| NSF Org: |
CCF Division of Computing and Communication Foundations |
| Recipient: |
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| Initial Amendment Date: | July 7, 2005 |
| Latest Amendment Date: | May 22, 2008 |
| Award Number: | 0515152 |
| Award Instrument: | Standard Grant |
| Program Manager: |
John Cozzens
CCF Division of Computing and Communication Foundations CSE Directorate for Computer and Information Science and Engineering |
| Start Date: | September 1, 2005 |
| End Date: | August 31, 2008 (Estimated) |
| Total Intended Award Amount: | $0.00 |
| Total Awarded Amount to Date: | $305,773.00 |
| Funds Obligated to Date: |
FY 2006 = $6,000.00 FY 2007 = $6,000.00 FY 2008 = $6,000.00 |
| History of Investigator: |
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| Recipient Sponsored Research Office: |
5000 FORBES AVE PITTSBURGH PA US 15213-3815 (412)268-8746 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
5000 FORBES AVE PITTSBURGH PA US 15213-3815 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): | SIGNAL PROCESSING SYS PROGRAM |
| Primary Program Source: |
app-0106 app-0107 01000809DB NSF RESEARCH & RELATED ACTIVIT |
| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.070 |
ABSTRACT
In the past couple of decades, multiresolution techniques in signal and image processing have revolutionized the field. Most of the multiresolution techniques in use are nonredundant, that is, the underlying mathematical structures used are bases. However, many of today's applications require some redundancy in the system.
The requirement of redundancy requires a mathematical structure more general than bases, termed frames. Although the initial work on frames dates back to the 1950s, frames have become more popular only recently, mostly due to emerging applications requiring tools which provide redundancy. A fair amount of work has already been done on frames; however, their level of maturity is nowhere near that of wavelets. This is about to change as a host of applications requires redundancy offered by frames; the theory needs to follow fast.
This research addresses gaps in the current knowledge and solves some of the open questions in frames. These are related to the characterization of certain classes as well as the construction of a frame toolbox motivated by problems in bioimaging, biometrics and robust transmission. Developing the frame theory to this extent brings frames to the level of maturity of wavelets and significantly expands the multiresolution toolbox.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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