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Single-Pixel Imaging via Compressive Sampling
Marco F. Duarte, Mark A. Davenport, Dharmpal Takhar, Jason N. Laska
Ting Sun, Kevin F. Kelly, Richard G. Baraniuk
Rice University
Humans are visual animals, and imaging sensors that extend our reach – cameras – have
improved dramatically in recent times thanks to the introduction of CCD and CMOS digital
technology. Consumer digital cameras in the mega-pixel range are now ubiquitous thanks to the
happy coincidence that the semiconductor material of choice for large-scale electronics integration
(silicon) also happens to readily convert photons at visual wavelengths into electrons. On the
contrary, imaging at wavelengths where silicon is blind is considerably more complicated, bulky,
and expensive. Thus, for comparable resolution, a $500 digital camera for the visible becomes a
$50,000 camera for the infrared.
In this paper, we present a new approach to building simpler, smaller, and cheaper digital
cameras that can operate efficiently across a much broader spectral range than conventional
silicon-based cameras. Our approach fuses a new camera architecture based on a digital mi-
cromirror device (DMD – see Sidebar: Spatial Light Modulators) with the new mathematical theory
and algorithms of compressive sampling (CS – see Sidebar: Compressive Sampling in a Nutshell).
CS combines sampling and compression into a single nonadaptive linear measurement process
[1–4]. Rather than measuring pixel samples of the scene under view, we measure inner products
between the scene and a set of test functions. Interestingly, random test functions play a key role,
making each measurement a random sum of pixel values taken across the entire image. When
the scene under view is compressible by an algorithm like JPEG or JPEG2000, the CS theory
enables us to stably reconstruct an image of the scene from fewer measurements than the number
of reconstructed pixels. In this manner we achieve sub-Nyquist image acquisition.
Our “single-pixel” CS camera architecture is basically an optical computer (comprising
a DMD, two lenses, a single photon detector, and an analog-to-digital (A/D) converter) that
computes random linear measurements of the scene under view. The image is then recovered or
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