Tuesday and Thursday, 12:30–2:00pm, Zoom Link
The lectures will be recorded and posted under the weekly schedule below.
Farzad Kamalabadi, farzadk at illinois dot edu
Office hours: Open
Office hours: Monday 3:00-4:00pm, Wednesday 4:00-5:00pm, Zoom Link
The Gradescope code is here.
You can access the midterm from here.
The take-home midterm exam will be available on Friday, March 19 at 7:00 pm on the website. The submission deadline will be 7:00 pm on Saturday, March 20. The answers will be scanned and submitted to Gradescope.
The course begins with introducing multidimensional signal theory, which constitutes a mathematical framework to study digital imaging systems. We revisit familiar concepts such as Fourier transform, convolution, sampling and interpolation in higher dimensions. Then we introduce image reconstruction, forward models of image formation, and related concepts of well-posed and ill-posed inverse problems, conditioning and stability. Classical regularization techniques and statistical methods for the solution of inverse imaging problems are introduced, followed by more recent sparsity based methods, and machine learning techniques in computational imaging. In the second half of the course, we study various imaging modalities including optical and diffraction imaging, tomography, radar and lidar, aperture synthesis and interferometry, and phase retrieval.
Prerequisites: ECE 310: Digital Signal Processing (or equivalent), and ECE 313: Probability with Engineering Applications (or equivalent)
Multidimensional Signal Theory
Multidimensional Fourier Transform and its properties
Spherically symmetric functions and transforms of useful functions
Resolution, sampling and interpolation in higher dimensions
Linear operators on images, convolution, DFT
Radon transform and Projection Slice Theorem
Image Reconstruction and Inverse Problems
Direct and inverse problems
Well-posed problems and ill-posed problems; conditioning and stability
Regularization techniques
Variational techniques
Iterative techniques
Transform domain filtering: inverse filtering, SVD and related methods
Statistical and information methods
Sparsity-promoting regularization and machine learning methods
Applications in deblurring and tomography
Physics of image formation / remote imaging for different modalities
Optical imaging
X-ray tomography
Principles of Range-Doppler radar and lidar; ambiguity function and waveform design
Synthetic-Aperture Radar
Interferometric Radio Astronomy
Phase Retrieval
There will be weekly problem sets assigned up to the week of mid-semester exam (prior to transition to the final project); they include both standard and computational problems. Solutions will be posted on the course website.
There will be one mid-semester exam scheduled tentatively for March 19. The exam will be take-home.
There will be one journal article to be chosen and reviewed by each student from a list of relevant research papers which will be posted by mid semester. A four to six page report demonstrating the understanding of the topic will be expected. The article will serve as the starting point for the formation of the final project.
There will be a final project consisting of an oral presentation and a written report on a topic of student's choosing related to this course. A list of suggested project topics will be provided. A ten minute oral presentation, a six to ten page report, and a software demo is expected.
All submissions will happen over Gradescope.
30% Homeworks
30% Mid-Semester Exam
10% Journal Review
30% Final project
| Time | Topic | Lecture Material | Additional material | Reading | Assignments |
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Week 1: 1/25 - 1/29 |
Overview & Introduction to Multidimensional Fourier Transform |
Blahut 1.1–1.5, 3.1 | |||
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Week 2: 2/1 - 2/5 |
Circularly symmetric functions, Resolution, Projection Slice Theorem |
Blahut 3.2–3.9 | |||
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Week 3: 2/8 - 2/12 |
Sampling, Linear operators, Convolution, DFT |
Blahut 3.2–3.9 | |||
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Week 4: 2/15 - 2/19 |
Introduction to Inverse Problems Tomography application |
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Week 5: 2/22 - 2/26 |
Discretization of Inverse Problems, SVD, Transform domain filtering, tomography application |
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Week 6: 3/1 - 3/5 |
Conditioning and stability, Regularization, Variational and Iterative Techniques |
Blahut 11.9 |
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Week 7: 3/8 - 3/12 |
Sparsity-promoting regularization and machine learning methods |
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Week 8: 3/15 - 3/19 |
Physics of image formation: optical imaging March 19-20: Take-home Midterm Exam |
Blahut 4.1-4.5, 4.7, 4.8 | Midterm Exam | ||
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Week 9: 3/22 - 3/26 |
Project Description Principles of Range-Doppler radar and lidar |
Paper List |
Journal Review/ Project proposal |
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Week 10: 3/29 - 4/2 |
Principles of Range-Doppler radar and lidar | Blahut 6.1-6.7, 4.7, 4.8 | |||
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Week 11: 4/5 - 4/9 |
Synthetic-Aperture Radar | Blahut 7.5-7.7 | |||
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Week 12: 4/12 - 4/16 |
Progress Presentations April 13: No instruction on Tuesday |
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Week 13: 4/19 - 4/23 |
Interferometric Radio Astronomy |
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Week 14: 4/26 - 4/30 |
Project Presentations | ||||
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Week 15: 5/3 - 5/7 |
Project Presentations May 5: Last day of instruction |