CS: Democracy in Action, Compressed Sensing for MIMO radar, TV Theorem for Compressed Sensing Based Interior Tomography

Today we have three papers:

Compressed Sensing for MIMO radar - Algorithms and Performance by Thomas Strohmer and Benjamin Friedlander. The abstract reads:

Compressed sensing techniques make it possible to exploit the sparseness of radar scenes to potentially improve system performance. In this paper compressed sensing tools are applied to MIMO radar to reconstruct the scene in the azimuth-range-Doppler domain. Conditions are derived for the radar waveforms and the transmit and receive arrays so that the radar sensing matrix has small coherence and sparse recovery becomes possible. Theoretical performance bounds are presented and validated by numerical simulations.

A General Total Variation Minimization Theorem for Compressed Sensing Based Interior Tomography by Weimin Han, Hengyong Yu, and Ge Wang. The abstract reads:

Recently, in the compressed sensing framework we found that a two-dimensional interior region-of-interest (ROI) can be exactly reconstructed via the total variation minimization if the ROI is piecewise constant (Yu and Wang, 2009). Here we present a general theorem charactering a minimization property for a piecewise constant function defined on a domain in any dimension. Our major mathematical tool to prove this result is functional analysis without involving the Dirac delta function, which was heuristically used by Yu and Wang (2009).

and finally from the Rice Compressive Sensing repository we have:

Democracy in Action: Quantization, Saturation, and Compressive Sensing by Jason Laska, Petros Boufounos, Mark Davenport, and Richard Baraniuk. The abstract reads:

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 analog to 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 democratic, 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.

Image Credit: NASA/JPL/Space Science Institut, Saturn's photo was taken on November 15, 2009 and received on Earth November 16, 2009.