Dr. Jacob Barhen Computer Science and Mathematics Division

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 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

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 3

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 4 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 Missile Defense Applications

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 5 What is CTIS?  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 University of Arizona Computer Tomography Imaging Spectrometer FPA Objective Field stop Disperser Reimaging lens Collimator f g H f

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 6 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 Raw CTIS images on FPA Each blurred images represents a 2D recording of a projection through the object cube at a different angle g gλgλ RESEARCH GOALS

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 7 1. Mixed Expectation Maximization Costs and Challenges 3 matrix-vector multiplications per iteration results in about 2 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 RECONSTRUCTION APPROACH

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 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

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 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 = H T 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

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY MULTIPLICATIVE ALGEBRAIC RECONSTRUCTION TECHNIQUE (MART) Iterative algorithm proposed by UOA Much faster than MEM Assume noise was prefiltered

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 11 Hyperspectral Object Reconstruction

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 12 Hyperspectral Object Reconstruction

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 13 Convergence to True Target Conjugate Gradient

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 14 Convergence to True Target: Conjugate Gradient

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 15 Convergence to True Target Asymptotic Attractor Dynamics

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 16 Convergence to True Target Asymptotic Attractor Dynamics

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 17 Convergence to True Target Mixed Expectation Maximization

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 18 Convergence to True Target Mixed Expectation Maximization

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 19 Convergence to True Target MART

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 20 Convergence to True Target MART

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 21 Convergence to True Target Voxel Recovery Error : MART – MEM

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 22 Convergence to True Target Voxel Recovery Error : AA – CG – MART – MEM

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 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

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 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

OAK RIDGE NATIONAL LABORATORY U. S. DEPARTMENT OF ENERGY 25 ANY QUESTIONS?