Search

In this article, a continuous-time complex-valued projection neural network (CCPNN) in a matrix state space is first proposed for a general complex-variable basis pursuit problem. The proposed CCPNN is proved to be stable in the sense of Lyapunov and to be globally convergent to the optimal solution under the condition that the sensing matrix is not row full rank. Furthermore, an improved discrete-time complex projection neural network (IDCPNN) is proposed by discretizing the CCPNN model. The proposed IDCPNN consists of a two-step stop strategy to reduce the calculational cost. The proposed IDCPNN is theoretically guaranteed to be global convergent to the optimal solution. Finally, the proposed IDCPNN is applied to the reconstruction of sparse signals based on compressed sensing. Computed results show that the proposed IDCPNN is superior to related complex-valued neural networks and conventional basis pursuit algorithms in terms of solution quality and computation time.

Compressive Sensing (CS) is a new sampling theory used in many signal processing applications due to its simplicity and efficiency. However, signal reconstruction is considered as one of the biggest challenge faced by the CS method. A lot of researches have been proposed to address this challenge, however most of the existing techniques start with the same forward step which does not provide the best reconstruction performance. In this paper, we aim to address this challenge by proposing an Adaptive Iterative Forward-Backward Greedy Algorithm (AFB). AFB algorithm is different from all other reconstruction algorithms as it depends on solving the least squares problem in the forward phase, which increases the probability of selecting the correct columns better than other reconstruction algorithms. In addition, AFB improves the selection process by removing the incorrect columns selected in the previous step. We evaluated the AFB’s reconstruction performance using two types of data: computer-generated data and real data set (Intel Berkeley data set). The simulation results show that AFB outperforms Forward-Backward Pursuit, Subspace Pursuit, Orthogonal Matching Pursuit, and Regularized OMP in terms of reducing reconstruction error.

The Binary Iterative Hard Thresholding (BIHT) algorithm is a popular reconstruction method for one-bit compressed sensing due to its simplicity and fast empirical convergence. There have been several works about BIHT but a theoretical understanding of the corresponding approximation error and convergence rate still remains open. This paper shows that the normalized version of BIHT (NBHIT) achieves an approximation error rate optimal up to logarithmic factors. More precisely, using $m$ one-bit measurements of an $s$-sparse vector $x$, we prove that the approximation error of NBIHT is of order $O \left(1 \over m \right)$ up to logarithmic factors, which matches the information-theoretic lower bound $\Omega \left(1 \over m \right)$ proved by Jacques, Laska, Boufounos, and Baraniuk in 2013. To our knowledge, this is the first theoretical analysis of a BIHT-type algorithm that explains the optimal rate of error decay empirically observed in the literature. This also makes NBIHT the first provable computationally-efficient one-bit compressed sensing algorithm that breaks the inverse square root error decay rate $O \left(1 \over m^{1/2} \right)$., Comment: Submitted to a journal

As an alternative to traditional meteorological methods, rain attenuation in satellite-to-Earth microwave communication signals has been used for rainfall reconstruction in recent years. In this article, the existing 2-D rain field reconstruction problem is extended to a 3-D scenario by leveraging the low Earth orbit satellite system. A compressive sensing approach is further proposed to solve the 3-D rain field reconstruction problem. The Starlink system is used as a reference, and two synthetic rain events near the Great Barrier Reef in Australia, which are generated from the weather research and forecasting model, are used to evaluate the reconstruction performance. Simulation results show that the compressive sensing approach performs better than both the traditional least squares and the least absolute shrinkage and selection operator approaches.

Compressed sensing (CS) ensures the recovery of sparse vectors from a number of randomized measurements proportional to their sparsity. The initial theory considers discretized domains, and the randomness makes the physical positions of the grid nodes irrelevant. Most imaging devices, however, operate over some continuous physical domain, and it makes sense to consider Dirac masses with arbitrary positions. In this article, we consider such a continuous setup and analyze the performance of the BLASSO algorithm, which is the continuous extension of the celebrated LASSO $$\ell ^1$$ regularization method. This approach is appealing from a numerical perspective because it avoids to discretize the domain of interest. Previous works considered translation-invariant measurements, such as randomized Fourier coefficients, in which it makes clear that the discrete theory should be extended by imposing a minimum distance separation constraint (often called “Rayleigh limit”) between the Diracs. These prior works, however, rule out many domains and sensing operators of interest, which are not translation invariant. This includes, for instance, Laplace measurements over the positive reals and Gaussian mixture models over the mean-covariance space. Our theoretical advances crucially rely on the introduction of a canonical metric associated with the measurement operator, which is the so-called Fisher geodesic distance. In the case of Fourier measurements, one recovers the Euclidean metric, but this metric can cope with arbitrary (possibly non-translation invariant) domains. Furthermore, it is naturally invariant under joint reparameterization of both the sensing operator and the Dirac locations. Our second and main contribution shows that if the Fisher distance between spikes is larger than a Rayleigh separation constant, then the BLASSO recovers in a stable way a stream of Diracs, provided that the number of measurements is proportional (up to log factors) to the number of Diracs. We measure the stability using an optimal transport distance constructed on top of the Fisher geodesic distance. Our result is (up to log factor) sharp and does not require any randomness assumption on the amplitudes of the underlying measure. Our proof technique relies on an infinite-dimensional extension of the so-called golfing scheme which operates over the space of measures and is of general interest.

For certain sensing matrices, the Approximate Message Passing (AMP) algorithm efficiently reconstructs undersampled signals. However, in Magnetic Resonance Imaging (MRI), where Fourier coefficients of a natural image are sampled with variable density, AMP encounters convergence problems. In response we present an algorithm based on Orthogonal AMP constructed specifically for variable density partial Fourier sensing matrices. For the first time in this setting a state evolution has been observed. A practical advantage of state evolution is that Stein's Unbiased Risk Estimate (SURE) can be effectively implemented, yielding an algorithm with no free parameters. We empirically evaluate the effectiveness of the parameter-free algorithm on simulated data and find that it converges over 5x faster and to a lower mean-squared error solution than Fast Iterative Shrinkage-Thresholding (FISTA)., Comment: 5 pages, 5 figures, IEEE International Conference on Image Processing (ICIP) 2020

Surface Electromyography (sEMG) is a non-invasive measurement process that does not involve tools and instruments to break the skin or physically enter the body to investigate and evaluate the muscular activities produced by skeletal muscles. The main drawbacks of existing sEMG systems are: (1) they are not able to provide real-time monitoring, (2) they suffer from long processing time and low speed, (3) they are not effective for wireless healthcare systems because they consume huge power. In this work, we present an analog-based Compressed Sensing (CS) architecture, which consists of three novel algorithms for design and implementation of wearable wireless sEMG bio-sensor. At the transmitter side, two new algorithms are presented in order to apply the analog-CS theory before Analog to Digital Converter (ADC). At the receiver side, a robust reconstruction algorithm based on a combination of ℓ1-ℓ1-optimization and Block Sparse Bayesian Learning (BSBL) framework is presented to reconstruct the original bio-signals from the compressed bio-signals. The proposed architecture allows reducing the sampling rate to 25% of Nyquist Rate (NR). In addition, the proposed architecture reduces the power consumption to 40%, Percentage Residual Difference (PRD) to 24%, Root Mean Squared Error (RMSE) to 2%, and the computation time from 22 s to 9.01 s, which provide good background for establishing wearable wireless healthcare systems. The proposed architecture achieves robust performance in low Signal-to-Noise Ratio (SNR) for the reconstruction process.

An effective visible light and infrared image fusion method using a deep learning framework is designed to obtain a fused image which contains all the features from infrared and visible images. First, the source images are decomposed into low frequency and high frequency sub bands using wavelet transform. Then the low frequency is fused by maximum fusion rule. For the high frequency sub bands a deep learning network is used to find activity level measurements and then fused using the maximum fusion rule. For reconstruction, the optimized orthogonal matching pursuit algorithm and inverse wavelet transform are used.

Data acquisition problem on large distributed wireless sensor networks (WSNs) is considered as a challenge in the growth of Internet of Things (IoT). Recently, the combination of compressive sensing (CS) and routing techniques has attracted much attention of researchers. An open question of this combination is how to integrate these techniques effectively for specific tasks. On the other hand, CS data reconstruction process is considered as one of the CS challenges because it requires to recover N data from only M measurement where M<

The next generation of communication technology is accelerating the transformation of industrial internet of things (IIoT). Filter bank multicarrier with offset quadrature amplitude modulation (FBMC/OQAM), as a candidate wireless transmission technology for beyond fifth generation (5G), has been widely concerned by researchers. However, effective channel estimation (CE) in IIoT communication should be solved. In practice, wireless channels have block–sparse structures. For the conventional sparse channel model, the general sparse channel estimation methods do not take the potential block–sparse structure information into account. In this paper, we have investigated the sparse Bayesian learning (SBL) framework for sparse multipath CE in FBMC/OQAM communications. Block SBL (BSBL) algorithm is proposed to estimate the channel performance by exploiting the block–sparse structure of sparse multipath channel model. The BSBL method can improve the estimation performance by using the block correlation of the training matrix. Computer simulation results demonstrate the robustness of the BSBL CE approach in FBMC/OQAM systems, which can achieve lower mean square error (MSE) and bit error rate (BER) than traditional least squares (LS) method and classical compressive sensing methods. The state of art compressive sampling matching pursuit (CoSaMP) greedy algorithm with a prior knowledge of sparse degree can provide slightly better CE performance than BSBL algorithm, but the proposed method maintains robustness in practical channel scenario without the prior knowledge of sparse degree.

In the compressed sensing (CS) reconstruction algorithms, the problems of overestimation and large redundancy of candidate atoms will affect the reconstruction accuracy and probability of the algorithm when using Sparsity Adaptive Matching Pursuit (SAMP) algorithm. In this paper, we propose an improved SAMP algorithm based on a double threshold, candidate set reduction, and adaptive backtracking methods. The algorithm uses the double threshold variable step-size method to improve the accuracy of sparsity judgment and reduces the undetermined atomic candidate set in the small step stage to enhance the stability. At the same time, the sparsity estimation accuracy can be improved by combining with the backtracking method. We use a Gaussian sparse signal and a measured shock wave signal of the 15psi range sensor to verify the algorithm performance. The experimental results show that, compared with other iterative greedy algorithms, the overall stability of the DBCSAMP algorithm is the strongest. Compared with the SAMP algorithm, the estimated sparsity of the DBCSAMP algorithm is more accurate, and the reconstruction accuracy and operational efficiency of the DBCSAMP algorithm are greatly improved.

Designing the time domain training sequences is very critical in multi carrier transmission which degrades the performance as it is contaminated by different blocks in different cells. To improve the spectral efficiency and high accuracy, MU-MIMO needs the sensing matrix to be reduced by using the training sequence design and optimization. Integrating the training sequence design and sparse channel estimation improves the capacity of the system. The capacity can be enhanced by reducing the bit error rate. The system capacity for multi user- multi-input and multi output (MU-MIMO) is studied by proper channel estimation with compressed sensing model. The design and optimization of training sequence is analysed for MU-MIMO model using auto coherence and block coherence matrices. The block coherence matrix is optimized using cuckoo algorithm for obtaining lower coherence value for different sparsity values. The performance improvement in terms of signal to noise ratio is 1 dB for single user- multi-input and multi output (SU-MIMO) using genetic algorithm and the performance of MU-MIMO is observed to be 0.93 dB using cuckoo algorithm.

With the rapidly increasing scale and complexity, millimeter-wave communication systems are getting more powerful, but are also less reliable. Due to hardware characteristics and connecting structures, millimeter-wave communication systems may experience device faults which result in performance degradation or even failure. Therefore, system diagnosis techniques for fault detection and localization are essential to system monitoring and maintenance. In this paper, two compressed sensing based diagnosis techniques are proposed, which can jointly detect and locate faulty antennas, phase shifters, and RF chains. The first technique is applicable to the diagnosis in a multipath-free environment where the channel state information can be obtained based on spatial coordinates. Furthermore, we propose the second technique that does not require the channel state information, which is suitable for outdoor online diagnosis in a multipath scattering environment. Finally, numerical simulations show that the proposed techniques can jointly detect all faulty devices with high probability.

This paper presents a compressed sensing (CS) based encryption scheme for wireless neural recording. An ultrahigh efficiency was achieved by leveraging CS for simultaneous data compression and encryption. CS enables sub-Nyquist sampling of neural signals by taking advantage of their intrinsic sparsity, while the CS process simultaneously encrypts the data with the sampling matrix being the cryptographic key. To share the key over an insecure wireless channel, we implemented an elliptic-curve cryptography (ECC) based key exchanging protocol. Local key shuffle and updating were adopted to eliminate the risks of potential information leakage. CS was executed in an application-specific integrated circuits (ASIC) fabricated in 180nm CMOS technology. Mixed-signal circuits were designed to optimize the power efficiency of the matrix-vector multiplication (MVM) of the CS operation. The ECC was implemented in a low-power Cortex-M0 based microcontroller (MCU). To be protected from timing attacks, the implementation avoided possible data-dependent branches. A wireless neural recorder prototype has been developed to demonstrate the proposed scheme. The prototype achieved an $8\times$ data rate reduction and a $35\times$ power saving compared with conventional implementation. The overall power consumption of ASIC and MCU was $442\mu \text{W}$ during the encrypted wireless transmission. The average correlated coefficient between the reconstructed signals and the uncompressed signals was 0.973, while the ciphertext-only attacks (CoA) achieved no better than 0.054 over 200,000 attacks. This work demonstrates a promising data compression and encryption scheme that can be used in a wide range of low-power signal recording systems with security requirements.

Multiview subspace clustering, which aims to cluster the given data points with information from multiple sources or features into their underlying subspaces, has a wide range of applications in the communities of data mining and pattern recognition. Compared with the single-view subspace clustering, it is challenging to efficiently learn the structure of the representation matrix from each view and make use of the extra information embedded in multiple views. To address the two problems, a novel correntropy-based multiview subspace clustering (CMVSC) method is proposed in this article. The objective function of our model mainly includes two parts. The first part utilizes the Frobenius norm to efficiently estimate the dense connections between the points lying in the same subspace instead of following the standard compressive sensing approach. In the second part, the correntropy-induced metric (CIM) is introduced to characterize the noise in each view and utilize the information embedded in different views from an information-theoretic perspective. Furthermore, an efficient iterative algorithm based on the half-quadratic technique (HQ) and the alternating direction method of multipliers (ADMM) is developed to optimize the proposed joint learning problem, and extensive experimental results on six real-world multiview benchmarks demonstrate that the proposed methods can outperform several state-of-the-art multiview subspace clustering methods.

In this paper, we investigate channel estimation for a large intelligent surface (LIS) aided multiple-input multiple-output (MIMO) communication system. Due to the close proximity of communication devices and LIS terminal, the desired channels can be modeled as line-of-sight channels which are ill-conditioned. To estimate these channel matrices with high quality, we propose a two-stage channel estimation method. In particular, we employ the conventional time-division duplexing based MIMO channel estimation technique in the first stage to estimate the direct MIMO channel between the end terminals. In the second stage, we propose to use a recently developed bilinear adaptive vector approximate message passing (BAdVAMP) algorithm to estimate ill-conditioned LIS channels. The BAdVAMP method has been shown to be accurate and robust for ill-conditioned dictionary learning problems in compressed sensing. We also propose a phase shift design for the LIS using the estimated channels. Specifically, we formulate an optimization problem that maximizes the total channel gain at the user. A closed-form expression to obtain the phase shift of each passive element in the LIS is also derived. Numerical results show that the proposed BAdVAMP based LIS channel estimation performs better than its counterpart scheme bilinear generalized AMP (BiGAMP), especially when channel matrices are ill-conditioned., 10 pages, 7 figures

Resolution probability is the most important indicator for signal parameter estimator, including estimating time delay, and joint Doppler shift and time delay. In order to get high-resolution probability, some procedures have been suggested such as compressed sensing. Based on the signal’s sparsity, compressed sensing has been used to estimate signal parameters in recent research. After solving ℓ0 norm Optimization problem, the methods would achieve high resolution. These methods all require high SNR. In order to improve the performance in low SNR, a novel implementation is proposed in this paper. We give a sparsity representation for the generalized matched filter output, or ambiguity function, while the former methods utilized the sparsity representation for channel response in time domain. By deconvolving the generalized matched filter output, 2-dimension estimation for Doppler shift and time delay would be gotten by greedy method, optimization method based on relaxation, or Bayesian method. Simulation demonstrates our method has better performance in low SNR than the method by the channel sparsity representation.

This paper investigates total variation minimization in one spatial dimension for the recovery of gradient-sparse signals from undersampled Gaussian measurements. Recently established bounds for the required sampling rate state that uniform recovery of all $s$-gradient-sparse signals in ${\mathbb{R}}^n$ is only possible with $m \gtrsim \sqrt{s n} \cdot{\operatorname{PolyLog}}(n)$ measurements. Such a condition is especially prohibitive for high-dimensional problems, where $s$ is much smaller than $n$. However, previous empirical findings seem to indicate that this sampling rate does not reflect the typical behavior of total variation minimization. The present work provides a rigorous analysis that breaks the $\sqrt{s n}$-bottleneck for a large class of “natural” signals. The main result shows that non-uniform recovery succeeds with high probability for $m \gtrsim s \cdot{\operatorname{PolyLog}}(n)$ measurements if the jump discontinuities of the signal vector are sufficiently well separated. In particular, this guarantee allows for signals arising from a discretization of piecewise constant functions defined on an interval. The key ingredient of the proof is a novel upper bound for the associated conic Gaussian mean width, which is based on a signal-dependent, non-dyadic Haar wavelet transform. Furthermore, a natural extension to stable and robust recovery is addressed.

Device-to-Device (D2D) communication has now become one of the most promising technologies in wireless communications of the Internet of Things (IoT). In view of the requirements on data security, response speed, signal decryption quality and storage cost of mobile devices in D2D networks, we propose chaotic deep network (CDN) to achieve secure transmission which is swifter, higher quality and lower cost. The proposed scheme consists of a prepositive nonrepetitive training procedure, a well-designed parallel encryption process, and a set of pretrained chaotic deep neural decryption networks. Benefiting from the utilization of deep learning methods, CDN achieves the swift and accurate decryption at a much lower sampling rate, which brings huge dimension reduction of both measurement matrices and ciphertext signals. Also, chaotic initial values and parameters are applied to matrix generation and network training, leading to great time reduction, storage saving and security improvement. In addition, CDN incorporates the frameworks of semitensor product (STP) and block-based image processing (BIP), which not only breaks through the dimension matching limitation of matrix multiplication by using STP but also maintains the parallelizable block-cipher mode of BIP. Proved by experiments, CDN at the sampling ratio of 25% achieves almost the same or even better peak signal to noise ratio compared to other 8 most frequently used methods at that of 50% for the same test images, and obtains better visual effects. When using a large-sized image of $2^{10}\times 2^{10}$ pixels for the experiments, CDN is dozens and even hundreds of times faster than those methods, while reduces the size of measurement matrix from a 500-kB level to a 3-kB level, and the size of compressed data to be transmitted can be reduced by more than 50% as well. Besides, the total key space is approximately $10^{93}$ . The adjacent pixel correlation is less than 0.01.

Two-way image communication in a wireless channel needs to be viable with channel properties such as transfer speed, energy-effective, time usage, and security because image capability consumes a huge space in the gadget and is quite effective. Is required in a manner. The figure goes through attacks. In addition, the quiesical issue for additional time of pressure is that the auxiliary interaction of pressure occurs through the dewar receiving extra time. To address these issues, compressed sensing emerges, which packs the image into hours of sensing, is generated in an expedient manner that reduces time usage and saves the use of data transfer capability, however Bomb in transmission. A variety of examinations cleared a way for dealing with security issues in compressive sensing (CS) through giving security as an alternative negotiation. In addition, univariate factors opted for CS as the issue of rearranging image quality is because of the aggregation of clutter. Along these lines related to the above issues, this paper proposed two-way image transmission to the Corvus Coron module, which presents an energy-effective with the CS model, as an inbuilt interaction in the CS transmission through the security framework. Receives what was designated as the pack-protected plot. Impeccable entertainment with the famous arbitrary network conjecture in CS. The result of the test is that the practical module presents energy-efficient and conserved transmission in the form of low error rate with low computational time.

We study the problem of downlink beamforming training and channel estimation for millimeter wave (mmWave) OFDM systems, where a hybrid analog and digital beamforming structure is employed at the transmitter (i.e., base station) and an omni-directional antenna or an antenna array is used at the receiver (i.e., user). To efficiently probe the channel, we form multiple directional beams simultaneously at the transmitter and steer them towards different directions. The objective is to devise the beam training sequence and develop an efficient algorithm to estimate the channel. By exploiting the sparse scattering nature of mmWave channels, the above problem is formulated as one of sparse encoding and signal recovery, which involves finding a sparse sensing matrix to compress the sparse channel and an efficient channel estimation algorithm to recover the sparse channel from compressive measurements. In this article, we propose a sparse bipartite graph code-based algorithm, where a set of bipartite graphs are employed to encode the sparse channel and a simple decoding procedure that relies on the presence of a No-Multiton-graph (NM-graph) is used to reconstruct the sparse channel. Theoretical analysis shows that our proposed method can help achieve a substantial training overhead reduction. Simulations are provided to show the effectiveness of the proposed algorithm and its performance advantage over compressed sensing-based methods.

Standard compressive sensing (CS) scenario assumes a single sparsifying basis used to reconstruct the signals from a small set of incoherent measurements. However, in many cases, the signal cannot be sparsely represented using a single transformation. Particularly, in ECG signal analysis, each signal segment is specific in nature and reflects different physical phenomena. Hence, using the same transformation for all segments may be inappropriate for efficient analysis and reconstruction. Moreover, in the CS scenario, it would be necessary to combine different transforms to achieve compact signal support and to provide successful reconstruction from randomly under-sampled data. This work proposes a hybrid CS reconstruction algorithm that combines different transform basis, based on the concept of orthogonal matching pursuit. The performance of the proposed approach is verified experimentally using the combination of the Fourier and the Hermite transform on the real ECG signals.

Millimeter wave (mmWave) communication is one viable solution to support Gbps sensor data sharing in vehicular networks. The use of large antenna arrays at mmWave and high mobility in vehicular communication make it challenging to design fast beam alignment solutions. In this paper, we propose a novel framework that learns the channel angle-of-departure (AoD) statistics at a base station (BS) and uses this information to efficiently acquire channel measurements. Our framework integrates online learning for compressive sensing (CS) codebook learning and the optimized codebook is used for CS-based beam alignment. We formulate a CS matrix optimization problem based on the AoD statistics available at the BS. Furthermore, based on the CS channel measurements, we develop techniques to update and learn such channel AoD statistics at the BS. We use the upper confidence bound (UCB) algorithm to learn the AoD statistics and the CS matrix. Numerical results show that the CS matrix in the proposed framework provides faster beam alignment than standard CS matrix designs. Simulation results indicate that the proposed beam training technique can reduce overhead by 80% compared to exhaustive beam search, and 70% compared to standard CS solutions that do not exploit any AoD statistics., Comment: 30 pages, 10 figures

The super-high-frequency band is used in the fifth-generation (5G) mobile communication system, and the introduction of massive multiple-input–multiple-output (MIMO) to 5G is being considered. In an environment with substantial propagation loss, such as that in the case of millimeter waves, massive MIMO can realize beamforming according to the position of terminal stations. Therefore, it is important to understand the direction of arrival of millimeter waves. In this letter, we clarify the relationship between power, delay time, and direction of arrival while focusing on the horizontal direction, using a 48-element massive array in the 20 GHz band in urban Japan. In addition, we obtain direction-of-arrival (DoA) estimation results using an iterative reduction threshold algorithm (ISTA), which is based on compressed sensing. It is shown that the dominant path can be estimated by using the ISTA even with approximately five elements.

The optimization problem with sparsity arises in many areas of science and engineering such as compressed sensing, image processing, statistical learning and data sparse approximation. In this paper, we study the dual-density-based reweighted $$\ell _{1}$$ ℓ 1 -algorithms for a class of $$\ell _{0}$$ ℓ 0 -minimization models which can be used to model a wide range of practical problems. This class of algorithms is based on certain convex relaxations of the reformulation of the underlying $$\ell _{0}$$ ℓ 0 -minimization model. Such a reformulation is a special bilevel optimization problem which, in theory, is equivalent to the underlying $$\ell _{0}$$ ℓ 0 -minimization problem under the assumption of strict complementarity. Some basic properties of these algorithms are discussed, and numerical experiments have been carried out to demonstrate the efficiency of the proposed algorithms. Comparison of numerical performances of the proposed methods and the classic reweighted $$\ell _1$$ ℓ 1 -algorithms has also been made in this paper.

Now-a-days due to advancements in technologies most of the applications in signal processing were using the models based on the sparse signal. Sub optimal strategies were used in these models to estimate the sparsest coefficients. In this work various algorithms were analyzed to address its optimal solutions. The sparsest solution can be found for the linear equations which are under determined. In this work, a complete study is carried out based on Compressive Sensing Matching Pursuit Back Tracking Iterative Hard Threshold (CMPBIHT) algorithm in the real-world scenario. As the BIHT algorithm may often fail to converge and its performance seems to be degraded if the conditions fail. To address these challenges, we have modified the BIHT algorithm to guarantee the convergence using the proposed method, even in this regime. Further the proposed CMPBIHT algorithm is evaluated and compared with the state of art techniques and it is observed that the proposed algorithm retains the similarities of the original algorithm. In this proposed model we have adopted the Compressive Sensing (CS) schemes along with Orthogonal Matching Pursuit (OMP). With this proposal we are able to solve the least squares problem for the new residual. We also investigated the reliability in sparse solutions along with compressive sensing techniques while decoding and over complete representations. An extensive research is carried out at the reconstruction side with the fundamental theme of CS, IHT and OMP techniques. The simulation results perform better efficiency at the reconstruction of the Gaussians signals by guaranteeing the productions in the residual error and noise. Further the proposed algorithm performs better at the reconstruction with nominal complexity in each of the iteration computationally.

The generalized space shift keying (GSSK) technique proposed for massive MIMO systems has significant advantages in terms of hardware costs. However, the maximum likelihood (ML) detection for GSSK is computationally intractable. Consequently many suboptimal schemes with varying performance complexity trade-offs like compressive sensing (CS) detectors are proposed. Nevertheless, the existing CS detectors estimate the transmitted signal only by single-stage, which results in a decrease in detection performance. In order to solve this issue, we proposed a novel detection framework in this letter. Different from the existing CS detectors, the framework includes two stages: rough and precise selection. In the rough selection stage, the Euclidean distance criterion is employed instead of the traditional inner product operation to determine an optimized superset of active antenna indices. The precise selection stage performs a further traversal search over the superset acquired by the first stage to obtain the final indices. The simulation results illustrate that the performance of the proposed scheme can exhibit significant performance enhancement over the existing CS detectors while retaining the low complexity advantage.

In this letter, a method is proposed for synthesizing sparse concentric ring arrays that use a minimum number of uniformly excited aperiodic concentric rings to match a predefined reference pattern. An auxiliary layout of concentric rings based on the Bessel function approximation of the circular array pattern is first synthesized using the off-grid compressive sensing framework and convex optimization to match the reference pattern using a minimum number of rings. Then, a density tapering technique is used to replace each ring with a ring of uniformly spaced isotropic radiating elements. Simulations were carried out to assess the effectiveness of the proposed method.

Many real-world problems can be modeled as sparse matrix recovery from two-dimensional (2D) measurements, which is recognized as one of the most important topics in signal processing community. Benefited from the roaring success of compressed sensing, many classical iterative algorithms can be directly applied or reinvented for matrix recovery, though they are computationally expensive. To alleviate this, we propose a neural network named 2D learned proximal gradient algorithm (2D-LPGA), which aims to quickly reconstruct the target matrix. Theoretical analysis reveals that if the parameters of the network satisfy certain conditions, it can reconstruct the sparse signal with linear convergence rate. Moreover, numerical experiments demonstrate the superiority of the proposed method over other classical schemes.

Energy-efficiency and reliability are vital metrics of the robustness of Wireless Sensor Networks (WSNs). Various data reduction techniques are used to improve them, among them compressive sensing (CS) is a data reduction technique used to recover extensive data from fewer samples in case of sparse representation of sensor-readings. Unfortunately, energy-efficiency and accuracy are contradictory metrics, as increased accuracy requires a large number of measurements, and data transmissions. Therefore, in this paper, a CS-based algorithm is proposed for efficient datatransfer through WSNs, which uses multiple objective genetic algorithms (MOGA) to optimize the number of measurements, transmission range, and the sensing matrix. The algorithm aims at striking the right balance between energy-efficiency and accuracy. It constructs a path in a multi hop manner based on the optimized values. Numerical simulations and experiments show that Paretofront, which is the output of MOGA, helps the user to select the right combination of the number of measurements and the transmission range fitting the application at hand, and to strike a good balance between energy efficiency and accuracy. The results also demonstrate the existence of measurement matrices which lower mutual coherency improve the accuracy of CS.

A stop condition without prior information, applied to compressed sensing recovery in millimeter-wave detection system considering the deceptive jamming signal, is proposed in this brief. The input observation signal is extended to the case consisting of the interference that is correlated to the recovery signal. By making the sufficient statistics of the input parameters and observation values generated from the iterative process, the recovery algorithm can be stopped more appropriately. The main contribution of this brief is to propose a stop criterion to improve the efficiency of the algorithm for random modulated signal recovery. Furthermore, different modulated parameters of the random modulated signal are investigated to verify the feasibility and adaptability of the proposed method. The comparable results show greater performance and the algorithm efficiency is improved by 53.2%.

Grant-free random access is a key enabler in massive machine-type communications (mMTC) to reduce signalling overhead and latency thereby improving the energy efficiency. One of its main challenges lies in joint user activity identification and channel estimation (JUICE). Due to the sporadic mMTC traffic, JUICE can be solved as a compressive sensing (CS) problem. We address CS-based JUICE in uplink with single-antenna transmitters and a multiantenna base station under spatially correlated fading channels. We formulate a novel CS problem that utilizes prior information on the second order statistics of the channel of each user to improve the performance. We propose a method based on alternating direction method of multipliers to solve the JUICE efficiently. The simulation results show that the proposed method significantly improves the user identification accuracy and channel estimation performance with lower signalling overhead as compared to the baseline schemes.

In this letter, an adaptively-regularized iterative reweighted least squares algorithm with sparsity bound learning is designed to efficiently recover sparse signals from measurements. In particular, at each iteration the support of estimated signal is exploited to construct a sparsity-promoting matrix and, then, formulate an adaptive regularization. Since this algorithm could learn sparsity information at each iteration, it ensures a sparser and sparser solution, and the mean squared error analysis corroborates its convergence. Experimental results demonstrate that the proposed algorithm outperforms other typical ones in terms of sparsity level, compressive ratio, and detection probability.

Although wireless sensor networks are considered as one of the prominent solutions for flood monitoring, the energy constraint nature of the sensors is still a technical challenge. In this letter, we tackle this problem by proposing a novel energy-efficient remote flood monitoring system, enabled by compressive sensing. The proposed approach compressively captures water level data using i) a random block-based sampler, and ii) a gradient-based compressive sensing approach, at a very low rate, exploiting water level data variability over time. Through extensive experiments on real water-level dataset, we show that the number of packet transmissions as well as the size of packets are significantly reduced. The results also demonstrate significant energy reduction in sensing and transmission. Moreover, data reconstruction from compressed samples are of high quality with negligible degradation, compared to classic compression techniques, even at high compression rates.

Unlike traditional tensor decompositions which model low-rankness in the original domain, the recently proposed tensor $*_L$ -Singular Value Decomposition ( $*_L$ –SVD) casts a new light on tensor analysis by exploiting low-rankness in the spectral domain. For convexized rank minimization within the framework of $*_L$ –SVD, the tensor $*_L$ –Tubal Nuclear Norm ( $*_L$ –TNN) outperforms classical tensorial extensions of matrix nuclear norm in many applications. In this paper, we first generalize $*_L$ –TNN to the $*_L$ -Spectral $k$ -Support Norm ( $*_L$ -SpSN- $k$ ) as a new low-rank regularizer, and then adopt it to formulate two estimators for tensor recovery from noisy linear observations. Further, statistical performance of the proposed estimators is analyzed by establishing both deterministic and non-asymptotic upper bounds on the estimation error, which indicates that the proposed tensor Dantzig selector enjoys near-optimal estimation error for tensor compressive sensing and tensor completion. Moreover, proximal operator of the proposed norm is derived and embeded in an efficient algorithm to compute the estimators. Experiments on synthetic datasets verify correctness of the proposed error bounds and image inpainting results demonstrate superiority of the proposed estimators.

Image steganography plays a vital role in securing secret data by embedding it in the cover images. Usually, these images are communicated in a compressed format. Existing techniques achieve this but have low embedding capacity. Enhancing this capacity causes a deterioration in the visual quality of the stego-image. Hence, our goal here is to enhance the embedding capacity while preserving the visual quality of the stego-image. We also intend to ensure that our scheme is resistant to steganalysis attacks. This paper proposes a Compressed Sensing Image Steganography (CSIS) scheme to achieve our goal while embedding binary data in images. The novelty of our scheme is the combination of three components in attaining the above-listed goals. First, we use compressed sensing to sparsify cover image block-wise, obtain its linear measurements, and then uniquely select permissible measurements. Further, before embedding the secret data, we encrypt it using the Data Encryption Standard (DES) algorithm, and finally, we embed two bits of encrypted data into each permissible measurement. Second, we propose a novel data extraction technique, which is lossless and completely recovers our secret data. Third, for the reconstruction of the stego-image, we use the least absolute shrinkage and selection operator (LASSO) for the resultant optimization problem. We perform experiments on several standard grayscale images and a color image, and evaluate embedding capacity, PSNR value, mean SSIM index, NCC coefficients, and entropy. We achieve 1.53 times more embedding capacity as compared to the most recent scheme. We obtain an average of 37.92 dB PSNR value, and average values close to 1 for both the mean SSIM index and the NCC coefficients, which are considered good. Moreover, the entropy of cover images and their corresponding stego-images are nearly the same.

In cognitive radio applications, a robust detector is essentially required for the determination of spectrum sensing. Gerschgorin radii and centers ratio (GRCR) detector is a robust detector for cooperative spectrum sensing techniques. Covariance matrix generates the test statistics for signal established from one or supplementary sources. Though the method is robust against noise uncertainty, it is not suitable for wideband sensing due to the complexity associated with the computation of covariance matrix. To tackle this challenge of extensive communication cost and high processing time complexity, an efficient GRCR detector using compressive sensing with non-reconstruction is proposed here. This method introduces relevance for multiple received signals by using same measurement matrix to all received signals. Computational complexity is analysed and the proposed method is compared with the existing method through ROC simulations, and it shown that the proposed method performs better even in the low SNR range of -20 dB. Throughput analysis is validated through simulations.

In this paper, we investigate jointly sparse signal recovery and jointly sparse support recovery in Multiple Measurement Vector (MMV) models for complex signals, which arise in many applications in communications and signal processing. Recent key applications include channel estimation and device activity detection in MIMO-based grant-free random access which is proposed to support massive machine-type communications (mMTC) for Internet of Things (IoT). Utilizing techniques in compressive sensing, optimization and deep learning, we propose two model-driven approaches, based on the standard auto-encoder structure for real numbers. One is to jointly design the common measurement matrix and jointly sparse signal recovery method, and the other aims to jointly design the common measurement matrix and jointly sparse support recovery method. The proposed model-driven approaches can effectively utilize features of sparsity patterns in designing common measurement matrices and adjusting model-driven decoders, and can greatly benefit from the underlying state-of-the-art recovery methods with theoretical guarantee. Hence, the obtained common measurement matrices and recovery methods can significantly outperform the underlying advanced recovery methods. We conduct extensive numerical results on channel estimation and device activity detection in MIMO-based grant-free random access. The numerical results show that the proposed approaches provide pilot sequences and channel estimation or device activity detection methods which can achieve higher estimation or detection accuracy with shorter computation time than existing ones. Furthermore, the numerical results explain how such gains are achieved via the proposed approaches., Comment: 16 pages, 12 figures, to appear in JSAC

In frequency-division duplexing mode, accurate channel state information (CSI) needs to be acquired at the base station by feedback from the terminals. However, the costly feedback overhead generated by large-scale arrays poses an arduous challenge to the traditional feedback scheme. In this letter, we propose a sparse learning-based CSI feedback method in a compressive sensing framework for massive MIMO systems. The key insights are to learn the sparse structure of CSI through the recursive least squares algorithm and process a continuous update of the sparse basis. Accordingly, a CSI sparse characteristic adaptive dictionary is constructed. The simulation results reveal that the proposed scheme achieves excellent performance in terms of both compression efficacy and recovery accuracy.

Electronically steerable parasitic array radiator (ESPAR) antenna is a novel low-cost technique to gain comparable diversity order to that of using multiple antennas while maintaining one radio frequency (RF) front-end, low power consumption, and simple wiring at the mobile receiver. It has huge potential to realize high energy efficiency for multiple and massive antennas systems. The main drawback of the ESPAR based OFDM system is that the channel estimation (CE) usually should be realized in time-domain with a huge computational complexity (CC) because the received signal to each parasitic element is overlapped each other both in frequency and time domain. This article will propose three ways to reduce the complexity of CE for the ESPAR-OFDM system. The parallel multi-column compressive sensing (CS) algorithm was first introduced to detect all locations of channel impulse response simultaneously using one small segment of sensing matrix. Furthermore, by exploiting the symmetrical properties of Digital Fourier transform (DFT), the size of matrix to decrease the CC of matrix operation. Finally, by selecting a small set of row vectors of sensing matrix at the receiver side, the CC involved in CS algorithm can be reduced. From the analysis and simulated results, the proposed method can obtain more than 90% CC reduction for CE of ESPAR-OFDM receiver can be confirmed.

Recently, channel sparsity has been considered as a nature of wireless channels in many researches of intelligent communications, and an increasing number of investigations are conducted by exploiting sparsity of wireless channels, such as deep-learning-based channel estimation and compressive sensing. Growing evidence from channel measurements show that the sparse or approximate sparse distribution assumption of wireless channel is reasonable, however, the observed sparse structure in wireless channels is mostly based on intuitive analysis. Several fundamental aspects of channel sparsity have not been well investigated, and among them, we find that choosing a reasonable measure of channel sparsity has not been fully addressed. To fill the gap, this paper presents several measures for wireless channel sparsity from propagation view and validates them based on realistic channel measurements and data mining methods. Following the spirit that a sparse representation implies a small number of elements contain a large proportion of the energy, the four measures of the number of multipath components (MPCs), channel degrees of freedom (DoF), the Gini index , and the Ricean ${K}$ factor are selected as the potential measures of channel sparsity and fully compared, and the channel diversity measure is used as an indicator of channel sparsity to show the inter-dependency between different measures and channel sparsity. The measurement-based analysis shows that the channel DoF and Gini index provide the best sensitivity and accuracy for measuring channel sparsity, whereas the number of MPCs has the worst performance. Moreover, the widely used channel parameter of Ricean ${K}$ factor is found to have fairly good sensitivity to channel sparsity and can be used for channel sparsity evaluation. The results in the paper can be used to accurately measure sparsity of wireless channel for the design of intelligent communications.

A novel sparsity adaptive compressed sensing (CS) scheme based on Reed-Solomon (RS) codes is proposed to reduce the amount of sampled data, which can adjust the sampling rate adaptively to achieve data sampling and reconstruct the original data accurately by any decoding algorithm on the finite field. Moreover, the proposed sparsity adaptive reconstruction architecture can greatly improve the data reconstruction efficiency of the proposed CS scheme. The simulation results show that the sparsity adaptive scheme can reduce 83.6% of the sampled data. The results illustrate that the proposed architecture needs about 95k gates and operates at 500 MHz to achieve the throughout of 4.0 Gb/s, which can greatly improve the efficiency of the communication system. Meanwhile, it is at least 21.4% more area-efficient compared with previously reported fixed sampling rate architecture based on RS codes.

We address the joint device activity detection and channel estimation (JACE) problem in a massive MIMO connectivity scenario in which a large number of mobile devices are connected to a base station (BS), while only a small portion are active at any given time. The main objective is to provide an efficient transmission and detection scheme with both spatial and temporal correlations. We formulate JACE as a multiple measurement vector (MMV) problem with correlated entries in the vectors to be estimated. We propose an MMV form of the orthogonal approximate message passing algorithm (OAMP-MMV). We derive a group Gram-Schmidt orthogonalization (GGSO) procedure for the realization of OAMP-MMV. We outline a state evolution (SE) procedure for OAMP-MMV and examine its accuracy using numerical results. We also compare OAMP-MMV with existing alternatives, including AMP-MMV and GTurbo-MMV. We show that OAMP-MMV outperforms AMP-MMV when pilot sequences are generated using Hadamard pilot matrices. Such a pilot design is attractive due to the low-cost signal processing technique using the fast Hadamard transform (FHT). We also show that OAMP-MMV outperforms GTurbo-MMV in correlated channels.

As the Internet of Things thrives, monitors and cameras produce tons of image data every day. To efficiently process these images, many compressed imaging frameworks are proposed. A compressed imaging framework comprises two parts, image signal measurement and reconstruction. Although a plethora of measurement devices have been designed, the development of the reconstruction is relatively lagging behind. Nowadays, most of existing reconstruction algorithms in compressed imaging are optimization problem solvers based on specific priors. The computation burdens of these optimization algorithms are enormous and the solutions are usually local optimums. Meanwhile, it is inconvenient to deploy these algorithms on cloud, which hinders the popularization of compressed imaging. In this article, we dive deep into the random projection to build reconstruction algorithms for compressed imaging. We first fully utilize the information in the measurement procedure and propose a combinatorial sparse random projection (SRP) reconstruction algorithm. Then, we generalize the SRP to a novel distributed algorithm called Cloud-SRP (CSRP), which enables efficient reconstruction on cloud. Moreover, we explore the combination of SRP with conventional optimization reconstruction algorithms and propose the Iterative-SRP (ISRP), which converges to a guaranteed fixed point. With minor modifications on the naive optimization algorithms, the ISRP yields better reconstructions. Experiments on real ghost imaging reconstruction reveal that our algorithms are effective. And simulation experiments show their advantages over the classical algorithms.

Greater compression ratio can be achieved while compressing images and videos by using the technique called compressive sensing or compressed sensing (CS). In CS, sparsity of the signal is exploited in order to achieve high compression. CS-based compression converts the images and video frames to a set of $$m

In this study, a new approach of random access and pilot allocation in crowded scenarios of massive multi-input multi-output (MIMO) systems is proposed. When the number of users in a cell is more than number of orthogonal pilots, random access to pilots (RAP) is a promising solution to solve the massive access problem of users; though the collision of pilots is a by-product of this method. There are several methods for pilot collision resolution such as strongest user collision resolution (SUCR), but they have one major limitation; i.e. they cannot serve users more than the number of orthogonal pilots simultaneously in coherent transmission mode. In this paper, angle of arrival (AOA) and angular spread (AS) of the received pilots in a compressed sensing approach are examined by applying sparsity of massive MIMO channels in angular domain. That allows to allocate same orthogonal pilot to non-overlapped users in spatial domain for coherent data transmission. By applying this approach in newly proposed protocol (SBPA), the limitation in number of adopted simultaneous users in crowded scenarios of a massive MIMO system would be resolved. Numerical results show improvement in access failures rate compared to SUCR in crowded massive MIMO systems.

Compressive sensing (CS) aims to accurately reconstruct high-dimensional signals from a small number of measurements by exploiting signal sparsity and structural priors. However, signal priors utilized in existing CS reconstruction algorithms rely mainly on hand-crafted design, which often cannot offer the best sparsity-undersampling tradeoff because high-order structural priors of signals are hard to be captured in this manner. In this article, a new recovery guarantee of the unified CS reconstruction model-weighted $\ell _{1}$ minimization (WL1M) is derived, which indicates universal priors could hardly lead to the optimal selection of the weights. Motivated by the analysis, we propose a deep unfolding network for the general WL1M model. The proposed deep unfolding-based WL1M (D-WL1M) integrates universal priors with learning capability so that all of the parameters, including the crucial weights, can be learned from training data. We demonstrate the proposed D-WL1M outperforms several state-of-the-art CS-based methods and deep learning-based methods by a large margin via the experiments on the Caltech-256 image data set.

Recently it has been shown that when Principal Component Analysis is applied as a dictionary learning technique to Compressive Sensing-based data aggregation, using a Deterministic Node Selection method for data collection in Wireless Sensor Networks can outperform Random Node Selection ones. In this paper, a new scheduling method for selection of measured nodes in a data collection round, called “Information-Based Deterministic Node Selection”, is proposed. Simulation results for synthetic and real data sets show that the proposed method outperforms a reference DNS method in terms of energy consumption per reconstruction error. Correlation (or covariance) matrix estimation is necessary for DNS strategies which are accomplished by gathering data from all network nodes in a few initial time slots of collection rounds. In this regard, we also propose the use of a particular type of shrinkage estimator in preference to the standard correlation matrix estimator. With the aid of the new estimator, we can obtain data correlations with the same accuracy of standard estimator while we need less number of observations. Our numerical experiments demonstrate that when the number of measured nodes is less than 50% of the total nodes, using shrinkage estimator causes extra energy savings in sensor nodes.

Single-snapshot direction-of-arrival (DOA) estimation plays an important role in dynamic target detection and tracking applications. Because a single-snapshot signal provides few information for statistics calculation, recently compressed sensing (CS) theory is applied to solve single-snapshot DOA estimation, instead of the traditional DOA methods based on statistics. However, when the unknown sources are closely located, the spatial signals are highly correlated, and its overcomplete dictionary is made up of dense grids, which leads to a serious decrease in the estimation accuracy of the CS-based algorithm. In order to solve this problem, this paper proposed a two-step compressed sensing-based algorithm for the single-snapshot DOA estimation of closely spaced signals. The overcomplete dictionaries with coarse and refined grids are used in the two steps, respectively. The measurement matrix is constructed by using a very sparse projection scheme based on chaotic sequences because chaotic sequences have determinism and pseudo-randomness property. Such measurement matrix is mainly proposed for compressing the overcomplete dictionary in preestimation step, while it is well designed by choosing the steering vectors of true DOA in the accurate estimation step, in which the neighborhood information around the true DOAs partly solved in the previous step will be used. Monte Carlo simulation results demonstrate that the proposed algorithm can perform better than other existing single-snapshot DOA estimation methods. Especially, it can work well to solve the issues caused by closely spaced signals and single snapshot.

Array diagnosis is an important tool for detecting and correcting array antenna failures. In this letter, a high-precision planar array diagnosis method based on the Bayesian compressive sensing (BCS) theory is proposed. The model of a near-field signal with a spherical wavefront is used to acquire the measured data. Then, the difference between the beam pattern of the reference array and the array under test is obtained. The array diagnosis problem involves finding the difference between the weights of the reference and of the array under test with known differences between patterns. This problem is reformulated in a Bayesian compressive sensing framework and can be efficiently solved using a fast relevance vector machine. Numerical results confirm the superiority of the proposed method in terms of diagnostic accuracy and computational efficiency than those in previous studies.