Orthogonal Multiwavelet Frames inL2Rd

Liu Zhanwei, Hu Guoen, Wu Guochang
2012 Journal of Applied Mathematics  
We characterize the orthogonal frames and orthogonal multiwavelet frames inL2Rdwith matrix dilations of the form(Df)(x)=detAf(Ax), whereAis an arbitrary expandingd×dmatrix with integer coefficients. Firstly, through two arbitrarily multiwavelet frames, we give a simple construction of a pair of orthogonal multiwavelet frames. Then, by using the unitary extension principle, we present an algorithm for the construction of arbitrarily many orthogonal multiwavelet tight frames. Finally, we give a
more » ... neral construction algorithm for orthogonal multiwavelet tight frames from a scaling function.
doi:10.1155/2012/846852 fatcat:cphlg56knjh2deunjx2xy4h4v4