Multivariate periodic wavelets of de la Vallée Poussin type (Q2342171)

The authors construct new \(d\)-variate periodic wavelets generated by scaling functions of de la Vallée Poussin type. These scaling functions and the corresponding wavelets of de la Vallée Poussin type are determined by their Fourier coefficients, which are sample values of a so-called admissible function. This admissible function can be chosen as compactly supported function of certain smoothness, even with different smoothness in each direction. Thus this construction of scaling functions and wavelets of de la Vallée Poussin type introduces a wide variety of periodic anisotropic multiresolution analyses. Further this approach permits the use of shear matrices as dilation matrices. This wavelet theory can be used to generate directional decompositions of a given \(d\)-variate function. The method is illustrated by detecting jumps of certain directional derivatives of higher order.