Summary
The problem of reconstructing images from measurements at the boundary of a domain belongs to the class of inverse problems. Although in different applications the techniques used to create the images work under different physical principles and map different physical parameters, they all share similar mathematical foundations. I will present here two mathematical approaches for image reconstruction. The first one is used to solve the so called history matching problem in the oil industry, and the second one is specially designed for the application of optical molecular imaging in biomedicine.
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Moscoso, M. (2010). New Mathematical Approaches for Image Reconstruction in the Oil and Medical Industries. In: Fitt, A., Norbury, J., Ockendon, H., Wilson, E. (eds) Progress in Industrial Mathematics at ECMI 2008. Mathematics in Industry(), vol 15. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-12110-4_2
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DOI: https://doi.org/10.1007/978-3-642-12110-4_2
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