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).
Samuli Siltanen, Paola Elefante and Zenith Purisha
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.)
Lecture 7 (January 27, 2015)
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.
Lecture 9 (January 30, 2015)
Two demonstrations of current research in X-ray tomography reconstruction methods.