525.628.81 - Compressed Sensing and Sparse Recovery

Course Structure

The course materials are divided into modules which can be accessed by clicking Course Modules on the course menu. A module will have several sections including the overview, content, readings, discussions, and assignments. You are encouraged to preview all sections of the module before starting. Most modules run for a period of seven (7) days, exceptions are noted in the Course Outline. You should regularly check the Calendar and Announcements for assignment due dates.

Course Topics

• Introduction. Motivation. Mathematical Background. Compressed Sensing Demonstration & Featured Applications.
• Nyquist Sampling Theorem. Traditional Sampling Techniques. Sparsity. Linear Signal Representation. Basis Functions. Traditional Compression.
• Pseudo-Inverse and Least-Squares Regression. Greedy Pursuit Strategy.
• Spark. General Convex Optimization Strategy. L1-norm minimization and Linear Programming.
• Null-space Property of Sensing Matrix A. Its role in Noiseless Exact Recovery.
• Restricted Isometry Property. Stability and Robustness of Recovery. Noisy Sparse Recovery.
• Coherence. Error Bounds and Relationship to RIP & NUP. Greedy Pursuit Revisited: Error bounds from Coherence.
• Optimal and Universal Sensing Matrix. Random Sampling. RIP of Random Matrices. Structured Random Matrices.
• Sparse Representation and Sparse Coding for Discriminative Applications. Sparse Representation Based Classification (SRC). Face Recognition.
• Efficient Iterative Sparse Recovery Algorithms for Large-Scale Applications. From Multi-Measurements to Joint-Sparsity.
• Extensions of Sparsity Framework: Matrix Completion. Robust Principal Component Analysis. Dictionary Learning.
• Extensions of Sparsity Framework: Non-negative Matrix Factorization. Deep Sparse Coding Networks.
• Compressed Sensing and Sparsity Applications.

Course Goals

The goal of this course is to provide students with the theoretical understanding, algorithmic tools, and implementation experience needed to use these tools to solve problems in their own area of interest, or even to begin doing novel work in this area.

Course Learning Outcomes (CLOs)

• Explain theoretical principles behind compressed sensing and understand the scenarios as well as theoretical limits in sensing below Nyquist rate.
• Apply appropriate strategies and computational tools to accurately recover a high-dimensional signal from a small set of measurements and provide performance guarantees for a variety of sparse recovery algorithms.
• Implement various sparse recovery algorithms and/or improve/modify existing sparse recovery algorithms.
• Extend the framework to various practical applications, from low-level signal processing applications such as denoising and enhancement to high-level discrimination applications such as target detection and face recognition.
• Apply the sparsity framework to learn optimal signal representation and relate it to deep learning techniques.
• Create written and oral communications in common academic publication format.

Textbooks

Not required.
All the readings materials are in Canvas.

Student Coursework Requirements

Weekly assignments: 45%
Discussions: 15%
Final design project: 40% (project proposal 10%, presentation 10%, peer review 10%, final project 10%)

Grading Policy

Academic Policies

Deadlines for Adding, Dropping and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. 

For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. 
 
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.