Structured random measurements in signal processing

摘要: Compressed sensing and its extensions have recently triggered interest in randomized signal acquisition. A key finding is that random measurements provide sparse reconstruction guarantees for efficient stable algorithms with a minimal number of samples. While this was first shown (unstructured) Gaussian measurement matrices, applications require certain structure the leading to structured matrices. Near optimal recovery such been developed over past years variety contexts. This article surveys theory three scenarios: compressed (sparse recovery), low rank matrix recovery, phaseless estimation. The matrices be considered include partial Fourier circulant (subsampled convolutions), completion, phase estimation from magnitudes type measurements. concludes brief discussion mathematical techniques analysis