My series of video lectures about X-ray tomography took the important step to explaining how to treat real measured data. I put two simple pieces of material into an X-ray device and show what happens when we try to calculate Radon transform-like line integrals from the pixel values. You can watch the video in YouTube
I had the pleasure to deliver a public talk at the National Museum of Mathematics on September 12, 2024. My topic was the mathematics of photography, which could be discussed from many points of view. Here I focused on changing the appearance of photos by altering their pixel values. Namely, in modern computers and smartphones
I gave a talk at the applied math colloquium of Columbia University. My colleagues Liliana Borcea and Kui Ren work there as professors. There were some 30 people in the audience, with lots of young researchers. My topic was my team’s new research on the surprising connections between electrical impedance tomography and classical X-ray tomography.
I had the honor to deliver a keynote address in the Science on Stage Festival in Turku, Finland, on August 15,2024. The title of the talk was The magic of math: three-dimensional X-ray vision. You can see the recording in YouTube. The lecture slides are available here in PDF format. Abstract: In the 1970’s, a
My new tomography video is out! Link to video in YouTube Mathematicians usually think that the starting point of tomography is a set of line integrals of an unknown function. Every pixel value in the Radon transform, or sinogram, is a value of a line integral along one X-ray. But in practice we measure intensities
I had a wonderful short trip to Edinburgh to give two talks in the Big Data Inverse Problems conference at the International Centre for Mathematical Sciences. The event took place in the amazing Bayes Centre. Here’s a peek: My first talk was a traditional scientific presentation with the topic Virtual X-rays: parallel-beam tomography hidden within
The newest addition to my video lectures on tomography is an explanation how we can simulate X-ray data formation with or without matrices.
I delivered my X-ray tomography show at the Finnish Mathematical Society colloquium on April 17, 2024. The presentation was followed by Zoom all over Finland, and the lecture hall at University of Helsinki was pretty full, too. This was fun!
I delivered a section plenary talk in the 94th GAMM Annual Meeting in Magdeburg on March 19, 2024. The title of my talk was Virtual X-rays: parallel-beam tomography hidden within electric probing, and it belonged to the Section S21 Mathematical signal and image processing, organized by Anne Wald and Johannes Maly. You can download my
This video illustrates “ill-posedness”, the nemesis of all inverse problems. We see how in a very simple 12×12 pixel tomography problem “almost-ghosts” can produce very different targets with almost the same X-ray data.
