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Lecture 9 (January 30, 2015) 

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

Paola Elefante: Dynamic X-ray sparse tomography

Motivation for sparse tomography: hints on how cancer is formed and X-rays as environmental factors, possible improvements for medical care. Motivation for dynamic tomography: veterinary applications, material testing, monitoring the effects of cancer medications, and angiography (with video). The level set method, brief introduction. Presenting simulated data, comparison with FBP and Tikhonov. State of the art of local research and upcoming challenges. Slides available here.

Zenith Purisha: X-ray tomography using MCMC and NURBS

1. Motivation for using NURBS, the building blocks in CAD modelling. Why does CAD use NURBS: it involves a few parameters only, making computation efficient. Taking sparse data from a homogenous object to have quick measurement process. In medical environment, sparse data will reduce radiation dose. The idea is implementing Bayesian Inversion and NURBS to recover the parameters.

2. Introduction about NURBS (one slide, a video), Tomographic Measurement model (Included Basic Xray measurement, Radon transform,  Discrete  tomographic Data, and of course NURBS-based tomographic model), Bayesian Inversion and MCMC. 

3. Results of reconstruction from real data

Slides available here.


Lecture 10 (February 3, 2015) 

Construction of tomographic data without inverse crime. The trick is to simulate the sinogram at higher resolution and then interpolate from that the sinogram corresponding to lower resolution.

Matlab resources: XR04_NoCrimeData_comp.mXR04_NoCrimeData_plot.m


Lecture 11 (February 4, 2015) 

Introduction to Tikhonov regularization. Finding the minimum of the Tikhonov functional using the singular value decomposition.

Book section 5.1.

Matlab resources: deconv6_Tikhonov_comp.mdeconv6_Tikhonov_plot.m


Lecture 12 (February 6, 2015) 

Introduction to the generation of X-rays. Tomography lab visit.

Slides available here.

 

Image RemovedLecture 13 (February 10, 2015) 

Introduction to normal equations and the stacked form method for computing Tikhonov regularized solutions.

Matlab resources: deconv7_genTikhonov_comp.mdeconv7_genTikhonov_plot.m

Book section 5.2.

Image Removed NO NO LECTURE ON WEDNESDAY, February 11


Image AddedLecture 14 (February 13, 2015)

Large-scale implementation. Matrix free formulation and the conjugate gradient method. Book section 5.5

Matlab resources: XR05_Tikhonov_comp.m, XR05_Tikhonov_plot.m, XRMC_NoCrime_bigData256_50.mat

Further reading material on optimization and conjugate gradient can be found here: http://www4.ncsu.edu/~ctk/lv/lvpub.html


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Matlab resources

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

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