520.648 - Sparse Recovery & Compressed Sensing

520.648 Sparse Recovery & Compressed Sensing

Department of Electrical and Computer Engineering
The Johns Hopkins University

Instructor
- Prof. Trac D. Tran
  Address: 215 Barton Hall
  Phone: (410) 516-7416
  Email: trac@jhu.edu
  Office Hours : Tues 11-1 or by appointment

Lectures
- Tues Thurs, 1:30 - 2:45, Shaffer 2
- 03/29/2018. Guest Lecture: Prof. Stuart Geman, "Real and Artificial Neural Networks"

Homework Assignments
- Homework Assignment I, measurements and sensing matrices, due Feb. 8 in class.
- Homework Assignment II, due Feb. 15 in class.
- Homework Assignment III, due Feb. 22 in class.
- Homework Assignment IV, due Mar 1st in class.
- Homework Assignment V, due Mar 8 in class. Data
- Homework Assignment VI, due Mar 15 in class.
- Homework Assignment VII, due April 10 in class.

Course Description
- Sparsity has become a very important concept in recent years in applied mathematics, especially in mathematical signal and image processing, as in inverse problems. The key idea is that many classes of natural signals can be described by only a small number of significant degrees of freedom. This course offers a complete coverage of the recently emerged field of compressed sensing, which asserts that, if the true signal is sparse to begin with, accurate, robust, and even perfect signal recovery can be achieved from just a few randomized measurements. The focus is on describing the novel ideas that have emerged in sparse recovery with emphasis on theoretical foundations, practical numerical algorithms, and various related signal processing applications.

Syllabus
- Week 1: Introduction. Motivation. Mathematical Background.
- Week 2: Sparse Recovery. l0-Recovery. Restricted Isometry Property (RIP), Coherence. Random Sampling.
- Week 3: Stable Recovery. Number of Measurements. l1-Recovery. Random Sampling. Sensing Matrix Design.
- Week 4: Practical Algorithms: l0- vs. l1- vs. l2-. Matching Pursuit. Message Passing. Alternate Direction. Iterative Thresholding.
- Week 5: Robustness. Sparse Noise. Matrix Completion and Approximation, Robust PCA.
- Week 6: Dictionary Learning, K-means, K-SVD. Non-Negative Matrix Factorization. Subspace Clustering.
- Week 7: Structured Sparsity. Multi-task. Multi-Modal. Multi-Measurement. Low-rank Models.
- Week 8: Spring Break
- Week 9: Face Recognition. Computer Vision. Video Processing. Deep Learning and Sparsity.
- Week 10: Sampling and RF Applications. Spectral CS.
- Week 11: Literature Survey/Preliminary Results
- Week 12: Medical Imaging. Biological Signal Analysis.
- Week 13: Hyperspectral and Radar Imaging. Classification. Clustering.
- Week 14: Project Presentations.

Final Project
- Final Project Direction and Suggestions.
- Students are expected to work in team of 3 on an assigned topic.
- A preliminary presentation, a final project report, and an oral demonstration/presentation are required from each team.

Grading
- Homework / Class Participation: 50%
- Final Project Report and Final Oral Presentation: 50%

Important Dates
- First lecture: Tues, 01/30/2018, 1:30PM, Shaffer 2.
- Spring Break: 03/19/2018 -- 03/25/2018

Ethics Issues
- Please read the information provided by the Ethics Board.
- On homework and projects, you are permitted to discuss the problems for clarification purposes, and to help each other with specific points. However, the overall solution and write-up should be your own work.