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  • Inverse problems, spring 2015

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Figure: high-resolution X-ray tomographic slice through a walnut (left), reconstruction from few data using an old method (middle), and reconstruction from few data using a modern method (right).

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Lecturers

Samuli Siltanen, Paola Elefante and Zenith Purisha

Scope

15 sp.

Type

Advanced studies

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Well-posedness and ill-posedness in the sense of Hadamard. Quick introduction to the concept of regularization. Minimum norm solution and the Moore-Penrose pseudoinverse. Book sections 3.1 and 3.4. and 4.1. (No computational stuff this time.) 

Image RemovedLecture 7 (January 27, 2015)

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Lecture 8 (January 28, 2015) 

Construction of X-ray measurement matrices using Matlab's built-in function radon.m. Naive reconstruction from data with inverse crime. Also: truncated SVD reconstructions from data with inverse crime. Book sections 2.3.4 and , 2.3.5, 4.2 and 4.4.3.

Matlab resources: Radon_demo.mXR01_buildA.mXR02_naivetest.mXR03_truncSVD.m


 

Image AddedLecture 9 (January 30, 2015) 

 

Two demonstrations of current research in X-ray tomography reconstruction methods.

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Matlab resources

You can always find the latest set of Matlab files in this Dropbox directory.

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