CIF: Small: Non-Linear Processing and Coding for Compressive Sensing with Applications in Imaging

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"This award is funded under the American Recovery and Reinvestment Act of 2009(Public Law 111-5)."Recently, the new field of compressive sensing has emerged with the promise to revolutionize digital processing broadly. The key idea is the use of nonadaptive linear projections to acquire an efficient, dimensionally reduced representation of a signal or image directly using just a few measurements. Surprisingly, Nyquist-rate sampling, which has dominated how signals are acquired and processed in science and technology since the origin of digital processing, can be leaped over through compressive sensing theory. Such results may have a profound impact broadly, including applications in spectroscopy, imaging, communications, as well as consumer electronics.In this research, the compressive sensing framework is ``extended" to make it an integral part of a discrete-time all-analog-processing communications system that completely skips the digital domain and shows an excellent robustness against noise. The key idea is the use of non-linear mappings that act as analog channel encoders, processing the samples or compressive sensing measurements proceeding from an analog source and producing continuous amplitude samples that are transmitted directly through the noisy channel. Thus, all the processing in the communications system is made in the analog domain. In addition to its theoretical interest, the potential of this approach in practical systems is substantial. For instance, the proposed framework is readily applicable in practical systems such as imaging, where it presents a performance that is very close to the theoretical limits and clearly outperforms systems based on standard compressive sensing. Furthermore, the idea of completely avoiding the digital domain can be applied not just in point-to-point communications systems, but also in more complex communications problems such as distributed coding in sensor networks.