Merci Monsieur Fourier … for time-resolved image demixing

April 4, 2016 | 14:30
Can we undo reflections in images?
Can we undo reflections in images?
At the recent IEEE International Conference on Acoustics, Speech, and Signal Processing, members of the MIT Media Lab's Camera Culture Group presented a fundamentally different approach to image separation. Their system fires light into a scene and gauges the differences between the arrival times of light reflected by nearby objects — such as panes of glass — and more distant objects.
If two light signals — one reflected from a nearby object such as a window and one from a more distant object — arrive at a light sensor at slightly different times, their Fourier decompositions will have different phases. So measuring phase provides a de facto method for measuring the signals' time of arrival. The algorithms adapt a technique from X-ray crystallography known as phase retrieval, which earned its inventors the Nobel Prize in chemistry in 1985.
MIT’s proposed  image separation system fires light into a scene and gauges the differences between the arrival times of light reflected by nearby objects — such as panes of glass — and more distant objects. Credit: MIT

For their report, some of the research, and the final experiment, 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, but all that’s needed is a bit of Monsieur Fourier’s maths. This is a very elegant and inspiring line of work.
 
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