Abstract
The concept of a two-direction multiscaling functions is introduced. We investigate the existence of solutions of the two-direction matrix refinable equation $$\Phi (x) = \sum\limits_{k \in \mathbb{Z}} {P_k^ + \Phi (2x - k) + } \sum\limits_{k \in \mathbb{Z}} {P_k^ - \Phi (k - 2x)} ,$$ where r × r matrices {Pk+} and {Pk−} are called the positive-direction and negative-direction masks, respectively. Necessary and sufficient conditions that the above two-direction matrix refinable equation has a compactly supported distributional solution are established. The definition of orthogonal two-direction multiscaling function is presented, and the orthogonality criteria for two-direction multiscaling function is established. An algorithm for constructing a class of two-direction multiscaling functions is obtained. In addition, the relation of both orthogonal two-direction multiscaling function and orthogonal multiscaling function is discussed. Finally, construction examples are given.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
