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Currently, the use of microseismic detection technology for crack detection and localization in rock masses has great potential in detecting structural damage. As engineering safety has always been a very important issue, this study investigated the problem of multi-crack identification in rock masses within the environment of track tunnels using transient waves. A tunnel rock was modeled using MIDAS GTS NX software (2019.v1.2) and a crack transient wave model in the frequency domain was obtained through data analysis and simulation. Then, this was combined with compressive sensing techniques to locate and detect multiple cracks in tunnel rock. The performance of the proposed approach was validated through experimental simulations, which included experiments on differences in the number of cracks, as well as spatial samples. The experimental results indicate that the technique performs well for single-crack localization in tunnel rock mass, where the average localization error is 4 m. Meanwhile, the localization error is larger in multi-crack localization, and the number of spatial sample points set using compressive sensing also has a large impact on the experimental results. [ABSTRACT FROM AUTHOR]

Seismic acquisition guided by the compressive sensing theory can significantly improve seismic data acquisition efficiency and reduce the cost. After reviewing the basic principles of compressive sensing, we propose an optimized random sampling method that can control the maximum sampling interval and improve the design flexibility. We analyze several factors that can introduce reconstruction errors from compressive sensed data and learn that besides sampling method, reconstruction errors increase with decimation degree and the complexity of structures and also depend on the reconstruction workflow. In addition, we provide a basic workflow of the geometry design of compressive sensing acquisition. We analyze the feasibility of the three types of receiving equipment that are widely used in marine environment and discuss the potential cost reduction and efficiency gain. Our field example demonstrates the detailed working process and the feasibility of the combination of random sailing line intervals and random shot intervals and verifies the effect of cost saving and efficiency increasing. [ABSTRACT FROM AUTHOR]

Sign information is the key for overcoming the inevitable saturation error in compressive sensing system, which causes loss of information and may result in great bias. For sparse signal recovery from saturation, we propose to use linear loss to improve the effectiveness from the existing methods that utilize hard constraints/hinge loss for sign consistency. Due to the use of linear loss, analytical solution in the update progress is obtained and some nonconvex penalties are applicable, e.g., minimax concave penalty, $\ell _0$ norm, and sorted $\ell _1$ norm. Theoretical analysis reveals that the estimation error can still be bounded. Generally, with linear loss and nonconvex penalties, the recovery performance can be significantly improved and the computational time is also largely saved, which is verified by the numerical experiments. [ABSTRACT FROM AUTHOR]

The high-order multiple-input multiple-output (MIMO) system can remarkably increase the data rate or enhance the reliability. However, it is difficult to perform channel estimation because of the massive number of antennas. The Narrow Band Estimation Antenna Processing (NBEAP) scheme is used to deal with this issue. Nevertheless, the accuracy of the channel estimation needs to be improved. In this paper, a compressive sensing based scheme named Narrow Band Estimation Fixed Antenna Processing (NBEFAP) is proposed to estimate the channel state information (CSI) for high-order MIMO systems. A simple pilot structure is designed to decrease the computation complexity. In addition, the pilot length is adjusted according to the time-varying sparsity level of the CSI. Compared with NBEAP scheme, NBEFAP scheme can improve the estimation error performance. Simulation results verify the effectiveness of the NBEFAP scheme. [ABSTRACT FROM AUTHOR]

In this paper, we study the problem of velocity estimation in vehicular networks by exploiting the sparsity of vehicle velocity trajectory. First, we exploit the sparsity of vehicular velocity trajectories to reduce the beaconing load on the channel. To this end, we propose a sublayer that reduces the number of transmitted packets through a superframe. At each superframe, each vehicle transmits a few samples of its velocity as well as an encoded measurement of its past velocities. Sparse recovery of each velocity vector is performed at the receiver. We propose the use of repetitions at the medium access control (MAC) layer. Moreover, we extend our scheme into a streaming estimation system without the superframe concept. The streaming system uses a sliding window concept. We thoroughly study the estimation error of the streaming system, and we propose an algorithm to find the best solution over a streaming sliding window. The proposed superframe and streaming schemes are tested with real velocity traces collected in the city of Toronto to capture the performance in the city and highway conditions. Experiment results show that the proposed schemes significantly reduce the number of exchanged packets while preserving the velocity information with an excellent accuracy at the receiver. We also demonstrate how past velocity can be used to enhance vehicle localization accuracy. [ABSTRACT FROM PUBLISHER]

This paper provides new error bounds on consistent reconstruction methods for signals observed from quantized random projections. Those signal estimation techniques guarantee a perfect matching between the available quantized data and a new observation of the estimated signal under the same sensing model. Focusing on dithered uniform scalar quantization of resolution \delta >0 , we prove first that, given a Gaussian random frame of \mathbb R^{N} with M vectors, the worst-case \ell 2 -error of consistent signal reconstruction decays with high probability as O(({N}/{M})\log ({M}/{\sqrt {N}})) uniformly for all signals of the unit ball \mathbb B^N \subset \mathbb R^N . Up to a log factor, this matches a known lower bound in \Omega (N/M) and former empirical validations in O(N/M) . Equivalently, if M exceeds a minimal number of frame coefficients growing like , any vectors in \mathbb B^{N} with M identical quantized projections are at most \epsilon 0 apart with high probability. Second, in the context of quantized compressed sensing with M Gaussian random measurements and under the same scalar quantization scheme, consistent reconstructions of K -sparse signals of \mathbb R^{N} have a worst case error that decreases with high probability as O(({K})/({M})\log ({MN})/({\sqrt {K}^{3}}))$ uniformly for all such signals. Finally, we show that the proximity of vectors whose quantized random projections are only approximately consistent can still be bounded with high probability. A certain level of corruption is thus allowed in the quantization process, up to the appearance of a systematic bias in the reconstruction error of (almost) consistent signal estimates. [ABSTRACT FROM PUBLISHER]

In compressive sensing, generalized Orthogonal Matching Pursuit (gOMP) algorithm generalizes OMP algorithm by selecting N ( N ≥ 1 ) atoms in each iteration. In this paper, we propose restricted isometry constant based sufficient conditions for gOMP algorithm to correctly recover the support of significant components of signal when both measurement dictionary and measurement signal are contaminated with noise. Bound of estimation error is also derived. Upper bound of restricted isometry constant could be relaxed if the original sparse signal is strong decaying. When sparsity of original sparse signal is unavailable, we give a stopping criterion of gOMP algorithm to ensure correct support recovery. [ABSTRACT FROM AUTHOR]

This paper establishes a nearly optimal algorithm for denoising a mixture of sinusoids from noisy equispaced samples. We derive our algorithm by viewing line spectral estimation as a sparse recovery problem with a continuous, infinite dictionary. We show how to compute the estimator via semidefinite programming and provide guarantees on its mean-squared error rate. We derive a complementary minimax lower bound on this estimation rate, demonstrating that our approach nearly achieves the best possible estimation error. Furthermore, we establish bounds on how well our estimator localizes the frequencies in the signal, showing that the localization error tends to zero as the number of samples grows. We verify our theoretical results in an array of numerical experiments, demonstrating that the semidefinite programming approach outperforms three classical spectral estimation techniques. [ABSTRACT FROM PUBLISHER]

Traffic estimation is crucial to a number of tasks such as traffic management and road engineering. We propose an approach for metropolitan-scale traffic estimation with probe vehicles that periodically send location and speed updates to a monitoring center. In our approach, we use the flow speed on a road link within a time slot to indicate the traffic condition of the road segment at the given time slot, which is approximated by the average value of probe speeds. By analyzing a large data set of two-year probe data collected from a fleet of around 4,000 taxis in Shanghai, China, we find that a set of probe data may contain a lot of spatiotemporal vacancies over both time and space. This raises a serious missing data problem for road traffic estimation, which results from the naturally uneven distribution of probe vehicles over both time and space. Through empirical study based on the data set of real probe data using principal component analysis (PCA), we have observed that there are hidden structures within the traffic conditions of a road network. Inspired by this observation, we propose a compressive sensing-based algorithm for solving the missing data problem, which exploits the hidden structures for computing estimates for road traffic conditions. Different from existing approaches, our algorithm does not rely on complicated traffic models, which usually require costly training with field study and large data sets. With extensive experiments based on the data set of real probe data, we demonstrate that our proposed algorithm performs significantly better than other completing algorithms, including KNN and MSSA. Surprisingly, our algorithm can achieve an estimate error of as low as 20 percent even when more than 80 percent of probe data are missing. [ABSTRACT FROM AUTHOR]

In this work, we obtain sufficient conditions for exact recovery of regularized modified basis pursuit (reg-mod-BP) and discuss when the obtained conditions are weaker than those for modified compressive sensing or for basis pursuit (BP). The discussion is also supported by simulation comparisons. Reg-mod-BP provides a solution to the sparse recovery problem when both an erroneous estimate of the signal's support, denoted by T, and an erroneous estimate of the signal values on T are available. [ABSTRACT FROM AUTHOR]