Projects
Compressive Imaging (single-pixel-camera)
In this project, we designed an image/video camera that directly acquires random projections of a scene without first collecting the pixels/voxels.
The camera architecture employs a digital micromirror array to optically calculate linear projections of the scene onto
pseudorandom binary patterns.
Its key hallmark is its ability to obtain an image or video with a single
detection element (the "single pixel") while measuring the scene fewer times than the number of pixels/voxels.
Since the camera relies on a single photon detector, it can also be adapted to image at wavelengths where conventional
CCD and CMOS imagers are blind.
Analog-to-Information Converters
Conventional analog-to-digital converters (ADCs) sample at the Nyquist rate, i.e., twice the bandwidth of the signal. As applications demand increased bandwidth, faster and more complicated ADCs are required, placing a burdern on hardware design. In this project, we employ the compressive sensing framework, to design devices that can acquire large swaths of bandwidth with low-rate ADCs.
One such design is known as the Random Demodulator. This device modulates an analog signal by a Nyquist-rate pseudo-random +/-1 sequence, integrates this, and samples the output at a sub-Nyquist rate.
The primary hallmark of this design is that a sub-Nyquist rate ADC can capture information from a large bandwidth without aliasing. This design assumes that it is easier to build the additional hardware imposed before the ADC than a high rate ADC.
Compressive sensing, democracy, and justice
Compressive sensing (CS) systems have the peculiar property that each measurement contains a similar amount of information. Such measurements are called democratic. In this project, we demonstrate that due to democracy, signal recovery is possible from any subset of randomized measurements.
We exploit democracy to increase the dynamic range of quantized CS measurements during acquisition. In addition, we introduce alternative methods for handling saturated measurements and determine that in many cases, improved performance occurs when the saturation rate is nonzero.
We also demonstrate that if CS measurements are sparsely corrupted, i.e., only a few measurements contain errors, then the signal and noise can be recovered exactly. We dub this algorithm Justice Pursuit, since it roots out and exposes corruption.