Imaging w/ data-driven models – CSE 8803

Instructor

Felix J. Herrmann
Phone: +1 (404) 385-7069
CODA, room S1375B

Time and Location Tuesday/Thursday 2:00 pm - 3:15 pm, Engineering Sci and Mechanics rm 201

Office Hours: by appointment via Microsoft Teams

Course Description

This course concerns inverse problems as they relate to imaging. After reviewing techniques from Compressive Sensing, Sparse Approximation, and Convex Optimization by means of lectures based on Mathematical Foundations of Data Sciences and computational assignments from Numerical Tours of Data Sciences (in Matlab, Python, Julia, or R), the course shifts towards the state of the art of "Imaging w/ data-driven models" as outlined in the review article Solving inverse problems using data-driven models and the references therein. Special emphasis will be given to Bayesian Inference with Normalizing Flows, a special type of invertible neural networks. The latter forms an important development since it alows for capturing uncertainty via distribution learning. The reviewed techniques are of interest to areas in Computational Science and Engineering where data is incomplete, noisy, and observed indirectly.

Topics

See Topics tab (adapted from Mathematical Foundations of Data Sciences and Solving inverse problems using data-driven models)

  • Overview: a Sparse Tour of Signal Processing

  • Signal and Image Processing with Orthogonal Decompositions

  • Fourier Processing

  • Wavelet Processing

  • Approximation with Orthogonal Decompositions

  • Linear and Non-linear Denoising

  • Variational Regularization of Inverse Problems

  • Sparse Regularization of Inverse Problems

  • Compressive Sensing

  • Statistical Regularization

  • Learning in Functional Analytic Regularization

  • Learning in Statistical Regularization

COVID

Georgia Tech is committed to promoting a campus community that supports holistic well-being, as well as empowering students to make choices that enable positive health outcomes. As we continue to live and learn through a pandemic, Georgia Tech strongly encourages students to utilize several tools not only to reduce their own risks of infection from Covid-19, but also to help reduce the overall levels of transmission in the community.

These tools include:

  1. Getting fully vaccinated. Getting vaccinated at Tech is easy and free.

  2. Wearing face coverings consistently in all indoor settings and also in outdoor settings when in close proximity to others.

  3. Getting tested on a regular basis, regardless of whether you are vaccinated or asymptomatic. No appointment is needed for Georgia Tech’s asymptomatic testing, and it is free.

  4. Avoiding touching your face until you have cleaned your hands with soap and water or used hand sanitizer.

  5. Immediately self-quarantining or self-isolating if you experience any symptoms that could be related to Covid-19 or if you have tested positive for Covid-19.

Additional information and resources are available on the Tech Moving Forward website.

Students are expected to be familiar with and abide by the Institute guidelines, information, and updates related to Covid-19. Find campus operational updates, Frequently Asked Questions, and details on campus surveillance testing and vaccine appointments on the Tech Moving Forward website.

Recordings of Class Sessions and Required Permissions

Classes may not be recorded by students without the express consent of the instructor unless it is pursuant to an accommodation granted by the Office of Disability services. Class recordings, lectures, presentations, and other materials posted on Canvas are for the sole purpose of educating the students currently enrolled in the course.

Students may not record or share the materials or recordings, including screen capturing or automated bots, unless the instructor gives permission. Digitally proctored exams may require students to engage the video camera, but those recordings will not be shared with or disclosed to others without consent unless legally permitted.

  • For classes where participation is voluntary, students who participate with their camera engaged or utilize a profile image are agreeing to have their video or image recorded.

  • For classes requiring class participation, if students are identifiable by their names, facial images, voices, and/ or comments, written consent must be obtained before sharing the recording with persons outside of currently enrolled students in the class.

Course Material

Textbook

none required

Lectures

The lectures will be based on

Assignments

There will be Computational Assignments, which will mostly involve geophysics-related programs, computer simulations, and data analysis. These assignments is designed for each student to work by him/herself. This assignments will count as 30% of your overall course grade.

Project

You are required to propose, complete and write up a term project on any topic related to the class. This project will count for 50% of the final course grade. The project grade will be based on a proposal stage (10% of project grade) where you quickly present and receive feedback from the class and instructor on the project and its scope. Then upon completion of the project you will be graded on an in-class presentation with slides (30% of project grade). Finally, the bulk of the project grade will be given on a written report (60% of project grade). Your written report should be written up in a journal form with length, figures and referencing in a format suitable for a conference or research letter submission.

You can find more details on the Projects page.

Evaluation

  • Assignments (30%)

  • Presentation of a journal paper in class (20%)

  • Final project + in-class presentation (50%)

These weights are approximate; we reserve the right to change them later.

Prerequisites

Numerical Linear Algebra, Statistics. Experience w/ matlab, python, or julia

Academic Honesty

It is expected that all students are aware of their individual responsibilities under the Georgia Tech Academic Honor Code, which will be strictly adhered to in this class. The complete text of the Georgia Tech Academic Honor Code is at http://www.honor.gatech.edu/.