An algorithm for matrix extension and wavelet construction
An algorithm for matrix extension and wavelet construction
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DOI：
10.1090/s0025-5718-96-00714-4
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发表时间：
1996-04
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影响因子：
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通讯作者：
W. Lawton;S. L. Lee;Zuowei Shen
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文献类型：
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作者：
W. Lawton;S. L. Lee;Zuowei Shen
本文给出了一种实用的方法，将n × r矩阵P(z), r≤n，在一个复变量z中具有洛朗多项式项，推广到同样具有洛朗多项式项的方阵。当z限定在环面T上时，如果P(z)具有正交列，则它可以推广为一个拟酉矩阵。如果P(z)对每个z∈T的秩为r，则可以将其推广为T上具有非消失行列式的矩阵，该方法在计算机中易于实现。将其应用于由多个具有任意膨胀参数的单变量尺度函数生成的多分辨率紧支持小波和预小波的构造。
This paper gives a practical method of extending an n x r matrix P(z), r ≤ n, with Laurent polynomial entries in one complex variable z, to a square matrix also with Laurent polynomial entries. If P(z) has orthonormal columns when z is restricted to the torus T, it can be extended to a paraunitary matrix. If P(z) has rank r for each z ∈ T, it can be extended to a matrix with nonvanishing determinant on T. The method is easily implemented in the computer. It is applied to the construction of compactly supported wavelets and prewavelets from multiresolutions generated by several univariate scaling functions with an arbitrary dilation parameter.