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Some generalized method for constructing nonseparable compactly supported wavelets in L2(R2)

Banaś W.

Opuscula Mathematica

2013

Vol. 33, no. 2

223--235

In this paper we show the construction of nonseparable compactly supported bi-variate wavelets. We deal with the dilation matrix [formula] and some three-row coefficient mask; that is a scaling function that satisfies a dilation equation with scaling coefficients which can be contained in the set {cn} n ∈ s where S = S1 x {0, 1, 2}, S1 ⊂ N, #S1 < ∞

Compactly supported multi-wavelets

Banaś W.

Opuscula Mathematica

2012

Vol. 32, no. 1

21-29

In this paper we show some construction of compactly supported multi-wavelets In L2(Rd), d ≥ 2 which is based on the one-dimensional case, when d = 1. We also demonstrate that some methods, which are useful in the construction of wavelets with a compact support at d = 1, can be adapted to higher-dimensional cases if A ∈Mdxd(Z) is an expansive matrix of a special form.