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The investigation focuses on the structures around knots. Specific projects look at the interconnections between their algebraic and geometric properties, connections between their geometric and topological properties, and when a local structure can give global information. The work will build on successful past collaborations and solidify new ones.

• Phase II: Practical Enhanced-Resolution Integrated Optical-Digital Imaging Camera
  Awarded $103,464 for the period 1/22/07 to 6/30/07
  Source: University of New Mexico

• DTO Advanced Imaging Seedling Project, A Practical Enhanced-Resolution Integrated Optical Imaging Camera (PERIODIC) System, Supplementary Funds
  Awarded $62,026 for the period 9/15/00 to 02/28/07
  Source: Army Research Office (ARO)
  
  
  This DTO project, A Practical Enhanced-Resolution Integrated Optical Imaging Camera (PERIODIC) System, aims to analyze, optimize, simulate, design, and fabricate a beta prototype, integrated, optical-digital, low-profile, low-cost, array-based imaging system. Considerable progress has been made in the theoretical, computational, and design/fabrication aspects, leading to the development of very promising workable prototype systems. Successful completion of this seedling effort is expected by the end of 2006, with the help of the supplemental funds, which will support two graduate and one undergraduate student, working with Professors Pauca, Plemmons, and Torgersen. Funds will also purchase additional equipment and supplies by the design and fabrication group at Catholic University (CUA).

• Postdetection Processing and Inverse Problems in Ground-Based Imaging
  Awarded $15,000 for the period 12/31/04 to 6/30/07
  Source: Air Force Office of Scientific Research (AFOSR), subcontract with University of New Mexico

  High-resolution images are essential to many important defense, science, engineering, law enforcement, and commercial applications. Extracting meaningful information from degraded images is especially vital for such biometric DoD applications as integrated optical imaging systems for personnel identification using the iris.

  This project conducts extensive, novel research in pupil phase engineering (PPE) to help develop, along with industrial partner CDM Optics Company, a reliable, easy-to-use, low-cost iris recognition system for personal verification to ensure computer network security. The primary technical goal is to make iris recognition easier to use by greatly expanding the imaging system's iris capture volume; we estimate that our methods can increase iris capture volume more than 100 times over current systems. The design of overall optical masks is a nontrivial problem and involves the numerical solution of highly nonlinear and ill-posed optimization problems with multiple design parameters.
  
  Dr. Plemmons serves as Senior Scientific Consultant to establish a major research and development program in ground-based imaging for the Air Force Research Laboratory, including the Maui High Performance Computing Center, which houses one of the world's largest supercomputers.

• A Practical, Enhanced-Resolution, Integrated Optical-Digital Imaging Camera (PERIODIC) System
  Awarded $63,486 for the period 05/23/05 to 8/30/06
  Source: United States Department of Energy (DOE)

  This project aims to design an end-to-end optimized, compact, integrated, digital camera system with a modular architecture. Novel interferometric enhancements of optical resolution and use of information theory as an optimization tool will lead to imaging-system designs that maximize information throughput. Surveillance imaging systems will be developed for intelligence agency applications.

• Innovative Computational Methods for Inverse Problems in Optical Imaging
  Awarded $51,255 for the period 6/29/05 to 2/28/06
  Source: Army Research Office (ARO)

  Dr. Plemmons and colleagues will investigate and implement innovative approaches to pupil-mask design to control the depth-of-focus of imaging systems. The traditional imaging system suffers from limited depth-of-focus that can be extended most simply by reducing the pupil size. This approach is undesirable, because the light flux and resolution are both decreased. Instead, the investigators plan to use multiple parameters that can control pupil phase variation rather finely. They foresee vigorous technology transfer to the military and industrial arenas and generalization of the theoretical concepts to other domains of imaging.

• Wavefront Coded Imaging System for Iris Recognition - Phase III
  Awarded $200,000 for the period 7/1/04 to 2/28/05
  Source: Army Research Office (ARO)

The Wake Forest Group (WFG) and CDM Optics in Boulder, Colorado, are working together to deliver a reliable, easy-to-use, low-cost iris-recognition system for computer network security. Researchers are meeting on a regular basis at appropriate sites to exchange information, review progress, and coordinate plans as the work proceeds. These highly qualified teams, working in complementary research areas, are in an ideal position to further develop effective image quality control for personal verification, using enhanced iris-recognition camera systems.

• Pupil Phase Engineering and Wavefront Coding for Iris-Recognition Systems
  Awarded $250,000 for the period 3/1/04 to 12/31/04
  Source: Army Research Office (ARO)

This joint project with industrial partner CDM Optics Company conducts extensive, novel research in pupil phase engineering (PPE) to develop reliable, easy-to-use, low-cost personal verification for computer network security, using an iris-recognition system. The primary technical goal is to greatly expand the imaging system's iris capture volume. Additional work will build on a growing understanding of the optimization strategies and requirements for iris- recognition algorithms. By phase-encoding optical images in the pupil plane and then digitally restoring them to remove certain aberrations, such as defocus, their quality can be greatly improved. The design of overall optical masks is a nontrivial problem involving the numerical solution of highly nonlinear and ill-posed optimization problems with multiple design parameters.

Sarah Raynor
Asymptotic Behavior of Solutions to the Nonlinear Schrodinger Equation
Awarded $5,000 for the period 1/1/06 to 12/31/06
Source: WFU Science Research Fund

This project will investigate the qualitative behavior of solutions to the nonlinear Schrodinger equation, which models important physical systems in quantum mechanics, optics, and fluid mechanics. It is also the canonical example of a nonlinear dispersive partial differential equation and provides a testing ground for a wide range of mathematical techniques and hypotheses. This project investigates long-term behavior