CAI: Cable And Igor's Adventures in Matrix Factorization: A Tornado Through a Parking Lot

I was reminded of this when I watched Yi Ma's presentation at MIA2014 but it somehow felt that this is still not widely known. Trusting the underlying structure of the signal can go a long way for separating events. This is why with Cable, we played with Tianyi Zhou and Dacheng Tao's GoDec solver to produce imagery decomposition in several youtube videos and featured in CAI: Cable And Igor's Adventures in Matrix Factorization. The very important fact to retain from these experiments is that they require no knowledge of image processing. Here is an example I dug up from our archives, a tornado hitting a parking lot. Here is the initial video:

and its attendant Robust PCA decomposition.The video is decomposed in three components, a low rank one (ideally a background image in the case of rank 1) on top left portion of the screen, a sparse and noisy component (both in the bottom row).

Solvers that do similar decomposition can be found in the Advanced Matrix Factorization Page

Other videos can be found in:

• How many lightbulbs does it take to locate somebody ?
• A glimpse of Lana and Robust PCA
• The Not So Invisible Mercedes
• Robust PCA and UFOs
• Lucky Imaging and Robust PCA
• Webcam as a radiation sensor (Part3) , Part 2, Part 1.
• Spotting the Falling debris during a Shuttle Launch
• Tank Implosion through Robust PCA

Also of interest the LinkedIn Advanced Matrix Factorization Page

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