Detecting Signal Structure from Randomly-Sampled Data

Abstract

Recent theoretical results in Compressive Sensing (CS) show that sparse (or compressible) signals can be accurately reconstructed from a reduced set of linear measurements in the form of projections onto random vectors. The associated reconstruction consists of a nonlinear optimization that requires knowledge of the actual projection vectors. This work demonstrates that random time samples of a data stream could be used to identify certain signal features, even when no time reference is available. Since random sampling suppresses aliasing, a small (sub-Nyquist) set of samples can represent high-bandwidth signals. Simulations were carried out to explore the utility of such a procedure for detecting and classifying signals of interest.

Block-Based Feature Adaptive Compressive Sensing for Video

“…However, in the sampling process when using such matrices, although the number of measurements is less than the total number of pixels, all the pixels are in fact obtained in the form of linear combinations. To achieve simpler hardware implementation, another technique, namely random sampling is proposed [24], [25]. In this scheme, only a small, uniformly distributed, randomly chosen fraction of the coefficients is captured.…”

“…To enable causal reconstruction (i.e., only the current measurements and the previously reconstructed frame are employed), in the rest of this paper, we consider Φ 1 as the identity matrix I, which means the first frame in the joint scheme is completely sampled as a reference or that it has been recovered in the previous step. We choose Φ 2 as a random sampling matrix [24], [25] as described in Section II.…”

Feedback control of switched stochastic systems using randomly available active mode information

“…In addition, we may also take advantage of random sampling for certain cases and observe the mode intentionally at random instants, as for such cases control under random sampling provides better results compared to periodic sampling. Note that random sampling has also been used for problems such as signal reconstruction and has been shown to have advantages over regular periodic sampling (see Boyle et al (2007), Carlen and Mendes (2009)).…”

Characterization of optically compressing diode array for spectroscopic applications

“…The key in Compressive Sensing is the non-uniform sampling of the original signal. Pseudorandom encoding is frequently preferred as a means to rapidly approach an entropy-limited, minimum encoding of the information 20 . This requires computationally intensive reconstruction in order to support the generic pseudo-random sampling proposed in the original proof.…”