Class Time and Instruction Information

Tuesday and Thursday, 12:30–2:00pm

Location: ECEB 2013

The lectures will be recorded and posted under the weekly schedule below.

Instructor

• Farzad Kamalabadi, farzadk at illinois dot edu

• Office hours: Open

Teaching assistant

• Jamila Taaki, jtaaki2 at illinois dot edu

• Office hours: M 2-3pm (in person, location: ECEB 3036), W 3-4pm (zoom only)

The Gradescope code is K37K43

Course description

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)

Syllabus

• 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

Course Activities

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. 

Journal Review

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.

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.

Grading

All submissions will happen over Gradescope.

• 30% Homeworks

• 30% Mid-Semester Exam

• 10% Journal Review

• 30% Final project

Textbook

• R. E. Blahut, Theory of Remote Image Formation, Cambridge University Press, 2004

Recommended Texts

• D. E. Dudgeon and R. M. Mersereau, Multidimensional Signal Processing, Prentice-Hall, 1984.
• R. N. Bracewell, Two-Dimensional Imaging, Prentice-Hall, 1995
• M. Bertero and P. Bocacci, Introduction to Inverse Problems in Imaging, 2002
• P. C. Hansen, Discrete Inverse Problems: Insight and Algorithms, SIAM, 2010
• E. L. Miller & W. Clem Karl, Fundamentals of Inverse Problems, 2003 (lecture notes). Available online at www.ece.neu.edu/faculty/elmiller/eceg398f03/notes.pdf

Week by week

Time	Topic	Lecture Material	Additional material	Reading	Assignments
Week 1: 1/16 - 1/20	Overview & Introduction to Multidimensional Fourier Transform	Lecture 2 Notes		Blahut 1.1–1.5, 3.1	Homework 1 Homework 1 Solutions
Week 2: 1/23 - 1/27	Circularly symmetric functions, Resolution, Projection Slice Theorem	Lecture 3 Notes Lecture 4 Notes		Blahut 3.2–3.9	Homework 2 Homework 2 Solutions
Week 3: 1/30 - 2/3	Sampling, Linear operators, Convolution, DFT	Lecture 5 Notes Lecture 6 Notes		Blahut 3.2–3.9	Homework 3 Homework 3 Solutions
Week 4: 2/6 - 2/10	Introduction to Inverse Problems Tomography application	Lecture 7 Notes Lecture 8 Notes Lecture 8 Recording			Homework 4 Homework 4 Solutions
Week 5: 2/13 - 2/17	Discretization of Inverse Problems, SVD, Transform domain filtering, tomography application	Lecture 9 Notes Lecture 9 Recording Lecture 10 Notes			Homework 5 Homework 5 Solutions
Week 6: 2/20 - 2/24	Conditioning and stability, Regularization, Variational and Iterative Techniques	Lecture 11 Notes Lecture 12 Notes		Blahut 11.9	Homework 6 Homework 6 Solutions
Week 7: 2/27 - 3/3	Sparsity-promoting regularization and machine learning methods	Lecture 13 Notes
Week 8: 3/6 - 3/10	Physics of image formation: optical imaging	Lecture 15 Notes Lecture 16 Notes		Blahut 4.1-4.5, 4.7, 4.8
Week 9: 3/20 - 3/24	Principles of Range-Doppler radar and lidar	Project Guide Lecture 17 Notes Lecture 18 Notes	Paper List		Journal Review/ Project proposal
Week 10: 3/27 - 3/31	Principles of Range-Doppler radar and lidar	Review Notes Lecture 19 Notes		Blahut 6.1-6.7, 4.7, 4.8	Due: Project Selection (3/28) Exam date: Thursday (3/30)
Week 11: 4/3 - 4/7	Synthetic-Aperture Radar	Lecture 20 Notes Lecture 21 Notes		Blahut 7.5-7.7	Due: Project Proposal/Review (4/6)
Week 12: 4/10 - 4/14	Project Presentations
Week 13: 4/17 - 4/21	Interferometric Radio Astronomy
Week 14: 4/24 - 4/28
Week 15: 5/1	5/2: Last day of instruction