Multimode waveguide speckle patterns for compressive sensing

Compressive sensing has usually been used to downconvert high frequency RF signals into low frequency ones such that the resulting signals can be sampled at a rate that fits with current technology. This is the premise of most A2I converters that includes Xampling for instance -all A2I instances listed under the A2I tag-. Today, however, instead of downconverting high frequency RF signals, the authors upconvert the RF signals into much higher frequency so that the newly convolved signal can be sampled in the visible spectrum. They then use a random mixer to insure that the signal is redundantly covered in order to ensure its decoding. Wow !

I note some nice experimental phase transitions.

Multimode waveguide speckle patterns for compressive sensing by George C. Valley, George A. Sefler, T. Justin Shaw

Compressive sensing (CS) of sparse GHz-band RF signals using microwave photonics may achieve better performance with smaller size, weight and power than electronic CS or conventional Nyquist rate sampling. The critical element in a CS system is the device that produces the CS measurement matrix (MM). We show that passive speckle patterns in multimode waveguides potentially provide excellent MMs for CS. We measure and calculate the MM for a multimode fiber and perform simulations using this MM in a CS system. We show that the speckle MM exhibits the sharp phase transition and coherence properties needed for CS and that these properties are similar to those of a subgaussian MM with the same mean and standard deviation. We calculate the MM for a multimode planar waveguide and find dimensions of the planar guide that give a speckle MM with performance similar to that of the multimode fiber. CS simulations show that all measured and calculated speckle MMs exhibit robust performance with equal amplitude signals that are sparse in time, in frequency, and in wavelets (Haar wavelet transform). The planar waveguide results indicate a path to a microwave photonic integrated circuit for measuring sparse GHz-band RF signals using CS

And earlier,

Compressive sensing to Reduce the Demands for On-board Processing, Storage and Communications Links, George C. Valley, George A. Sefler, T. Justin Shaw

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