Here are four items that makes me think that, maybe, the issue of compression should not be the main concern, several evidences:
* Sparse Spectral Factorization: Unicity and Reconstruction Algorithms by Yue Lu and Martin Vetterli
* CS: Sparse Spectral Factorization for FROG ?
* Sparsity based sub-wavelength imaging with partially incoherent light via quadratic compressed sensing by Yoav Shechtman, Yonina Eldar, Alexander Szameit, Mordechai Segev
Above a number of measurements comparable to the Nyquist rate (~25 measurements), the reconstruction does not improve dramatically. The problem of bandwidth extrapolation is not solved by adding more samples, since the physical cutoff frequency of the optical system obviously does not depend on this quantity.* CS: Multiplicative Noise Effect on the Donoho-Tanner Phase Transition (Part 2)
The wording "Sparse Sensing" has not been overused and the few first hits on the Google show application of SLAM in Robotics...