Compressive Sensing: Squeezing the Most Out of Signals

March 2011
Topics: Signal Processing
Transmitting, processing, and storing signal data requires a lot of bandwidth.
soldiers wearing camouflage uniforms

The military is always searching for signals: a radar signal that might warn of enemy movements, a radio signal that might betray enemy secrets, an acoustic signal that may reveal enemy locations.

Once intercepted, signals must be processed to determine what information they contain. That data is then often broadcast to intelligence centers for further analysis. Receiving and broadcasting large amounts of signal data can tax communication systems, so researchers are investigating methods for compressive sensing to squeeze the needed amount of information from or into smaller amounts of signals.

A New Revolution

Every so often, a new signal processing technique promises to revolutionize our processing capabilities. Unfortunately, many of these techniques fail to live up to the hype. But occasionally, researchers are lucky enough to discover a technique with lasting impact. (One recent example is wavelets, the basis for the JPEG 2000 image compression standard, an improvement on the well-known JPEG standard.)

Compressive sensing has a real potential to be one of the techniques that has lasting impact in the processing field. It is a technique that alters the way in which we capture, process, and store information. Although the theoretical foundations for compressive sensing have been around for some time, it has been only recently that researchers have been able to exploit some of these ideas for practical applications.

Not Your Standard Signal Processing

Digital signal processors do not need to listen to an entire signal to identify it. They can sample the signal at regular intervals to gain the necessary information about it. Of course, the more a signal changes along its wavelength, the more samples a processor must take of the signal to accurately measure it. This sampling requirement is known as the Nyquist criterion. If the Nyquist criterion is not adhered to, accurate and unambiguous signal recognition is simply not possible.

Compressive sensing does not negate the Nyquist criterion. It does, however, create the opportunity to sample a signal at only a fraction of the intervals mandated by Nyquist when the right ingredients are available. Compressive sensing is effective because it measures information rather than simply sampling signals.

Compressive Sensing in a Nutshell

Compressive sensing has three components: sparsity, measurement, and reconstruction. Sparsity indicates that the signal of interest can be represented by relatively few basic elements. Measurement requires that the signal contain a significant amount of information for each of its basic elements. Reconstruction is the process of using optimization algorithms to refit the noisy information from the measurement into a clear signal. All three of these ingredients must work together for effective compressive sensing.

There are several challenges to bringing compressive sensing out of the lab and into the field. For reconstruction, where the bulk of the compressive sensing work is done, the research challenge lies in separating the target signal from the clutter of additional signals in the measured data. For sparsity and measurement, we need a greater understanding of how to match the right sensors to the right signals. One approach is to more effectively characterize the sparsity data to enable a better match for the sensors used in the measurement.

But an alternative for which there is more promise is choosing the proper sensors for the application. For example, researchers at Rice University have developed a single-pixel camera that can effectively capture an image by using a well-orchestrated series of lenses. Additionally, MITRE is exploring several opportunities for imaging applications as well as modified chip architectures for improving the back-end processing for signal recovery in compressive sensing applications.

From Theory to Practice

Although expectations based on theoretical calculations are impressive, the implementation of compressive sensing is not without its hurdles. In many cases, we are just beginning to understand how to effectively apply this technique to various application domains. And there is still much research to be conducted into the ABCs of compressive sensing itself without regard to any application. For example, researchers are investigating the benefits of incorporating a compressive sensing construct for machinelearning algorithms.

Ultimately, compressive sensing's ability to improve on sensing, transmitting, and storing large amounts of information lends it to applications in data compression, communications, and beam forming. Imaging applications—such as image compression, medical imaging, synthetic aperture radar, and hyperspectral imaging—can benefit from compressive sensing's abilities to take advantage of information sparsity. All evidence suggests that a compressive sensing approach will be able to improve performance for signal detection algorithms and uphold its potential for having a lasting impact on information processing.

—by David Colella

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