ECE 580-02 Special Topics (2 Credits)

Inverse Problems in Imaging and Adaptive Optics

  • Class Meets: 9:00-9:50 Tues & Thurs in Cobleigh 632

  • Instructor:
    Curt Vogel
    2-210 Wilson Hall
    ph. 994-5332
    E-mail: vogel@math.montana.edu
    Home Page: www.math.montana.edu/~vogel

  • Textbook:
    None required. I'm putting together some notes that I'll post on the web.

  • Reference Books:
    Imaging Through Turbulence, Roggeman & Welsh, CRC Press, 1996.
    Introduction to Fourier Optics, 2nd Ed, Goodman, McGraw-Hill, 1996.
    Adaptive Optics for Astronomical Telescopes, Hardy, Oxford University Press, 1998.
    Introduction to Inverse Problems in Imaging, Bertero & Boccacci, IOP Publishing, 1998.
    Computational Methods for Inverse Problems, Vogel, SIAM, 2002.

  • Software:
    MATLAB

  • Course Outline:
    1. Review of Fourier Optics and Diffraction Theory.
    2. Models for Atmospheric Wave Propagation and Turbulence.
    3. Wavefront Sensors and Deformable Mirrors.
    4. Estimation and Correction of Volume Turbulence.
    5. Computational Tools for Large Linear Systems.
    6. Inverse Problems Related to Image Postprocessing (Deconvolution and Deblurring)

  • Grading:
    Homework, project, and exam schedules will be announced later.

    The final exam is scheduled for 12:00 - 1:50 pm, Tues, Dec. 17, 2002. Students are strongly encouraged to work together on homework assignments. Late homework will be accepted only with the advanced permission of the instructor.

  • 9/5/02 Lecture on Wave Equations (includes 2 homework exercises)
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  • 9/10/02 Lecture on Solutions to Wave Equations (includes 5 homework exercises)
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  • 9/12/02 Lecture on Green's Functions (includes 4 homework exercises)
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  • 9/17/02 Lecture on Rayleigh-Sommerfeld Diffraction Theory (includes 2 homework exercises)
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  • 9/19/02 Lecture on Fresnel and Fraunhofer Diffraction (includes 5 homework exercises)
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    Download MATLAB m-file with far-field pattern demo

  • 9/24/02, 9/26/02 Lectures on the Applied Optics of MOSES, by Charles Kankelborg (includes 7 homework exercises)
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  • 10/1/02 Lecture on Fourier Imaging

  • 10/3/02 Lecture on the Eikonal Equation (includes 5 homework exercises)
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  • 10/8/02 Introduction to Inverse Problems (includes 2 homework exercises)
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  • 10/10/02 Regularization by Linear Filtering (includes 4 homework exercises)
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    MATLAB m-files for Tikhonov demo: Gen_data.m, Tikh.m

  • 10/15/02, 10/17/02 Regularization Parameter Selection (includes 5 homework exercises)
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    UNIX tar file containing MATLAB demo codes for regularization parameter selection reg_param.tar

  • 10/22/02 Review of Probability (includes 5 homework exercises)
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  • 10/24/02 Conditional Probability and Bayesian Estimation (includes 3 homework exercises)
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  • 10/29/02 Linear Least Squares Estimation (includes 4 homework exercises)
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  • 10/31/02 Image Reconstruction (includes 4 homework exercises)
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  • 11/4/02 Discrete Image Model (includes 4 homework exercises)
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  • 11/12/02 Introduction to Optimization (includes 3 homework exercises)
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  • 11/19/02 The Conjugate Gradient Method (includes 6 homework exercises)
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  • 11/21/02 Miscellaneous Topics (includes 3 homework exercises)
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  • 11/26/02 Preconditioning (includes 3 homework exercises)
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  • 12/3/02 Nonnegativity Constraints (includes 2 homework exercises)
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  • 12/5/02 System Identification and Phase Diversity
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