Stretching the bandwidth of physical measurements by compressed sensing

The bandwidth limit is an issue in any class of physical measurements. To restore the original full-band spectrum from the available data sets that have been severely bandwidth-limited due to measurement is a challenge. Compressed sensing (CS), which is essentially an estimation based on L1 norm minimization, is a powerful technique to retrieve signals using a small number of clues on the assumption of sparsity. Here we attempt the CS in frequency domain to restore the otherwise lost part of the spectrum with good fidelity. The proof-of-concept experiment was done on a model system with bandwidth-limiting properties by first acquiring the prior knowledge of its step response in the form of discretized impulse response function. The original input waveform was mixed with random signal to spread the spectrum over the entire frequency range, i.e., omni-frequency heterodyne. Then the CS was implemented by using repetitive interleaved random sampling over the captured signals that are linearly coupled with the random mixing signals through the step response. Successful recovery of the original full-band spectrum with well over 70-% fidelity holds promise for high-Z and the many strongly bandwidth-limiting measurements. Single-shot and real-timeliness issues will also be discussed.