MATH 76.02 Computational Inverse Problems

Inverse problems are ubiquitous in scientific research, and occur in applications ranging from medical imaging to radar sensing. The input data are often under-sampled, noisy and may additionally be blurry. Physical obstructions may also prevent accurate data acquisition. Recovering an underlying signal or image can be critical for diagnosis, classification, or inference. This course describes fundamental aspects of inverse problems and various computational approaches for solving them. Importantly, the students will learn how to choose the appropriate methodology for the particular challenges presented by the given application, and moreover how to critically analyze the quality of their results. Specifically, students will analyze accuracy, efficiency and convergence properties of the computational techniques for various classes of problems and when possible to quantify the uncertainty of their results. Although programming will not be formally taught as part of the course, students will write numerical code in languages
such as MATLAB or Python to compute their solutions. Resources will be provided to help students learn to write MATLAB code.

Instructor

Gelb

Prerequisite

MATH 22 or 24. MATH 20 or 60 recommended. Programming experience (e.g. COSC 1, ENGS 20) recommended.

Degree Requirement Attributes

Dist:QDS

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Offered

• Summer