Two-Dimensional Imaging

Winter 2018-2019

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Class Info

Syllabus

References

Homework

Software

Announcements

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

Week 2

• Coherent and incoherent imaging mechanisms
• Methods of representation
• Functions of two variables
• Projections
• Image simulation

Week 3

• Two-dimensional impulses
• Shah function and Line impluses
• Ring impulse functions
• Derivatives of impulse functions

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

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

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

Week 7

• Fourier transform of the sampling function
• Convolutional models
• Rotational symmetry
• Bessel functions and the Hankel transform
• Jinc and sinc functions

Week 8

• Antennas and radio astronomy
• Aperture synthesis
• Interferometry
• Generating high-resolution pictures of the skies
• Finding extrasolar planets

Week 9

• Other applications of two-dimensional imaging
• Restoration
• Reconstruction
• Tomography and medical imaging

Week 10

• Back projection
• Microwave sensors - Radar
• Range modulation and azimuth compression
• Last day of class Mar. 13

Finals Week

• FINAL PROJECT DUE, NOON, MONDAY