Abstract
For the design of regular higher multiplicity wavelets it is useful to specify matrices of wavelet coefficients by their first row. This still leaves some freedom in the construction. In the case of classical wavelets (i.e., the wavelet matrix has only two rows), it means that a suitable characteristic matrix (the sum of square blocks) can be chosen. It is shown, however, that for m > 2 rows, given such data, the uniqueness fails, and when m ≥ 4 there are infinitely many possibilities. They can all be described by choices of some nontrivial linear subspaces in an m-dimensional space. This leads to a simple, explicit, and numerically reliable algorithm for constructing any of them. On the way, the existence and uniqueness of the factorization of wavelet matrices with respect to the Pollen product is also resolved.
Sign-in/Register to access full text options 
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.
