Compressed sensing (CS) is an emerging field that has attracted considerable research interest over the past few years. Previous review articles in CS limit their scope to standard discrete-to-discrete measurement architectures using matrices of randomized nature and signal models based on standard sparsity. In recent years, CS has worked its way into several new application areas. This, in turn, necessitates a fresh look on many of the basics of CS. The random matrix measurement operator must be replaced by more structured sensing architectures that correspond to the characteristics of feasible acquisition hardware. The standard sparsity prior has to be extended to include a much richer class of signals and to encode broader data models, including continuous-time signals. In our overview, the theme is exploiting signal and measurement structure in compressive sensing. The prime focus is bridging theory and practice; that is, to pinpoint the potential of structured CS strategies to emerge from the math to the hardware. Our summary highlights new directions as well as relations to more traditional CS, with the hope of serving both as a review to practitioners wanting to join this emerging field, and as a reference for researchers that attempts to put some of the existing ideas in perspective of practical applications.

Structured Compressed Sensing: From Theory to Applications

Time-delay estimation arises in many applications in which a multipath medium has to be identified from pulses transmitted through the channel. Previous methods for time delay recovery either operate on the analog received signal, or require sampling at the Nyquist rate of the transmitted pulse. In this paper, we develop a unified approach to time delay estimation from low-rate samples. This problem can be formulated in the broader context of sampling over an infinite union of subspaces. Although sampling over unions of subspaces has been receiving growing interest, previous results either focus on unions of finite-dimensional subspaces, or finite unions. The framework we develop here leads to perfect recovery of the multipath delays from samples of the channel output at the lowest possible rate, even in the presence of overlapping transmitted pulses, and allows for a variety of different sampling methods. The sampling rate depends only on the number of multipath components and the transmission rate, but not on the bandwidth of the probing signal. This result can be viewed as a sampling theorem over an infinite union of infinite dimensional subspaces. By properly manipulating the low-rate samples, we show that the time delays can be recovered using the well-known ESPRIT algorithm. Combining results from sampling theory with those obtained in the context of direction of arrival estimation, we develop sufficient conditions on the transmitted pulse and the sampling functions in order to ensure perfect recovery of the channel parameters at the minimal possible rate.

/pdf/time-delay-estimation-from-low-rate-samples-a-union-of-5eef4i54yv.pdf

Time-Delay Estimation From Low-Rate Samples: A Union of Subspaces Approach

Bearing fault diagnosis based on vibro-acoustic data fusion and 1D-CNN network

In this paper, we present a low-cost wireless sensor network platform, called wireless ad hoc system for positioning (WASP), that has been developed for high-accuracy localization and tracking. This platform uses the time of arrival (TOA) of beacon signals periodically transmitted by the nodes at known times for localization. The system was designed to have a unique tradeoff between hardware complexity and processing complexity to provide high accuracy at minimal cost in complex radio propagation environments. To enable the system to perform well in realistic environments, it was also necessary to develop novel extensions to existing algorithms for the measurement of TOA, localization, and tracking. In this paper, we describe the architecture, hardware, and algorithms of WASP and present results based on field trials conducted in different radio propagation environments. The results show that WASP achieves a ranging accuracy of 0.15 m outdoors and 0.5 m indoors when around 12 anchor nodes are used. These accuracies are achieved with operating range of up to 200 m outdoors and 30 m indoors. This compares favorably to other published results for systems operating in realistic environments.

WASP: A System and Algorithms for Accurate Radio Localization Using Low-Cost Hardware

Joint sparse representation (JSR) has shown great potential in various image processing and computer vision tasks. Nevertheless, the conventional JSR is fragile to outliers. In this paper, we propose a weighted JSR (WJSR) model to simultaneously encode a set of data samples that are drawn from the same subspace but corrupted with noise and outliers. Our model is desirable to exploit the common information shared by these data samples while reducing the influence of outliers. To solve the WJSR model, we further introduce a greedy algorithm called weighted simultaneous orthogonal matching pursuit to efficiently approximate the global optimal solution. Then, we apply the WJSR for mixed noise removal by jointly coding the grouped nonlocal similar image patches. The denoising performance is further improved by incorporating it with the global prior and the sparse errors into a unified framework. Experimental results show that our denoising method is superior to several state-of-the-art mixed noise removal methods.

Weighted Joint Sparse Representation for Removing Mixed Noise in Image

The super-resolution time delay estimation in multipath environment is very important for many applications. Conventional super-resolution approaches can only deal with signals with wideband and flat spectra. In this paper, we propose a novel super-resolution time delay estimation method that can treat signals with narrowband spectra. In our method, the time delay estimation is first transformed into the frequency domain, in which the problem is converted into the parameter estimation of sinusoidal signals with lowpass envelopes. Then a MUSIC-type algorithm taking account of the envelope variation is applied to achieve the super-resolution estimation. Time delay estimation in active and passive systems are considered. Simulation results confirm that the proposed estimators provide better performance than the classical correlation approach and the conventional MUSIC algorithm for separating closely spaced signals with narrowband spectra.

/pdf/super-resolution-time-delay-estimation-in-multipath-3ak1eq0hr1.pdf

Super-Resolution Time Delay Estimation in Multipath Environments

Multisensor bearing fault diagnosis based on one-dimensional convolutional long short-term memory networks

The problem of super-resolution time delay estimation in multipath environments is addressed in this paper. Two cases, active and passive systems, are considered. The time delay estimation is first converted into a sinusoidal parameter estimation problem. Then the sinusoidal parameters are estimated by generalizing the multiple signal classification (MUSIC) algorithm for single-experiment data. The proposed method, referred to as the MUSIC-type algorithm, approximates the Cramer-Rao bound (CRB) in terms of the mean square errors (MSKs) for different signal-to-noise ratios (SNRs) and separations of multipath components. Simulation results show that the MUSIC-type algorithm performs better than the classical correlation approach and the conventional MUSIC method for the closely spaced components in multipath environments.

/pdf/super-resolution-time-delay-estimation-in-multipath-44mu0m9mnw.pdf

Super-resolution time delay estimation in multipath environments

In this paper, frequency estimation of sinusoidal signals in multiplicative and additive noise is addressed. Based on the parametric localization of distributed sources and the minimax theorem, an eigenanalysis-based frequency estimator is proposed. Furthermore, we present processing and analysis for pseudofrequency estimates in the proposed method. Especially, a priori knowledge of multiplicative noise is not required as compared with the distributed signal parameter estimator (DSPE). Monte Carlo experiments are carried out to evaluate performance. Simulation results confirm that the proposed method provides better performance than the nonlinear least squares (NLS) approach and the conventional MUSIC algorithm for separating closely spaced sinusoidal signals in multiplicative and additive noise.

Frequency Estimation of Sinusoidal Signals in Multiplicative and Additive Noise

Passive localization of weak sources in the presence of strong interferences is generally a difficult task. In this paper, an eigenanalysis-based adaptive interference suppression (EAAIS) method is proposed for estimating the bearing and subsequently the weak source range. Assuming the target of interest (TOI) is in a known bearing sector, first we define a contribution ratio for each eigenvector of the cross-spectral density matrix (CSDM). The eigenvectors not dominated by the TOI are adaptively identified and removed for interference suppression. The remaining eigenvectors are then used to reconstruct the CSDM for TOI bearing estimation. Finally, the acoustic source range estimation is achieved with the reconstructed CSDM, by matching the beam intensity striation pattern, where it is not required to estimate the waveguide-invariant parameter. The effectiveness of the proposed TOI localization is demonstrated using several experimental data sets.

Feng-Xiang Ge

Papers

Super-Resolution Time Delay Estimation in Multipath Environments

Multisensor bearing fault diagnosis based on one-dimensional convolutional long short-term memory networks

Super-resolution time delay estimation in multipath environments

Frequency Estimation of Sinusoidal Signals in Multiplicative and Additive Noise

Eigenanalysis-Based Adaptive Interference Suppression and Its Application in Acoustic Source Range Estimation