6533b861fe1ef96bd12c4c65

RESEARCH PRODUCT

Polynomial Spline-Wavelets

Amir AverbuchPekka NeittaanmäkiValery A. Zheludev

subject

Zak transformComputingMethodologies_IMAGEPROCESSINGANDCOMPUTERVISIONMathematicsofComputing_NUMERICALANALYSISWavelet transformData_CODINGANDINFORMATIONTHEORYMathematics::Numerical AnalysisMatrix polynomialAlgebraSpline (mathematics)Computer Science::GraphicsWaveletOrthonormal basisMonic polynomialComputingMethodologies_COMPUTERGRAPHICSMathematicsCharacteristic polynomial

description

This chapter presents wavelets in the spaces of polynomial splines. The wavelets’ design is based on the Zak transform, which provides an integral representation of spline-wavelets. The exponential wavelets which participate in the integral representation are counterparts of the exponential splines that were introduced in Chap. 4. Fast algorithms for the wavelet transforms of splines are presented. Generators of spline-wavelet spaces are described, such as the B-wavelets and their duals and the Battle-Lemarie wavelets whose shifts form orthonormal bases of the spline-wavelet spaces.

yearjournalcountryeditionlanguage
2015-08-28
https://doi.org/10.1007/978-3-319-22303-2_8