Tuesday and Thursday, 12:30–2:00pm
Location: ECEB 2013
The lectures will be recorded and posted under the weekly schedule below.
Farzad Kamalabadi, farzadk at illinois dot edu
Office hours: Open
Jamila Taaki, jtaaki2 at illinois dot edu
Office hours: M 23pm (in person, location: ECEB 3036), W 34pm (zoom only)
The Gradescope code is K37K43
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 wellposed and illposed 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.
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
Wellposed problems and illposed problems; conditioning and stability
Regularization techniques
Variational techniques
Iterative techniques
Transform domain filtering: inverse filtering, SVD and related methods
Statistical and information methods
Sparsitypromoting regularization and machine learning methods
Applications in deblurring and tomography
Physics of image formation / remote imaging for different modalities
Optical imaging
Xray tomography
Principles of RangeDoppler radar and lidar; ambiguity function and waveform design
SyntheticAperture Radar
Interferometric Radio Astronomy
Phase Retrieval
There will be weekly problem sets assigned up to the week of midsemester 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 midsemester exam scheduled for the week prior to spring break.
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% MidSemester Exam
10% Journal Review
30% Final project
Time  Topic  Lecture Material  Additional material  Reading  Assignments 
Week 1: 1/16  1/20 
Overview & Introduction to Multidimensional Fourier Transform 
Blahut 1.1–1.5, 3.1  
Week 2: 1/23  1/27 
Circularly symmetric functions, Resolution, Projection Slice Theorem 
Blahut 3.2–3.9  
Week 3: 1/30  2/3 
Sampling, Linear operators, Convolution, DFT 
Blahut 3.2–3.9  
Week 4: 2/6  2/10 
Introduction to Inverse Problems Tomography application 

Week 5: 2/13  2/17 
Discretization of Inverse Problems, SVD, Transform domain filtering, tomography application 

Week 6: 2/20  2/24 
Conditioning and stability, Regularization, Variational and Iterative Techniques 
Blahut 11.9 

Week 7: 2/27  3/3 
Sparsitypromoting regularization and machine learning methods 



Week 8: 3/6  3/10 
Physics of image formation: optical imaging 
Blahut 4.14.5, 4.7, 4.8  
Week 9: 3/20  3/24 
Principles of RangeDoppler radar and lidar 
Paper List 
Journal Review/ Project proposal 

Week 10: 3/27  3/31 
Principles of RangeDoppler radar and lidar  Blahut 6.16.7, 4.7, 4.8 
Due: Project Selection (3/28) Exam date: Thursday (3/30) 

Week 11: 4/3  4/7 
SyntheticAperture Radar  Blahut 7.57.7  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 