tind.io:63053$$pSTI$$pGLOBAL_SET$$particle
000063053 937__ $$aLIB-ARTICLE-1998-006
000063053 970__ $$amueller9801/LIB
000063053 973__ $$aEPFL$$rREVIEWED$$sPUBLISHED
000063053 980__ $$aARTICLE