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Single-Pixel Imaging
Modern cameras based on CCD and CMOS digital technology have a high image resolution but also a high price and a limited spectral range. Cameras based on silicon need added complexity in order to expand their spectral range, making their price very high when modified for wavelengths outside their range (i.e. infrared). The single-pixel imaging technique is a method that aims to build simpler, smaller, and cheaper digital cameras that can operate efficiently across a wider spectral range than the usual silicon-based cameras. The technique couples a new camera architecture based on the DMD (Digital Micrometer Device).

The Single-Pixel Camera Architecture
The single-pixel camera architecture’s setup is comprised of a light source that illuminates the object/image. The image is then focused with a lens onto a DMD array, which has is array orientations controlled by test functions, 𝜙𝑚. The reflections of the DMD array are then focused with another lens onto a single sensor, which then gets digitized through use of an A/D converter. The single-pixel camera measures multiple inner products, 𝑦 =< 𝑥,𝜙𝑚 >, where x represents a mirror in the DMD array, and 𝜙𝑚 is a test function that determines the orientation of each mirror in the array. The mirror orientations can be set to point at the sensor (1) or away from the sensor (0). Intermediate values can also be set by wavering a mirror back and forth during the sampling time of a capture.

Single-Pixel Multiplexing Methodologies
There are multiple types of single-pixel multiplexing methodologies. Some of the most prominent ones are the Raster Scan, the Basis Scan and Scanning via Compressive Sampling.

Raster Scan:
This is a single-pixel architecture that takes N measurements, one for each pixel of the image. Its test functions are basically deltas, in which only one mirror of the DMD is reflecting to the sensor at a time. In this methodology each pixel is getting 1/N of the full sampling time, T.

Basis Scan:
This is a single-pixel architecture that also takes N measurements of the image. Its test functions are not delta’s though, and instead a combination of the N pixels in the image that form a basis. In the paper a Walsh basis is used for the test functions. Unlike the previous two camera methodologies, the basis scan is resistant to dark currents, because during each sampling vector about N/2 pixels of the image are being focused on the sensor.

Scanning via Compressive Sampling:
This is is the single-pixel architecture that is newer than the above. Only M measurements are taken, M<<N. The test functions used for this are composed of randomly drawn columns of the Walsh basis, and then randomly permutated. Like the basis scan, compressive sampling is also resistant to dark currents.

Single-Pixel Imaging via Compressive Sampling
Compressive sampling is the idea that a signal or image that is compressible can be sampled at a low rate and still have enough information to be reconstructed and processed. Unlike traditional sampling, compressive sampling allows the use of very few samples compared to the number of samples required by the Nyquist rate. In digital cameras a high-resolution picture is compressed by creating a basis for the image in which the coefficient vector is sparse.

The sample then compress method acquires N samples then discards all but K of them. The compressive sampling method starts of by acquiring a smaller number of samples M<N. The original image can be accurately reconstructed by carefully choosing the test functions,, so that a sparse/compressible x can be recovered (, x is the original image). Some possible  can be created from randomly chosen values and randomly permutated vectors from standard orthonormal bases such as the Fourier, Walsh, and Noiselet bases.

Applications of the Single-Pixel Camera Architecture Using Compressive Sampling
Compressive sampling has usually been focused on image and signal reconstruction. Applications in signal processing and computer vision don’t always require this though. For many applications data is only needed in order to make detection, classification, and recognition decisions. These tasks don’t require a full reconstruction, only a sufficient amount of statistics. It is possible to measure these statistics with the random measurements of the compressive sampling technique without reconstructing the entire image or signal.