000130317 001__ 130317
000130317 005__ 20190225185140.0
000130317 0247_ $$2doi$$a10.1109/LSP.2006.872396
000130317 02470 $$2DAR$$a8883
000130317 02470 $$2ISI$$a000238547400013
000130317 037__ $$aARTICLE
000130317 245__ $$aMatérn B-Splines and the Optimal Reconstruction of Signals
000130317 269__ $$a2006
000130317 260__ $$bIEEE$$c2006
000130317 336__ $$aJournal Articles
000130317 520__ $$9eng$$a Starting from the power spectral density of Matérn stochastic processes, we introduce a new family of splines that is defined in terms of the whitening operator of such processes. We show that these Matérn splines admit a stable representation in a B-spline-like basis. We specify the Matérn B-splines (causal and symmetric) and identify their key properties; in particular, we prove that these generate a Riesz basis and that they can be written as a product of an exponential with a fractional polynomial B-spline. We also indicate how these new functions bridge the gap between the fractional polynomial splines and the cardinal exponential ones. We then show that these splines provide the optimal reconstruction space for the minimum mean-squared error estimation of Matérn signals from their noisy samples. We also propose a digital Wiener-filter-like algorithm for the efficient determination of the optimal B-spline coefficients.
000130317 6531_ $$aMatérn B-Splines
000130317 700__ $$0240170$$g166205$$aRamani, S.
000130317 700__ $$aUnser, M.$$g115227$$0240182
000130317 773__ $$j13$$tIEEE Signal Processing Letters$$k7$$q437–440
000130317 8564_ $$uhttp://bigwww.epfl.ch/publications/ramani0602.ps$$zURL
000130317 8564_ $$uhttp://bigwww.epfl.ch/publications/ramani0602.html$$zURL
000130317 8564_ $$uhttps://infoscience.epfl.ch/record/130317/files/ramani0602.pdf$$zn/a$$s250691
000130317 909C0 $$xU10347$$0252054$$pLIB
000130317 909CO $$ooai:infoscience.tind.io:130317$$pSTI$$pGLOBAL_SET$$particle
000130317 937__ $$aLIB-ARTICLE-2006-007
000130317 970__ $$aramani0602/LIB
000130317 973__ $$rREVIEWED$$sPUBLISHED$$aEPFL
000130317 980__ $$aARTICLE