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Democracy in Action: Quantization, Saturation, and Compressive Sensing
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BibTeX
@MISC{Laska_democracyin,
author = {Jason N. Laska and Petros T. Boufounos and Mark A. Davenport and Richard G. Baraniuk},
title = { Democracy in Action: Quantization, Saturation, and Compressive Sensing},
year = {}
}
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Abstract
Recent theoretical developments in the area of compressive sensing (CS) have the potential to significantly extend the capabilities of digital data acquisition systems such as analogto-digital converters and digital imagers in certain applications. A key hallmark of CS is that it enables sub-Nyquist sampling for signals, images, and other data. In this paper, we explore and exploit another heretofore relatively unexplored hallmark, the fact that certain CS measurement systems are democractic, which means that each measurement carries roughly the same amount of information about the signal being acquired. Using the democracy property, we re-think how to quantize the compressive measurements in practical CS systems. If we were to apply the conventional wisdom gained from conventional Shannon-Nyquist uniform sampling, then we would scale down the analog signal amplitude (and therefore increase the quantization error) to avoid the gross saturation errors that occur when the signal amplitude exceeds the quantizer’s dynamic range. In stark contrast, we demonstrate that a CS system achieves the best performance when it operates at a significantly nonzero saturation rate. We develop two methods to recover signals from saturated CS measurements. The first directly exploits the democracy property by simply discarding the saturated measurements. The second integrates saturated measurements as constraints into standard linear programming and greedy recovery techniques. Finally, we develop a simple automatic gain control system that uses the saturation rate to optimize the input gain.
Keyphrases
compressive sensing democracy property saturation rate saturated measurement key hallmark simple automatic gain control system unexplored hallmark practical c system c measurement certain c measurement system digital imagers conventional shannon-nyquist uniform sampling stark contrast analog signal amplitude quantizer dynamic range digital data acquisition system c system recent theoretical development signal amplitude input gain compressive measurement quantization error conventional wisdom standard linear programming greedy recovery technique nonzero saturation rate second integrates certain application gross saturation error analogto-digital converter
