CAI: Robust PCA better than Lucky Imaging ?

Continuing on the Cable and Igor's (CAI) adventures series, you recall our investigation of a video of the Moon and its decomposition using Robust PCA ( see CAI: Ever glance at the skies with the devil in a pale moon light ?). The initial finding of interest was the ability to extract the turbulent flow of the atmosphere from the field of view. Cable and I continued looking at the results of this decomposition and we wondered how some of these components would fare compared to the traditional lucky imaging technique. Lucky imaging generally entails adding several frames together, and through averaging, one expects a cleaner picture as a result. 

In the following figure, the top two images represent a lucky imaging shot (average of all the frames) and the first frame of the video respectively. The bottom two images represent an average of all the low rank images and the first component of the low rank decomposition. Clearly the low rank component is as clean as the first image of the sequence. At that point, it seem obvious that one would need to have the same field of view during the 4 seconds of the movie, which is not the case as the Moon slightly moves to the side.    

If you want to have fun with this four seconds movie in a .mat file format and its decomposition (also in .mat files), you may want to download the dataset directly from here (it will be available until April 23)

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