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This module describes the application of compressive sensing to the design of a novel imaging architecture called the "single-pixel camera".


Several hardware architectures have been proposed that apply the theory of compressive sensing (CS) in an imaging setting  [link] , [link] , [link] . We will focus on the so-called single-pixel camera   [link] , [link] , [link] , [link] , [link] . The single-pixel camera is an optical computer that sequentially measures the inner products y [ j ] = x , φ j between an N -pixel sampled version of the incident light-field from the scene under view (denoted by x ) and a set of N -pixel test functions { φ j } j = 1 M . The architecture is illustrated in [link] , and an aerial view of the camera in the lab is shown in [link] . As shown in these figures, the light-field is focused by a lens (Lens 1 in [link] ) not onto a CCD or CMOS sampling array but rather onto a spatial light modulator (SLM). An SLM modulates the intensity of a light beam according to a control signal. A simple example of a transmissive SLM that either passes or blocks parts of the beam is an overhead transparency. Another example is a liquid crystal display (LCD) projector.

Single-pixel camera block diagram. Incident light-field (corresponding to the desired image x ) is reflected off a digital micromirror device (DMD) array whose mirror orientations are modulated according to the pseudorandom pattern φ j supplied by a random number generator. Each different mirror pattern produces a voltage at the single photodiode that corresponds to one measurement y [ j ] .

The Texas Instruments (TI) digital micromirror device (DMD) is a reflective SLM that selectively redirects parts of the light beam. The DMD consists of an array of bacterium-sized, electrostatically actuated micro-mirrors, where each mirror in the array is suspended above an individual static random access memory (SRAM) cell. Each mirror rotates about a hinge and can be positioned in one of two states ( ± 10 degrees from horizontal) according to which bit is loaded into the SRAM cell; thus light falling on the DMD can be reflected in two directions depending on the orientation of the mirrors.

Each element of the SLM corresponds to a particular element of φ j (and its corresponding pixel in x ). For a given φ j , we can orient the corresponding element of the SLM either towards (corresponding to a 1 at that element of φ j ) or away from (corresponding to a 0 at that element of φ j ) a second lens (Lens 2 in [link] ). This second lens collects the reflected light and focuses it onto a single photon detector (the single pixel) that integrates the product of x and φ j to compute the measurement y [ j ] = x , φ j as its output voltage. This voltage is then digitized by an A/D converter. Values of φ j between 0 and 1 can be obtained by dithering the mirrors back and forth during the photodiode integration time. By reshaping x into a column vector and the φ j into row vectors, we can thus model this system as computing the product y = Φ x , where each row of Φ corresponds to a φ j . To compute randomized measurements, we set the mirror orientations φ j randomly using a pseudorandom number generator, measure y [ j ] , and then repeat the process M times to obtain the measurement vector y .

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Source:  OpenStax, Introduction to compressive sensing. OpenStax CNX. Mar 12, 2015 Download for free at http://legacy.cnx.org/content/col11355/1.4
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