Academic Journal
A Physical Interpretation for Finite Tight Frames
| العنوان: | A Physical Interpretation for Finite Tight Frames |
|---|---|
| المؤلفون: | P. G. Casazza, M. Fickus , J. Kovačević , M. T. Leon , J. C. Tremain |
| المساهمون: | The Pennsylvania State University CiteSeerX Archives |
| المصدر: | http://www.math.missouri.edu/~pete/pdf/85.fiftf.pdf. |
| سنة النشر: | 2003 |
| المجموعة: | CiteSeerX |
| الوصف: | Though finite tight frames arise in many applications, they have often proved difficult to understand and construct. We investigate the nonlinear problem of finding a tight frame for which the lengths of the frame elements have been prescribed in advance. Borrowing several ideas from Classical Mechanics, we show that this problem has a natural, intuitive interpretation. In particular, we show that such frames may be characterized as the minimizers of a potential energy function, and justify their interpretation as “maximally orthogonal” sequences. By exploiting this idea, we are able to show that such frames always exist, provided the requisite lengths satisfy a “fundamental inequality.” In so doing, we characterize those sequences of nonnegative numbers which arise as the lengths of a tight frame’s elements. |
| نوع الوثيقة: | text |
| وصف الملف: | application/pdf |
| اللغة: | English |
| Relation: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.67.7802; http://www.math.missouri.edu/~pete/pdf/85.fiftf.pdf |
| الاتاحة: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.67.7802 http://www.math.missouri.edu/~pete/pdf/85.fiftf.pdf |
| Rights: | Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
| رقم الانضمام: | edsbas.2D90DE5F |
| قاعدة البيانات: | BASE |
| الوصف غير متاح. |