Two-Dimensional Imaging

Winter 2014-2015

 

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Week of / topics


Jan. 5

  • Overview and class procedures
  • Basic concepts and notation
  • Examples of digital images
  • Coherent and incoherent images
  • Computer representations of images
  • Histograms, contrast, and stretching images
Handouts for lectures: Handout 1 Handout 2 Handout 3

Jan. 12

  • Coherent and incoherent imaging mechanisms
  • Methods of representation
  • Functions of two variables
  • Projections
  • Image simulation
Handouts for lectures: Handout 6 Handout 7 Handout 8 Handout 10

Jan. 19

  • Monday - Martin Luther King Day, no class
  • Two-dimensional impulses
  • Shah function and Line impluses
  • Ring impulse functions
  • Derivatives of impulse functions
Handouts for lectures: Handout 11 Handout 12 Handout 12 additional notes

Jan. 26

  • In-class snap review of sifting functions
  • The two-d Fourier transform
  • Analysis vs. synthesis
  • Corrugation viewpoint
  • Transform pairs
  • Theorems for the two-d Fourier transform
  • FFTs
Handouts for lectures: Handout 15 Handout 16 Handout 17

Feb. 2

  • Image spectra
  • Digital implementation of the shift theorem
  • Convolution in two dimensions
  • Cross- and autocorrelation
  • Central value and volume of autocorrelation
  • The two-dimensional convolution theorem
  • Handouts for lectures: Handout 18 Handout 22 Handout 22 notes Handout 23

    Feb. 9

    • Midterm Examination through Lecture 2/2
    • Point response of a system
    • Factorization and separation
    • Assignment and Discussion of Final Project
  • Sampling and interpolation
  • Sampling functions
  • Seismic imaging beneath the Earth's surface
  • Handouts for lectures: Handout 26 Handout 28

    Feb. 16

    • Monday - President's Day, no class
    • Fourier transform of the sampling function
    • Convolutional models
    • Rotational symmetry
    • Bessel functions and the Hankel transform
    • Jinc and sinc functions
    Handouts for lectures: Handout 31 Handout 32

    Feb. 23

    • Antennas and radio astronomy
    • Aperture synthesis
    • Interferometry
    • Generating high-resolution pictures of the skies
    • Finding extrasolar planets
    Handouts for lectures: Handout 33 Handout 33 notes Handout 34 Handout 36

    Mar. 2

    • Other applications of two-dimensional imaging
    • Restoration
    • Reconstruction
    • Tomography and medical imaging
    Handouts for lectures: Handout 38 Handout 39 Handout 41 Handout 43

    Mar. 10

    • Back projection
    • Microwave sensors - Radar
    • Range modulation and azimuth compression
    • Last day of class Mar. 11
    Handouts for lectures: Handout 46 Handout 47 Handout 49 Handout 50

    Mar. 16

    • FINAL PROJECT DUE, NOON, MARCH 16