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The algorithms adapt a technique from X-ray crystallography known as phase retrieval, which earned its inventors the Nobel Prize in chemistry in 1985. “We can also exploit the fact that there should be some continuity in the intensity values in 2-D,” says Bourquard. “If your planes, for instance, are a glass window and a scene behind it, both these planes should exhibit some spatial continuity. Typically, the intensity values will not vary too fast on every separate plane. So essentially, what this phase retrieval does is use some techniques of frequency estimation, coupled with the assumption that local intensity variations within every single plane are moderate relative to the average intensity difference between these planes.”
In theory, the number of light frequencies the camera needs to emit is a function of the number of reflectors. If there is just one pane of glass between the camera and the scene of interest, the technique should require only two frequencies. If there are two panes of glass, the technique should require four frequencies.
But in practice, the light frequencies emitted by the camera are not pure, so additional measurements are required to filter out noise. In their experiments, the researchers swept through 45 frequencies to enable almost perfectly faithful image separation. That takes a full minute of exposure time, but it should be possible to make do with fewer measurements. “The interesting thing is that we have a camera that can sample in time, which was previously not used as machinery to separate imaging phenomena,” Bhandari says.
“What is remarkable about this work is the mixture of advanced mathematical concepts, such as sampling theory and phase retrieval, with real engineering achievements,” says Laurent Daudet, a professor of physics at Paris Diderot University. “I particularly enjoyed the final experiment, where the authors used a modified consumer product — the Microsoft Kinect One camera — to produce the untangled images. For this challenging problem, everyone would think that you’d need expensive, research-grade, bulky lab equipment. This is a very elegant and inspiring line of work.”
