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Novel Mathematical/Computational Approaches to Image Exploi

Award Information

Agency:
Department of Defense
Branch:
Air Force
Award ID:
40257
Program Year/Program:
1998 / STTR
Agency Tracking Number:
40257
Solicitation Year:
N/A
Solicitation Topic Code:
N/A
Solicitation Number:
N/A
Small Business Information
MASSACHUSETTS TECHNOLOGICAL LABORATORY
330 Pleasant Street Belmont, MA 02178
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Woman-Owned: No
Minority-Owned: Yes
HUBZone-Owned: No
 
Phase 1
Fiscal Year: 1998
Title: Novel Mathematical/Computational Approaches to Image Exploi
Agency / Branch: DOD / USAF
Contract: N/A
Award Amount: $100,000.00
 

Abstract:

We propose to develop a unifying framework and formalism for the rapid and novel design and implementation of new families of image transforms based on the theory of groups and diffraction geometry. Our approach calls on such high-level imaging tools as graphs and aperiodic tilings to relate image data geometry with group structures on image data indexing sets and complex group algebra theory to define transforms on image data from group structures. This effort will lead to a unifying conceptual basis and algebra for structuring and developing fast algorithms for 1) traditionally used unitary transforms and their nonseparable multidimensional extensions, 2) new families of image transforms. 3) new classes of nonstandard filtering systems.Two classes of image transforms will be developed and tested. One class is based on direct sum decompositions of group algebras into left ideals and is implemented by nonabelian group filtering determined by complete systems of idempotents. The second is based on classical spectral decompositions of recoordinatized image data using aperiodic tilings and diffraction geometry. These transforms and filtering systems have clear path for digital implementation and offer greater variety, flexibility and resolution for advancing imaging technology as compared to standard methods.

Principal Investigator:

Richard Tolimieri
617373458

Business Contact:

Ta-Ming Fang
617484731
Small Business Information at Submission:

Massachusetts Technological
330 Pleasant Street Belmont, MA 02178

EIN/Tax ID:
DUNS: N/A
Number of Employees:
Woman-Owned: No
Minority-Owned: No
HUBZone-Owned: No
Research Institution Information:
Northeastern University
161 Cullinane Hall
Boston, MA 02115
Contact: Richard McNeil
RI Type: Nonprofit college or university