Syllabus for MA797 - Section 003,  Spring 2024

Mathematics of radar imaging

The course meets on Monday and Wednesday between 11:45am and 1:00pm in SAS Hall 1218



1. Instructor:
Dr. Semyon V. Tsynkov
Office: SAS Hall 4222
Office Hours: By appointment
Phone Number: (919)515-1877
E-mail address: tsynkov@math.ncsu.edu


2. Written sources:

The course will be taught out of the monograph Transionospheric Synthetic Aperture Imaging, by Mikhail Gilman, Erick Smith, and Semyon Tsynkov; published by Birkhauser/Springer in 2017.


The following books are not mandatory and can be used as supplementary material:

  • Margaret Cheney and Brett Borden, Fundamentals of Radar Imaging, Vol. 79 of CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 2009.
  • Brett Borden, Radar Imaging of Airborne Targets: A Primer for Applied Mathematicians and Physicists, 1st edition, Taylor & Francis, 1999.
  • Charles V. Jakowatz, Daniel E. Wahl, Paul H. Eichel, Dennis C. Ghiglia, and Paul A. Thompson, Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach, Springer, New York, 1996.
  • Ian G. Cumming and Frank H. Wong, Digital Processing of Synthetic Aperture Radar Data: Algorithms and Implementation, Artech House Publishers, Boston, 2005.

  • 3. Objectives: Radar imaging is a mature technology with a broad range of applications. Yet in spite of its many demonstrated successes, a number of difficult issues are still outstanding, e.g., mitigation of the various distortions. Addressing these issues requires going beyond the standard engineering practices and calls for employing an array of mathematical methods. Accordingly, in the course we adopt the interpretation of radar imaging as a mathematical inverse problem. Our goal is to cover the key aspects of construction and analysis of the pertinent mathematical models using tools from differential equations, perturbation theory, and Fourier analysis. Students will learn the main quantitative concepts of radar imaging: matched filtering, synthetic aperture, imaging operator, focusing, resolution, signal compression, and others. They will also be exposed to the fundamentals of electromagnetic wave propagation and scattering, from the standpoint of both physics and mathematics. Those include Maxwell's, d'Alembert (wave), and Helmholtz equations, geometrical optics, diffraction (Fresnel and Fraunhofer regimes), Doppler effects, first Born approximation and Neumann series, Bragg scattering, and more.


    4. Structure: Two class meetings per week, homework every two to three weeks, final project. All classroom lectures will be videotaped. Recordings can subsequently be viewed on Panopto.


    5. Grading Policy: 70% of the credit will be earned during the semester via homework assignements, while the remaining 30% will come from the final project, which will be due on Friday, April 26, as per the Spring 2024 examination schedule. All homework papers must be computer typeset. Homework submitted after the due date may still be accepted but will earn a lower grade unless there is a documented excused absence. In the latter case, assignments must still be completed but may be submitted at a later date with no penalty.


    6. Classroom attendance does not contribute to the overall grade directly, but is recommended on the substance. Viewing the videotaped lectures may help.


    7. Topics to be covered (ideally): Please see the course description in MS Word or PDF.


    8. Prerequisites: Discuss with the instructor.


    9. Please familiarize yourself with Protect the Pack: NCSU COVID-19 readiness protocols .



    When completing all course assignments, students must adhere to NC State acedemic integrity standards, as per the Code of Student Conduct policy (NCSU POL11.35.1).
    Reasonable accommodations will be made for students with verifiable disabilities. Please note that, concerns/fears about COVID-19 do not constitute a disability. A common example of accommodations for students with verifiable disabilities is extended time on tests. In order to take advantage of available accommodations, students must be properly registered with the Disability Resource Office. For more information on NC State's policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation (REG 02.20.01).
    Students are responsible for reviewing the policies, rules, and regulations that pertain to their course rights and responsibilities. Those include:
    Equal Opportunity and Non-Discrimination Policy Statement,
    Code of Student Conduct,
    and Grades and Grade Point Average.