Last month the greatest event in Inverse Problems ever took place in Helsinki: the Applied Inverse Problems 2015 conference. In addition, I gave my first technical presentation at the 4D tomography minisymposium (find the slides here). I take the chance to write a series of posts as a walkthrough of my project and its current state.
When I started, I basically took up the good work of soon-to-be-doctor Esa Niemi. Esa studied a novel tomography algorithm based on a level set method in the case of a dynamic 2D object. Such approach had been already investigated in the paper by Kolehmainen, Lassas and Siltanen in the static 2D case. My aim is to expand the algorithm to the dynamic 3D cases and to include non-trivial acquisition geometries.
Why dynamic tomography?
The motivation behind this project is strong and our team is definitely not the only one working on these issues. In our case, we are mostly - but not limited to - interested in biomedical applications. One powerful example of potential applications is angiography. In the featured image of this post, you can see a 2D radiography of a hand where a contrast agent has been injected. Angiography represents a fundamental non-invasive diagnostic and treatment tool in medicine.
In the video above you can observe a contrast agent injected into some heart's blood vessels, while dynamic CT allows to monitor what happens. Coronary angiography can be useful to detect obstructions or ruptures. During the treatment procedure known as angioplasty, it is fundamental for the physician to monitor the evolution of the operation. To date, coronary angiography is available only in the dynamic 2D case, meaning that it is possible to observe only a section of the heart. It would be extremely useful for a doctor to have a sense of the missing spatial dimension.
Another interesting biomedical application of dynamic CT is radiation therapy. During radiation therapy, cancerous cells are hit by ionizing radiation. If a tumour is placed along moving organs (i.e. lungs, etc.), the radiation flow would miss it for a portion of time and irradiate healthy tissue. As I mentioned in a previous post, radiation can contribute to cancer, so you want to tune the radiation dose down.
Dynamic tomography could allow to synchronise a radiation therapy machinery with the real movement of the tumour, thus reducing useless and potentially damaging radiation.
Then we come to the other attribute: sparse. Sparse measurement is synonym of undersampling, meaning that one tries to get the best he can with few data. Few measured data means lower X-ray dose in tomography. To date, industrial machineries mostly reconstruct measured data through the Filtered Back Projection algorithm (FBP). FBP usually guarantees good image quality but asks for a lot of sampled data (*). Iterative methods - that is what we use and research - reconstruct images with less quality (anyway good enough) but with definitely fewer data (even one tenth!). This idea motivates our testing of a novel algorithm, in the hope of massively reduce a patient irradiation.
If the radiation is minimised, CT can be safely prescribed as a prevention examination to monitor some cases. Also, this would mean less sensors and detectors (= less money) and less time (if we succeed to beat FBP computationally speaking).
Here is my/our motivation so far. Next I'll explain what level set method and how we apply it in the dynamic tomography case. To next time!
(*) I here promise I'll take the time to develop in a post what FBP is and show some comparisons with other reconstruction methods, with fewer projections.
Featured image comes from Wikipedia.