ELEC445 Inverse Problems and Imaging

Classical and modern solution methods for inverse problems including image deblurring and analysis of experimental data.

Paper title	Inverse Problems and Imaging
Paper code	ELEC445
Subject	Electronics
EFTS	0.0833
Points	10 points
Teaching period	Not offered in 2022 (On campus)
Domestic Tuition Fees (NZD)	$685.39
International Tuition Fees	Tuition Fees for international students are elsewhere on this website.

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Limited to

BSc(Hons), PGDipSci, MSc, MAppSc

Contact

colin.fox@otago.ac.nz

Teaching staff

Director of Electronics: Associate Professor Colin Fox

Textbooks

Textbooks are not required for this paper.

Graduate Attributes Emphasised

Global perspective, Interdisciplinary perspective, Lifelong learning, Scholarship, Communication, Critical thinking, Information literacy, Self-motivation, Teamwork.
View more information about Otago's graduate attributes.

Learning Outcomes

After completing this paper students are expected to:

1. Identify the essential elements of an inverse problem and describe examples of inverse problems, including image deblurring and curve-fitting
2. Know the defining properties and identify well-posed and ill-posed problems and well-conditioned and ill-conditioned operators
3. Know the defining properties of the singular value matrix decomposition, explain the action of multiplying a matrix and vector in terms of the singular value decomposition and explain how small singular values lead to noise blow-up of the least-squares solution to a linear inverse problem
4. Solve a linear inverse problem using Tihkonov regularisation
5. Solve a linear inverse problem using truncated singular value decomposition regularisation
6. Explain the effect of varying the regularisation parameter and use the L-curve strategy to find a suitable regularisation parameter
7. Code up a regularisation method to solve a linear inverse problem in MatLab or Python
8. Model a physical experiment in which data is measured as an inverse problem, stating a suitable prior distribution and likelihood function
9. Use Bayes' rule to solve an inverse problem in terms of a posterior probability distribution
10. Define, and in simple cases compute, maximum likelihood and maximum a posteriori estimates for the solution of an inverse problem
11. Given independent samples from the posterior distribution, estimate the solution and uncertainty of the solution to an inverse problem
12. Compare classical regularisation with the Bayesian approach for solving inverse problems
13. Code up an MCMC method that solves a linear inverse problem

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