An algorithm for constructing the compactly supported multidimensional orthogonal symmetric wavelets with dilation factor 3 is provided based on paraunitary matrix symmetric extension. Namely, let Φ(x)∈L2(Rd)
be a d dimensional compactly supported orthogonal scaling function with dilation factor 3; P(ξ) and (p0, ν(ξ))ν, ν ∈Ed, respectively, be the mask symbol and the polyphase symbol of Φ(x). Firstly, the authors propose a symmetric orthogonal transform of vectors, and take the symmetric orthogonal transform to (p0, ν(ξ))ν, ν ∈Ed，
then get a symmetric unit vector. Secondly, based on paraunitary matrix symmetric extension, 3d-1 compactly supported orthogonal symmetric wavelets associated with Φ(x) are obtained. The support of ψν, ν ∈Ed, is not larger than that of Φ(x). In addition, the algorithm can also be used to construct orthogonal wavelets with the dilation factor M(M ≥ 3). Finally, an example is given.
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