TY - JOUR

T1 - On construction of multivariate symmetric MRA-based wavelets

AU - Krivoshein, A.V.

PY - 2014

Y1 - 2014

N2 - Let n be an integer and c be an integer or a semi-integer. For an arbitrary matrix dilation, we describe all masks that are symmetric with respect to the point c and have sum rule of order n. For each such mask, we give explicit formulas for the wavelet masks that are point symmetric/antisymmetric and generate a frame-like wavelet system providing approximation order n. For any matrix dilation (that is appropriate for the axial symmetry group on Zd in some natural sense), axial symmetric/antisymmetric frame-like wavelet systems providing approximation order n are constructed. Also, for several matrix dilations, the explicit construction of highly symmetric frame-like wavelet systems providing approximation order n is presented.

AB - Let n be an integer and c be an integer or a semi-integer. For an arbitrary matrix dilation, we describe all masks that are symmetric with respect to the point c and have sum rule of order n. For each such mask, we give explicit formulas for the wavelet masks that are point symmetric/antisymmetric and generate a frame-like wavelet system providing approximation order n. For any matrix dilation (that is appropriate for the axial symmetry group on Zd in some natural sense), axial symmetric/antisymmetric frame-like wavelet systems providing approximation order n are constructed. Also, for several matrix dilations, the explicit construction of highly symmetric frame-like wavelet systems providing approximation order n is presented.

KW - MRA-based wavelet systems

KW - Frame-type expansion

KW - Approximation order

KW - Symmetry

U2 - 10.1016/j.acha.2013.04.001

DO - 10.1016/j.acha.2013.04.001

M3 - Article

VL - 36

SP - 215

EP - 238

JO - Applied and Computational Harmonic Analysis

JF - Applied and Computational Harmonic Analysis

SN - 1063-5203

IS - 2

ER -