Friday, April 27, 2012

CAI: A Glimpse of Lana and Robust PCA

It's Friday, It's Cable And Igor's adventures in Matrix Factorization, Today, Cable And I are going to play with two scenes. A static scene featuring a wall made of drawings and a video of Lana Del Rey on top of that background, watch it first we'll wait and join us below.

The idea here is to project this video on a wall that is very well lit with a nonuniform background as follows:

and see if by performing a Robust PCA decomposition using Godec, one can deconvolute the background from the much fainter video:


Mission semi-accomplished! Our decomposition for the noise (right bottom) and sparse (left bottom) terms are in the canonical basis and therefore much of the video lands in the noise section. One would be expecting it to land in the sparse section. We could probably have gotten that result, but call us snobs, we're a bit partial to Lana as opposed to a canonical basis. One wonders if by using a dictionary, the sparse section could not grab entirely Lana's video clip. We'll need to investigate this further. The Low Rank decomposition (right top video) removed the video entirely... so that is good.

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