We consider a classic compressed sensing–based wireless sensor network (WSN) where a large number of sensors observe a common sparse signal. Under the partial-view assumption, each sensor acquires only a portion of the signal, with its support restricted to a unknown subset. To maintain energy efficiency, every sensor employs a sparse sensing vector to measure the (possibly masked) signal and applies the ternary censoring rule proposed in [1] to decide whether its measurement is informative; only qualified measurements are transmitted to the fusion center. The multi-view nature of this setting poses challenges to reconstruction stability as different sensors observe distinct partial views of the signal. To address this, we propose an algorithm, called CSC-modSP, which dynamically refines the qualified measurements to enhance the overall signal reconstruction quality. Simulation results validate the effectiveness of the proposed method.

Beamspace channel estimation is crucial for unlocking the potential of millimeter-wave (mmWave) communications in low Earth orbit (LEO) satellite networks. Effective channel estimation tailored to the unique characteristics of LEO channels, including hybrid beamforming architectures, is imperative. This paper presents a novel joint design framework integrating transmit pilot waveforming and receive compressive sensing (CS) for downlink beamspace channel estimation in LEO satellite communications. By exploiting channel sparsity and deep learning with an autoencoder (AE), the joint design is formulated as a sensing matrix design problem. We explore a simple AE training method utilizing 1-sparse channel patterns, enabling efficient decoding with orthogonal matching pursuit (OMP) and its variants. Subsequently, a low-rank approximation method is employed to extract the precoder and compressor from the trained sensing matrix. We further propose a machine learning (ML)-OMP method using a customized multilayer perceptron (MLP) network for iterative support selection. Simulation results demonstrate that the proposed transmit pilot waveforming and receive CS methods significantly enhance beamspace channel estimation performance with fewer pilot time slots. Furthermore, the proposed ML-OMP method outperforms conventional OMP, particularly in scenarios with non-customized precoders and compressors.

Conventional sparse phase retrieval schemes can recover sparse signals from the magnitude of linear measurements only up to a global phase ambiguity. This work proposes a novel approach that instead utilizes the magnitude of affine measurements to achieve ambiguity-free signal reconstruction. The proposed method relies on two-stage approach that consists of support identification followed by the exact recovery of nonzero signal entries. In the noise-free case, perfect support identification using a simple counting rule is guaranteed subject to a mild condition on the signal sparsity, and subsequent exact recovery of the nonzero signal entries can be obtained in closed-form. The proposed approach is then extended to two noisy scenarios, namely, sparse noise (or outliers) and non-sparse bounded noise. For both cases, perfect support identification is still ensured under mild conditions on the noise model, namely, the support size for sparse outliers and the power of the bounded noise. Under perfect support identification, exact signal recovery can be achieved using a simple majority rule for the sparse noise scenario, and reconstruction up to a bounded error can be achieved using linear least-squares (LS) estimation for the non-sparse bounded noise scenario. The obtained analytic performance guarantee for the latter case also sheds light on the construction of the sensing matrix and bias vector. In fact, we show that a near optimal performance can be achieved with high probability by the random generation of the nonzero entries of the sparse sensing matrix and bias vector according to the uniform distribution over a circle. Computer simulations using both synthetic and real-world data sets are provided to demonstrate the effectiveness of the proposed scheme.

Sparse subspace clustering (SSC) relies on sparse regression for accurate neighbor identification. Inspired by recent progress in compressive sensing, this paper proposes a new sparse regression scheme for SSC via two-step reweighted$\ell _{1} $-minimization, which also generalizes a two-step$\ell _{1} $-minimization algorithm introduced by E. J. Candèset al.in [The Annals of Statistics, vol. 42, no. 2, pp. 669–699, 2014] without incurring extra algorithmic complexity. To fully exploit the prior information offered by the computed sparse representation vector in the first step, our approach places a weight on each component of the regression vector, and solves a weighted LASSO in the second step. We propose a data weighting rule suitable for enhancing neighbor identification accuracy. Then, under the formulation of the dual problem of weighted LASSO, we study in depth the theoretical neighbor recovery rates of the proposed scheme. Specifically, an interesting connection between the locations of nonzeros of the optimal sparse solution to the weighted LASSO and the indexes of the active constraints of the dual problem is established. Afterwards, under the semi-random model, analytic probability lower/upper bounds for various neighbor recovery events are derived. Our analytic results confirm that, with the aid of data weighting and if the prior neighbor information is accurate enough, the proposed scheme with a higher probability can produce many correct neighbors and few incorrect neighbors as compared to the solution without data weighting. Computer simulations are provided to validate our analytic study and evidence the effectiveness of the proposed approach.

This work proposes a collaborative sensor caching and data reconstruction method based on the sequential compressed sensing framework. Here, multiple caches are assumed to exist in the wireless sensor network to store the most recent data gathered from sensors within their respective coverage areas. To reduce the cache size and the data-acquisition overhead, each cache accesses measurements only from a small subset of sensors. This work proposes a collaborative sparse-signal reconstruction method that exploits the presence of sensors simultaneously accessible by multiple caches as anchor nodes to introduce dependency in the reconstruction. The reconstruction is based on the use of the alternating direction method of multipliers (ADMM), which enables distributed implementation of the algorithm. Simulations are provided to demonstrate the effectiveness of the proposed scheme.

This work proposes efficient methods for the detection of malicious crowdsourcing workers using only privacy-aware group queries. In the proposed system, the crowdsourcing platform first issues a series of standard tasks to the workers, and allows users (i.e., data owners) to access aggregate responses from the workers through group queries that can be described by sparse encoding vectors. The identities of workers associated with individual responses are not explicitly revealed. By exploiting the sparse nature of the encoding vectors, we first propose an approximate maximum a posteriori probability (Approx. MAP) detector to perform the detection. Then, to further reduce computational complexity, we devise a generalized likelihood ratio test (GLRT) where probable malicious workers are first identified before a simple hypothesis test is performed. The identification of malicious workers is performed by a low-complexity probability-based rule that exploits a certain sparse structure inherent in the crowd data as well as the associated statistical assumptions. Computer simulations show that the proposed methods outperform the conventional energy detector.

Built on the sparse representation framework, sparse subspace clustering (SSC) received considerable attention in the recent years. Conventional SSC employs ℓ1-minimization based sparse regression for neighbor identification on a sample-by-sample basis, and is unaware of the neighbor information revealed by those already computed sparse representation vectors. To rid this drawback, this paper proposes a weighted ℓ1-minimization based sparse regression method, and an associated data ordering rule able to reflect the reliability of neighbor information for further enhancing the clustering accuracy. The selection of weighting coefficients for SSC is also discussed. Computer simulations using both the synthesis and real data are provided to evidence the effectiveness of the proposed method.

This paper proposes a compressive sensing (CS) based active user identification scheme over frequency-selective fading channels. Unlike the conventional cyclic prefix (CP) based preamble transmission, our approach does not utilize CP in order to conserve signaling overhead, in turn reducing the system-wide processing latency. Our approach first estimates the multi-user channel impulse response vectors by solving a mixed ℓ2/ℓ1-norm optimization problem; then, the active users are identified via a sorting of the norms of the estimated channel vectors. By exploiting the Toeplitz channel matrix structure resulting from CP-free preamble transmission, analytic performance guarantee in term of the block restricted isometry property of the preamble matrix is given. Computer simulations are used to illustrate the performance of the proposed method.

To strike a balance between energy efficiency and data quality control, this paper proposes a sensor censoring scheme for distributed sparse signal recovery via compressive-sensing-based wireless sensor networks. In the proposed approach, each sensor node employs a sparse sensing vector with known support for data compression, meanwhile enabling making local inference about the unknown support of the sparse signal vector of interest. This naturally leads to a ternary censoring protocol, whereby each sensor: 1) directly transmits the real-valued compressed data, if the sensing vector support is detected to be overlapped with the signal support; 2) sends a one-bit hard decision if empty support overlap is inferred; and 3) keeps silent if the measurement is judged to be uninformative. Our design then aims at minimizing the error probability that empty support overlap is decided but otherwise is true, subject to the constraints on a tolerable false-alarm probability that non-empty support overlap is decided but otherwise is true, and a target censoring rate. We derive a closed-form formula of the optimal censoring rule; a low complexity implementation using bi-section search is also developed. In addition, the average communication cost is analyzed. To aid global signal reconstruction under the proposed censoring framework, we propose a modified ℓ1-minimization based algorithm, which exploits certain sparse nature of the hard decision vector received at the fusion center. Analytic performance guarantees, characterized in terms of the restricted isometry property, are also derived. Computer simulations are used to illustrate the performance of the proposed scheme.

Collaborative detection for continuously-varying event-region scenarios using wireless sensor networks (WSNs) has attracted much attention recently. However, most existing works adopt either a centralized approach, in which a powerful control center is used to reconstruct the entire random field, or a semi-centralized approach, in which extensive data exchange takes place among the sensors by means of real-value data communications. By contrast, the present study proposes a distributed dynamic event-region detection scheme for WSNs. The proposed scheme is based on a two-phase cooperative space-time decision fusion protocol. In Phase I, each sensor makes an initial decision in accordance with its Gaussian corrupted observation and previous decision. In Phase II, the nodes update their decisions in accordance with the decision information received from their neighboring nodes. The performance of the proposed scheme is compared with that of a semi-centralized detection scheme by means of computer simulations.

Various methods have been proposed for monitoring continuously varying event-region scenarios using wireless sensor networks (WSNs). However, these methods use either a centralized approach, in which a powerful control center is used to reconstruct the entire random field, or a semi-centralized approach, in which extensive real-value data exchange takes place among the sensors. By contrast, this paper proposes a two-phase distributed dynamic event-region detection scheme for WSNs characterized by a space-time Markov random field with a particular Gibbs distribution. In Phase I of the proposed scheme, each sensor makes an initial decision in accordance with its current Gaussian corrupted observation and previous decision. In Phase II, the nodes update their decisions based on the decision information received from their neighbors. Notably, the proposed scheme has a low-communication-rate characteristic, and is thus ideally suited to WSN applications. The performance of the proposed scheme is compared with that of a semicentralized detection scheme by means of computer simulations.