The basic idea behind the new camera is to drastically reduce the amount of information needed to represent an image. This takes place by compressing information in the image as it is digitized, rather than compressing image data after digitization. It involves a single-photon detector whose output is digitized and then transmitted to a digital signal processor. The DSP uses sophisticated algorithms to reassemble the data into a version of the original image.
Researchers at Rice University recently constructed a bench-top setup that demonstrates these principles. Their demo uses a single- photon detector, some lenses, and a digital micromirror chip. The DM chip is a key component. Often used in video projection systems, it has several hundred thousand microscopic mirrors arranged in a rectangular array on its surface. The mirrors can be individually rotated about 10° to an on or off state. A mirror in the on state reflects light in one direction, and elsewhere when off.
In the Rice demo, light from the object of interest is reflected through a lens onto the DM chip. Meanwhile, the DM chip is fed a long series of random numbers which control the orientation of the mirrors on its surface. The result is a series of random orientations for the surface mirrors. Another set of lenses picks up the light reflected from the DM chip and focuses it onto a single-photon photodetector. The analog output of this detector is proportional to the light level.
An a/d converter digitizes each level from the photodetector corresponding to a new random pattern of the DM chip mirrors. The resulting stream of digital numbers gets beamed to a receiver and then to a digital signal processor. The DSP uses knowledge about the random patterns imparted on the DM chip, plus advanced algorithms such as 3D wavelet transformations, to assemble the stream of digital numbers into an image of the original object.
All in all, the single-pixel camera converts a scene that would be captured as one image in a conventional camera into a series of intensity values registered on the single-photon detector. The recording process takes place without any of the components in the setup physically moving (other than the microscopic mirrors on the DM chip). The DSP knows enough about the recording process to reassemble the series into an image of the original scene.
Rice’s single-pixel camera uses principles from an emerging branch of study called compressive sensing. The advantage of the technique is that it needs far less data to digitize an image or a video stream than predicted by the Nyquist-Shannon sampling theorem. Nyquist-Shannon dictates that a signal be sampled at a rate of at least twice that of its lowest-frequency content. Otherwise, the sampled version loses information present in the original signal. This idea works fine for situations where there is enough bandwidth to transmit the sampled signal. But it can cause problems for video signals because of the amount of data needed to represent each video frame. So video signals often get compressed before they are transmitted back to processing electronics, where they are in turn decompressed.
Compressive sensing techniques avoid the compress/decompress overhead because the signal is compressed as it is digitized and decompressed when reassembled. The key factor that lets compressive sensing work on images and video is that these kinds of signals are generally what is called sparse data. In scenes being videoed, for example, not much changes from one instant to the next. Mathematically, this lets a small amount of data relative to the overall number of pixels represent successive images.
Rice researchers say compressive sensing tehcniques are in the their infancy, but they hold promise in a number of areas. For example, single-pixel cameras can be super small, so they could conceivably be deployed in large arrays to image expansive areas. Surveillance applications, where scenes typically change little, are another area where single-pixel cameras could provide significant cost savings.
University of Minnesota, Institute for Mathematics and its Applications, www.ima.umn.edu
Rice University, compressive sensing resources, www.dsp.ece.rice.edu/cs
Massachusetts Institute of Technology, random lens imaging, dspace.mit.edu/handle/1721.1/33962
Duke University, thin camera work, www.disp.duke.edu/