Construction of a class of multivariate compactly supported wavelet bases for L²(ℝ^d)

Abstract

In this paper, for a given d×d expansive matrix M with |detM| = 2, we investigate the compactly supported M-wavelets for L²(ℝ^d). Starting with a pair of compactly supported refinable functions ϕ and $\tilde \varphi $ satisfying a mild condition, we obtain an explicit construction of a compactly supported wavelet ψ such that {2^j/2ψ(M^j · −k): j ∈ ℤ, k ∈ ℤd} forms a Riesz basis for L²(ℝ^d). The (anti-)symmetry of such ψ is studied, and some examples are also provided.

Keywords

Riesz basis / wavelet / refinable function

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