Abstract
In this chapter, we introduce the general idea of inverse problems particularly with applications to imaging. We use two well-known imaging modalities namely electrical impedance and diffuse optical tomography to introduce and describe inverse problems involving PDEs. We also discuss the mathematical difficulties and challenges for image reconstruction in practice. We describe both deterministic and statistical regularization techniques including Gauss–Newton method, Bayesian inversion, and sparsity approaches to provide a broad exposure to the field.
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Acknowledgements
The author would like to thanks the organizers of ISIAM particularly Professor Pammy Manchanda and Professor Abul Hasan Siddiqi for editing the book chapters and with the opportunity to attend the conference at Amritsar that brought together both pure and applied mathematicians to help provide the platform to discuss various ideas for applied math research.
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Khan, T. (2020). Inverse Problems Involving PDEs with Applications to Imaging. In: Manchanda, P., Lozi, R., Siddiqi, A. (eds) Mathematical Modelling, Optimization, Analytic and Numerical Solutions. Industrial and Applied Mathematics. Springer, Singapore. https://doi.org/10.1007/978-981-15-0928-5_9
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DOI: https://doi.org/10.1007/978-981-15-0928-5_9
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