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13 November 2003 Armlets and balanced multiwavelets
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Abstract
In the scalar-valued setting, it is well-known that the two-scale sequences {qk} of Daubechies orthogonal wavelets can be given explicitly by the two-scale sequences {pk} of their corresponding orthogonal scaling functions, such as qk = (-1)kp1-k. However, due to the non-commutativity of matrix multiplication, there is little such development in the multi-wavelet literature to express the two-scale matrix sequence {Qk} of an orthogonal multi-wavelet in terms of the two-scale matrix sequence {Pk} of its corresponding multi-scaling function vector. This paper, in part, is devoted to this study for the setting of orthogonal multi-wavelets of dimension r = 2. We will apply our results to constructing a family of the most recently introduced notion of armlet of order n and a family of the n-balanced orthogonal multi-wavelets.
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Jian-ao Lian "Armlets and balanced multiwavelets", Proc. SPIE 5207, Wavelets: Applications in Signal and Image Processing X, (13 November 2003); doi: 10.1117/12.506295; https://doi.org/10.1117/12.506295
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