Random Acquisition in Compressive Sensing

Compressive sensing has the ability of reconstruction of signal/image from the compressive measurements which are sensed with a much lower number of samples than a minimum requirement by Nyquist sampling theorem. The random acquisition is widely suggested and used for compressive sensing. In the random acquisition, the randomness of the sparsity structure has been deployed for compressive sampling of the signal/image. The article goes through all the literature up to date and collects the main methods, and simply described the way each of them randomly applies the compressive sensing. This article is a comprehensive review of random acquisition techniques in compressive sensing. Theses techniques have reviews under the main categories of (1) random demodulator, (2) random convolution, (3) modulated wideband converter model, (4) compressive multiplexer diagram, (5) random equivalent sampling, (6) random modulation pre-integration, (7) quadrature analog-to-information converter, (8) randomly triggered modulated-wideband compressive sensing (RT-MWCS).

Analog-to-Information Conversion with Random Interval Integration

A novel method of analog-to-information conversion—the random interval integration—is proposed and studied in this paper. This method is intended primarily for compressed sensing of aperiodic or quasiperiodic signals acquired by commonly used sensors such as ECG, environmental, and other sensors, the output of which can be modeled by multi-harmonic signals. The main idea of the method is based on input signal integration by a randomly resettable integrator before the AD conversion. The integrator’s reset is controlled by a random sequence generator. The signal reconstruction employs a commonly used algorithm based on the minimalization of a distance norm between the original measurement vector and vector calculated from the reconstructed signal. The signal reconstruction is performed by solving an overdetermined problem, which is considered a state-of-the-art approach. The notable advantage of random interval integration is simple hardware implementation with commonly used components. The performance of the proposed method was evaluated using ECG signals from the MIT-BIH database, multi-sine, and own database of environmental test signals. The proposed method performance is compared to commonly used analog-to-information conversion methods: random sampling, random demodulation, and random modulation pre-integration. A comparison of the mentioned methods is performed by simulation in LabVIEW software. The achieved results suggest that the random interval integration outperforms other single-channel architectures. In certain situations, it can reach the performance of a much-more complex, but commonly used random modulation pre-integrator.

Nonlinear Time-Series Prediction Using a Single MEMS Reservoir

In this work, we show the computational potential of MEMS devices by predicting the dynamics of a 10th order nonlinear auto-regressive moving average (NARMA10) dynamical system. Modeling this system is considered complex due to its high nonlinearity and dependency on its previous values. To model the NARMA10 system, we used a reservoir computing scheme by utilizing one MEMS device as a reservoir, produced by the interaction of 100 virtual nodes. The virtual nodes are attained by sampling the input of the MEMS device and modulating this input using a random modulation mask. The interaction between virtual nodes within the system was produced through delayed feedback and temporal dependence. Using this approach, the MEMS device was capable of adequately capturing the NARMA10 response with a normalized root mean square error (NRMSE) = 6.18% and 6.43% for the training and testing sets, respectively. In practice, the MEMS device would be superior to simulated reservoirs due to its ability to perform this complex computing task in real time.