Classical and modern solution methods for inverse problems including image deblurring and analysis of experimental data.
About this paper
|Inverse Problems and Imaging
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- Limited to
- BSc(Hons), PGDipSci, MSc, MAppSc
- Teaching staff
- Director of Electronics: Associate Professor Colin Fox
- 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.
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- Learning Outcomes
- After completing this paper students are expected to:
- Identify the essential elements of an inverse problem and describe examples of inverse problems, including image deblurring and curve-fitting
- Know the defining properties and identify well-posed and ill-posed problems and well-conditioned and ill-conditioned operators
- 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
- Solve a linear inverse problem using Tihkonov regularisation
- Solve a linear inverse problem using truncated singular value decomposition regularisation
- Explain the effect of varying the regularisation parameter and use the L-curve strategy to find a suitable regularisation parameter
- Code up a regularisation method to solve a linear inverse problem in MatLab or Python
- Model a physical experiment in which data is measured as an inverse problem, stating a suitable prior distribution and likelihood function
- Use Bayes' rule to solve an inverse problem in terms of a posterior probability distribution
- Define, and in simple cases compute, maximum likelihood and maximum a posteriori estimates for the solution of an inverse problem
- Given independent samples from the posterior distribution, estimate the solution and uncertainty of the solution to an inverse problem
- Compare classical regularisation with the Bayesian approach for solving inverse problems
- Code up an MCMC method that solves a linear inverse problem