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

    About this paper

    Paper title Inverse Problems and Imaging
    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.
    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
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    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


    Not offered in 2022

    Teaching method
    This paper is taught On Campus
    Learning management system
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