Orthogonality criteria for compactly supported refinable functions and refinable function vectors
摘要:
A refinable function phi(x) : R-n --> R or, more generally, a refinable function vector Phi(x) = [phi(1)(x),..., phi(r)(x)](T) is an L-1 solution of a system of (vector-valued) refinement equations involving expansion by a dilation matrix A, which is an expanding integer matrix. A refinable function vector is called orthogonal if {phi(j)(x - alpha) : alpha epsilon Z(n), 1 less than or equal to j less than or equal to r} form an orthogonal set of functions in L-2(R-n). Compactly supported orthogonal refinable functions and function vectors can be used to construct orthonormal wavelet and multi-wavelet buses of L-2(R-n). In this paper we give ct comprehensive set of necessary and sufficient conditions for the orthogonality of compactly supported refinable functions and refinable function vectors.
Orthogonality criteria for compactly supported refinable functions and refinable function vectors
作者:Jeffrey C. Lagarias、Yang Wang
DOI:10.1007/bf02510658
日期:2000.3
A refinable function phi(x) : R-n --> R or, more generally, a refinable function vector Phi(x) = [phi(1)(x),..., phi(r)(x)](T) is an L-1 solution of a system of (vector-valued) refinement equations involving expansion by a dilation matrix A, which is an expanding integer matrix. A refinable function vector is called orthogonal if phi(j)(x - alpha) : alpha epsilon Z(n), 1 less than or equal to j less than or equal to r} form an orthogonal set of functions in L-2(R-n). Compactly supported orthogonal refinable functions and function vectors can be used to construct orthonormal wavelet and multi-wavelet buses of L-2(R-n). In this paper we give ct comprehensive set of necessary and sufficient conditions for the orthogonality of compactly supported refinable functions and refinable function vectors.
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