Monday, April 09, 2012

Deconvoluting a Radiation Field using a Webcam and Robust PCA

Just as we used the videos provided by TEPCO on their website to figure out if a robust PCA could decompose the image field into a full image (the low rank component) and a sparse component that would pick up the radiation hits only, we were faced with another issue: water droplets. Those droplets would alternatively be part of the sparse component or the noisy component of the Robust PCA decomposition and therefore make it difficult for us to simply evaluate the radiation field based on this decomposition. Additional complex filtering would need to be performed. Yes, I know what you are about to say:

 "You poor little things, the endoscopic camera looking into one of the reactors at Fukushima did not allow for a simple demonstration of what Robust PCA can do" 

and you would be right. But our take is more along the lines of: the following: Next time some endoscopic camera is used into reactor 1, 2 or 3 at Fukushima, it ought to do certain things like wait a few seconds every once in a while and in a view free of flying droplets to get a easy sense of the radiation level at those locations.

But in order to provide a more compelling example and as part of Cable And Igor's adventures in the evaluation of Matrix Factorization for Images and Videos (CAI),  Cable and I went through some YouTube videos who could help us make that point clearer. And here we are presenting to you a video featuring the illumination of a webcam with a 230 MeV proton beam (it looks like this beam was used to calibrate an experiment that eventually flew on the Lunar Reconnaissance Orbiter -LRO-)

There is no movement in the video just a static scene with the random hit from the radiation with the webcam CMOS. Here is the Robust PCA decomposition:

We could not visually see much so we focused on using Matlab's imagesc instead of imshow for the sparse and noisy components and here what we have::

focusing only on the sparse component, I believe we nailed it:


As we have done in the previous examples, the Robust PCA was implemented using GoDec one of the recent Advanced Matrix Factorization solver.

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