Dr. Jacob Barhen Computer Science and Mathematics Division

1. Advances in Algorithms for Processing... ...CTIS Flash Hyperspectral Imagery Deirdre' Johnson Research Alliance in Math and Science Program Fisk University Dr. Jacob Barhen Computer Science and Mathematics Division August 8, 2007 Oak Ridge, Tennessee

2. OUTLINE • MDA context for flash hyperspectral imaging • Signal processing • Approach • CTIS: information processing model and computational challenges • Advances in algorithms • Mixed expectation • Asymptotic attractor dynamics • Sparse conjugate gradient • MART • Conclusions and Future Work

4. Missile DefenseApplications MDA Signal Processing and Computation • MDA’s objective is to detect, track and assess the “killing” of targets • Target intercept generates spatially-distributed radiation • Hyperspectral sensors collect spectrally-contiguous images of the target intercept in 3D ( produces “data cube” x, y, • Process collected data in shortest possible time The Approach • Recover target information from data collected on FPA • Solve very large scale system of noise-perturbed equations • Analysis and identification based on spectral response to material content or temperature

5. Computed Tomography Imaging Spectrometer Sensor built by the University of Arizona Measures objects in a manner that requires complex post-processing Object cube projected on sensor’s focal plane Diffractive optics causes dispersion Images are blurred (noise) Requires solution of inverse problem g f H Objective FPA Disperser Field stop Reimaging lens Collimator What is CTIS? f University of Arizona Computer Tomography Imaging Spectrometer

6. Raw CTIS images on FPA RESEARCH GOALS Develop , implement, and test innovative algorithms for CTIS image reconstruction Compare • Speed of recovery • Accuracy of reconstruction Identify a computer platform that would benefit this MDA application • processing speed • power required Each blurred images represents a 2D recording of a projection through the object cube at a different angle gλ g

7. RECONSTRUCTION APPROACH • Mixed Expectation Maximization • Costs and Challenges • 3matrix-vector multiplications per iteration • results in about2 m per iteration assuming some overlap can be achieved • algorithm exhibits oscillatory behavior • convergence requires over 100 iterations (typically, 500) • UA stops at 10-20!   40 m / run

8. 2. Attractor Dynamics Benefits and Costs Limitations of conventional image inversion • Conventional algorithms are too expensive because FPA is noisy • optical system matrix H is non-square, non-symmetric, and singular Benefits of attractor dynamics paradigm • no inversion of H required: readily applies to non-square, non-symmetric, even singular matrices • sparsity of H is fully exploited, and no transpose of H is used

9. 3. Conjugate Gradients Benefits and Costs Limitations of Conventional CG • matrix A is assumed square, symmetric, and positive definite (SSPD) • not the case for CTIS optical system matrix H • For overdetermined systems, conventional CG considers the associated normal equations • an SSPD matrix obtained by defining A = HT H Benefits and costs of Sparse (NS)2 CG • Sparsity of H is fully exploited, and no explicit transpose of H is required • Readily applies to (NS)2 , i.e., non-square, non-symmetric matrices • One additional (but sparse) matrix-vector multiplication needed per iteration • Preconditioning required for large scale systems

10. 4. MULTIPLICATIVE ALGEBRAIC RECONSTRUCTION TECHNIQUE (MART) • Iterative algorithm proposed by UOA • Much faster than MEM • Assume noise was prefiltered

11. Hyperspectral Object Reconstruction

12. Hyperspectral Object Reconstruction

13. Convergence to True Target Conjugate Gradient

14. Convergence to True Target: Conjugate Gradient

15. Convergence to True Target Asymptotic Attractor Dynamics

16. Convergence to True Target Asymptotic Attractor Dynamics

17. Convergence to True Target Mixed Expectation Maximization

18. Convergence to True Target Mixed Expectation Maximization

19. Convergence to True Target MART

20. Convergence to True Target MART

21. Convergence to True Target Voxel Recovery Error : MART – MEM

22. Convergence to True Target Voxel Recovery Error : AA – CG – MART – MEM

23. CONCLUSIONS and FUTURE WORK • Algorithms were implemented and tested • Considerable speedup compared to previous methods were obtained • Excellent accuracy in target acquisition • Fastest algorithms will be implemented in IBM cell multi-core processor • ORNL will support MDA on algorithms on real flight test missile experience • CTIS will take measurements in real time • Code will analyze data in real time

24. Acknowledgements • Department of Energy Office of Science/Advanced Scientific Computing Research (ASCR) • Missile Defense Agency/Advanced Concepts Directorate • Research Alliance in Math and Science (RAMS) • ORNL • Mrs. Debbie McCoy • Dr. Jacob Barhen

25. ANY QUESTIONS?