Two-Dimensional Imaging

Winter 2018-2019

 

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Week / topics


Week 1

  • 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

Week 2

  • 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

Week 3

  • 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

Week 4

  • 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

Week 5

  • 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

Week 6

  • Midterm Examination
  • 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

Week 7

  • 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

Week 8

  • 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

Week 9

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

Week 10

  • Back projection
  • Microwave sensors - Radar
  • Range modulation and azimuth compression
  • Last day of class Mar. 13
Handouts for lectures: Handout 46 Handout 47 Handout 49 Handout 50

Finals Week

  • FINAL PROJECT DUE, NOON, MONDAY