Abstract
A finite frame is said to be scalable if its vectors can be rescaled so that the resulting set of vectors is a tight frame. The theory of scalable frame has been extended to the setting of Laplacian pyramids which are based on (rectangular) paraunitary matrices whose column vectors are Laurent polynomial vectors. This is equivalent to scaling the polyphase matrices of the associated filter banks. Consequently, tight wavelet frames can be constructed by appropriately scaling the columns of these paraunitary matrices by diagonal matrices whose diagonal entries are square magnitude of Laurent polynomials. In this paper we present examples of tight wavelet frames constructed in this manner and discuss some of their properties in comparison to the (non tight) wavelet frames they arise from.
| Original language | English |
|---|---|
| Title of host publication | Wavelets and Sparsity XVI |
| Editors | Vivek K. Goyal, Dimitri Van De Ville, Dimitri Van De Ville, Manos Papadakis, Dimitri Van De Ville, Manos Papadakis, Vivek K. Goyal, Dimitri Van De Ville |
| Publisher | SPIE |
| ISBN (Electronic) | 9781628417630, 9781628417630 |
| DOIs | |
| Publication status | Published - 2015 |
| Event | Wavelets and Sparsity XVI - San Diego, United States Duration: 2015 Aug 10 → 2015 Aug 12 |
Publication series
| Name | Proceedings of SPIE - The International Society for Optical Engineering |
|---|---|
| Volume | 9597 |
| ISSN (Print) | 0277-786X |
| ISSN (Electronic) | 1996-756X |
Other
| Other | Wavelets and Sparsity XVI |
|---|---|
| Country/Territory | United States |
| City | San Diego |
| Period | 15/8/10 → 15/8/12 |
Bibliographical note
Publisher Copyright:© 2015 SPIE.
All Science Journal Classification (ASJC) codes
- Electronic, Optical and Magnetic Materials
- Condensed Matter Physics
- Computer Science Applications
- Applied Mathematics
- Electrical and Electronic Engineering