Each frame of the recorded video records 148 frames of raw data which is then retrieved by reconstructing each frame of data mathematically. With essentially the same technique images with only 2% of data can give the full image after processing. This includes images with text, blur, noise, or other interference. The video is taken with an unmodified 30 fps camera and adding a coded aperture, which blocks 50% of the image randomly, is vibrated at 5000 fps. This method has been advanced to color images and much better clarity.
This could also be used to increase the frame rate of high-speed cameras beyond current capabilities among other possibilities. When cameras are developed using compressive sensing techniques, ultraviolet, infra-red, multi-spectral, and low lighting cameras can exceed current technology with the enhanced images. Many other applications exist in other fields such as MRI, finding oil or other materials with sound, putting secret codes in images, and cameras with one pixel (useful for very expensive sensors).
The math works because the structure in images reduces their complexity in one of many domains. Only certain data such as lower frequency data is required to sufficiently reproduce the image. Randomly blocking large amounts of the image leaves most of the image intact after processing. Convex optimization is one of the algorithms involved. A great introduction once you know normed vector spaces, is the second video link.