The aim of the paper is to construct a multiresolution analysis of L2(IRd) based on generalized kernels which are fundamental solutions of differential operators of the form ∏ℓ=1m(−Δ+κℓ2I). We study its properties and provide a set of pre-wavelets associated with it, as well as the filters which are indispensable to perform decomposition and reconstruction of a given signal, being very useful in applied problems thanks to the presence of the tension parameters κℓ.
Bozzini, M., Rabut, C., Rossini, M. (2018). Decomposition and reconstruction of multidimensional signals by radial functions with tension parameters. ADVANCES IN COMPUTATIONAL MATHEMATICS, 44(4), 1003-1040 [10.1007/s10444-017-9571-7].
Decomposition and reconstruction of multidimensional signals by radial functions with tension parameters
Rossini, M
2018
Abstract
The aim of the paper is to construct a multiresolution analysis of L2(IRd) based on generalized kernels which are fundamental solutions of differential operators of the form ∏ℓ=1m(−Δ+κℓ2I). We study its properties and provide a set of pre-wavelets associated with it, as well as the filters which are indispensable to perform decomposition and reconstruction of a given signal, being very useful in applied problems thanks to the presence of the tension parameters κℓ.
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