Compressive Sensing Theory Research Articles

Multi-angle speed-of-sound imaging with sparse sampling to characterize medical tissue properties

Medical Speed-of-sound (SoS) imaging, which can characterize medical tissue properties better by quantifying their different SoS, is an effective imaging method compared with conventional B-mode ultrasound imaging. As a commonly used diagnostic instrument, a hand-held array probe features convenient and quick inspection. However, artifacts will occur in the single-angle SoS imaging, resulting in indistinguishable tissue boundaries. In order to build a high-quality SoS image, a number of raw data are needed, which will bring difficulties to data storage and processing. Compressed sensing (CS) theory offers theoretical support to the feasibility that a sparse signal can be rebuilt with random but less sampling data. In this study, we proposed an SoS reconstruction method based on CS theory to process signals obtained from a hand-held linear array probe with a passive reflector positioned on the opposite side. The SoS reconstruction method consists of three parts. Firstly, a sparse transform basis is selected appropriately for a sparse representation of the original signal. Then, considering the mathematical principles of SoS imaging, the ray-length matrix is used as a sparse measurement matrix to observe the original signal, which represents the length of the acoustic propagation path. Finally, the orthogonal matching pursuit algorithm is introduced for image reconstruction. The experimental result of the phantom proves that SoS imaging can clearly distinguish tissues that show similar echogenicity in B-mode ultrasound imaging. The simulation and experimental results show that our proposed method holds promising potential for reconstructing precision SoS images with fewer signal samplings, transmission, and storage.

An Off-Grid Compressive Sensing Algorithm Based on Sparse Bayesian Learning for RFPA Radar

In the application of Compressive Sensing (CS) theory for sidelobe suppression in Random Frequency and Pulse Repetition Interval Agile (RFPA) radar, the off−grid issues affect the performance of target parameter estimation in RFPA radar. Therefore, to address this issue, this paper presents an off−grid CS algorithm named Refinement and Generalized Double Pareto (GDP) distribution based on Sparse Bayesian Learning (RGDP−SBL) for RFPA radar that utilizes a coarse−to−fine grid refinement approach, allowing precise and cost−effective signal recovery while mitigating the impact of off−grid issues on target parameter estimation. To obtain a high-precision signal recovery, especially in scenarios involving closely spaced targets, the RGDP−SBL algorithm makes use of a three−level hierarchical prior model. Furthermore, the RGDP−SBL algorithm efficiently utilizes diagonal elements during the coarse search and exploits the convexity of the grid energy curve during the fine search, therefore significantly reducing computational complexity. Simulation results demonstrate that the RGDP−SBL algorithm significantly improves signal recovery performance while maintaining low computational complexity in multiple scenarios for RFPA radar.

Three-dimensional optical watermarking scheme using compressed sensing in integral imaging system

The elemental image array (EIA) is a special form of the integral imaging three-dimensional (3D) display system for recording, transmitting and displaying 3D image information, which consists of a series of small image units taken from different perspectives. There is an urgent need for protecting the copyright of EIA to improve security and anti-aggressive capability. In this paper, we propose a 3D optical watermarking scheme for integral imaging system based on compressed sensing (CS) theory. The proposed watermarking scheme consists of two subsystems, one is the EIA watermark compression and embedding subsystem, and the other is the EIA watermark extraction and display subsystem. CS theory using by phase coding mask is applied for realizing the EIA encryption and compression simultaneously, which can reduce the total amount of embedded watermark information, expand the space of secret keys and make the system more flexible and compact. The experimental results are presented to demonstrate the feasibility and effectiveness of the proposed method. The parameters of the integral imaging watermark encryption system, including the focal length and aperture of the lenslet array, the object distance, the wavelength, the diffraction distance, and the measurement matrix of CS, can all be used as the secret keys. The method proposed in this paper can effectively broaden the keys space and enhance the security of the integral image 3D display system.

Unmanned Aerial Vehicle-Based Compressed Data Acquisition for Environmental Monitoring in WSNs.

With the increasing concerns for the environment, the amount of the data monitored by wireless sensor networks (WSNs) is becoming larger and the energy required for data transmission is greater. However, sensor nodes have limited storage capacity and battery power. The WSNs are faced with the challenge of handling larger data volumes while minimizing energy consumption for transmission. To address this issue, this paper employs data compression technology to eliminate redundant information in the environmental data, thereby reducing energy consumption of sensor nodes. Additionally, an unmanned aerial vehicle (UAV)-assisted compressed data acquisition algorithm is put forward. In this algorithm, compressive sensing (CS) is introduced to decrease the amount of data in the network and the UAV serves as a mobile aerial base station for efficient data gathering. Based on CS theory, the UAV selectively collects measurements from a subset of sensor nodes along a route planned using the optimized greedy algorithm with variation and insertion strategies. Once the UAV returns, the sink node reconstructs sensory data from these measurements using the reconstruction algorithms. Extensive experiments are conducted to verify the performance of this algorithm. Experimental results show that the proposed algorithm has lower energy consumption compared to other approaches. Furthermore, we employ different data reconstruction algorithms to recover data and discover that the data can be better reconstructed in a shorter time.

Void fraction measurement of gas–liquid two-phase flow based on compressed sensing theory and capacitively coupled electrical resistance tomography system

Capacitively coupled electrical resistance tomography (CCERT) is an innovative technique for electrical resistance tomography based on capacitively coupled contactless conductivity detection (C4D). Despite its potential, there are only a few studies on image reconstruction algorithms for CCERT. To address this, a CCERT measurement system is developed, and the compressed sensing (CS) theory is applied to the inverse problem imaging of CCERT to improve the image reconstruction quality and speed. Firstly, a mathematical CCERT image reconstruction model is constructed under CS theory and three algorithms under CS theory are employed to solve the convex optimization problem of the reconstruction model. Then a thresholding operation is applied to obtain the post-processed image and compared it with the classical linear back projection and Landweber algorithms. The simulation results demonstrate that the Barzilai–Borwein gradient projection for sparse reconstruction (GPSR-BB) algorithm yields more satisfactory imaging results than the other four algorithms. Additionally, three sensitivity matrix optimization methods for GPSR-BB algorithm are compared and find that the new method of screening the rows of the sensitivity matrix to zero is more effective than the other two common optimization methods in terms of reconstructed image quality. Finally, the static experiments of void fraction measurement are conducted using the developed CCERT system. The results indicated that the absolute error of void fraction measurement by GPSR-BB algorithm was less than 6.59% in the range of void fraction from 0.90% to 66.29%.

A novel block compressive sensing algorithm for SAR image formation

Compressive Sensing (CS) theory has been used for Synthetic Aperture Radar (SAR) imaging due to the sparsity feature of SAR images. Therefore, some well-known CS algorithms like Orthogonal Matching Pursuit (OMP) and Regularized OMP (ROMP) methods have been employed for SAR image formation with a very small number of samples. On the other hand, it has been shown that the SAR signal is consistent with the definition of block sparsity. Hence, compressive sensing methods employing block structure, known as Block Compressive Sensing (BCS), are presented and used for SAR image formation to achieve more accuracy with a smaller number of samples. In this paper, first, a new BCS-based algorithm, namely, Block Norm Regularized Orthogonal Matching Pursuit (BNROMP), is introduced which can be used in all BCS applications. Then, this novel method is used for SAR image formation to achieve more accuracy and excellent resolution with a small number of samples. The simulation results for the synthesized data, as well as real data, show that by using the novel BNROMP method, we could form SAR images with higher quality, as compared to those for the standard image formation algorithms and other CS-SAR or BCS-SAR methods.

Diesel Engine Noise Source Visualization by Using Compressive Sensing Algorithms

To identify sound source locations by using Near-field Acoustical Holography (NAH), a large number of microphone measurements is generally required in order to cover the source region and ensure a sufficiently high spatial sampling rate: it may require hundreds of microphones. As a result, such measurements are costly, a fact which has limited the industrial application of NAH to identify sound source locations. However, recently, it has been shown possible to identify concentrated sound sources with a limited number of microphone measurement based on Compressive Sensing theory. In the present work, sound radiation from the front face of a diesel engine was measured by using one set of measurements from a thirty-five-channel combo-array placed in front of the engine. The locations of significant noise sources were then identified by using two algorithms: i.e., l1-norm minimization and a hybrid approach which combined Wideband Acoustical Holography (WBH) and l1-norm minimization. It was found that both algorithms can successfully localize and visualize the major noise sources over a broad range of frequencies, even though using a relatively small number of microphones. Finally, comments are made on sound field reconstruction differences between the two algorithms.

Optimal Sensor Positioning for the Sparse Measurement in the Acoustic Reconstruction of a Large Source

Near-field acoustic holography (NAH) has become an effective tool for acoustic source identification. It usually requires many microphones near the source surface to catch sufficient evanescent waves for good spatial resolution. Besides, such a measurement is time-consuming and uneconomical in practice; standard measurements using densely and uniformly populated sensors are sometimes impossible when dealing with massive sources. Eventually, the compressive sensing (CS) technique has been suggested for NAH, which employs a sparse number of sensors. Most existing works in NAH based on compressive sensing theory have focused on developing acoustic models and algorithms; In contrast, less attention has been paid to the best practice of sensor placement. The present study aims to propose and validate the methods for the optimal selection of sparse measuring points using the compression technique for NAH. Due to the small number of measuring sensors, the transfer matrix between source and hologram points becomes underdetermined. Under such a data condition, even though every piece of data would be felt precious for the reconstruction, the information from some sensors should be discarded further because not all data provide meaningfully independent information. To this end, effective independence and singular-value monitoring methods are used to test the selection of the optimal sensor position from a set of candidate positions. The former chooses non-redundant measurement data, whereas the latter keeps the low condition number of the transfer matrix. Simulation results with vibrating plates show that optimized sensor positions could effectively facilitate the optimality of the approximate solution for CS theory compared to uniformly or randomly distributed measurements. It is because the established transfer matrix has the lowest condition number due to being sparser and more independent sensor positions. Experimental results exhibit a better reconstruction error (10–40%) at 200–2,000 Hz when the sensor positions are optimized than the uniform or random selection approaches.

Convergence rates for the joint solution of inverse problems with compressed sensing data

Compressed sensing (CS) is a powerful tool for reducing the amount of data to be collected while maintaining high spatial resolution. Such techniques work well in practice and at the same time are supported by solid theory. Standard CS results assume measurements to be made directly on the targeted signal. In many practical applications, however, CS information can only be taken from indirect data related to the original signal by an additional forward operator. If inverting the forward operator is ill-posed, then existing CS theory is not applicable. In this paper, we address this issue and present two joint reconstruction approaches, namely relaxed co-regularization and strict co-regularization, for CS from indirect data. As main results, we derive error estimates for recovering and . In particular, we derive a linear convergence rate in the norm for the latter. To obtain these results, solutions are required to satisfy a source condition and the CS measurement operator is required to satisfy a restricted injectivity condition. We further show that these conditions are not only sufficient but even necessary to obtain linear convergence.

Model calibration for compressive sensing based linear antenna array fault diagnosis

ABSTRACT The Compressive Sensing (CS) theory has been widely studied as it requires only a small number of measurements to identify faulty elements of antenna arrays. However, the model for linear antenna array fault diagnosis based on CS is much sensitive to model mismatch and the identification results usually turn out to be much worse than expected in the practical situation. In this study, the model mismatch for linear antenna array fault diagnosis is first analyzed and then a CS model calibration method is proposed to improve the performance of the CS-based linear antenna array fault diagnostic method by solving a convex optimization model. Numerical results demonstrate that the calibrated CS model is much more accurate in identifying faulty antenna elements under model mismatch and noise than the traditional one.

Adaptive High-Resolution Imaging Method Based on Compressive Sensing.

Compressive sensing (CS) is a signal sampling theory that originated about 16 years ago. It replaces expensive and complex receiving devices with well-designed signal recovery algorithms, thus simplifying the imaging system. Based on the application of CS theory, a single-pixel camera with an array-detection imaging system is established for high-pixel detection. Each detector of the detector array is coupled with a bundle of fibers formed by fusion of four bundles of fibers of different lengths, so that the target area corresponding to one detector is split into four groups of target information arriving at different times. By comparing the total amount of information received by the detector with the threshold set in advance, it can be determined whether the four groups of information are calculated separately. The simulation results show that this new system can not only reduce the number of measurements required to reconstruct high quality images but can also handle situations wherever the target may appear in the field of view without necessitating an increase in the number of detectors.

Thermal Sensor Placement for Multicore Systems Based on Low-Complex Compressive Sensing Theory

As the complexity of the multicore system grows, the large workload diversity results in serious thermal problems. In a practical way, the number of placed thermal sensors is usually limited due to the manufacturing cost. In recent years, the compressive sensing (CS) theory is proven as an efficient way to reconstruct the original signal by using fewer sampling data. However, due to the high computational complexity during the signal reconstruction, the CS theory is not appropriate to apply to the real-time temperature monitoring in the current multicore system. In this article, we propose a grid-based sensor placement approach to placement the number-limited thermal sensors on the target multicore system. On the other hand, we adopt the matrix inversion bypass (MIB) property to reduce the computational complexity of two widely used signal reconstruction approaches in CS theory [i.e., the orthogonal matching pursuit (OMP) and stagewise OMP (StOMP)]. Due to the characteristic of random sampling in CS theory, the complexity of thermal sensor placement for multicore systems can be reduced significantly. In addition, the proposed MIB-based temperature reconstruction method helps to satisfy the requirement of real-time temperature estimation. The experimental results show that the proposed approach can reduce 57%–93% average full-system temperature reconstruction error compared with the previous non-CS-based approaches. Besides, we can also reduce 22%–41% computing latency compared with the current CS-based reconstruction algorithm. Due to the MIB-based operation, we can bypass the matrix inversion operation for temperature reconstruction. Therefore, the hardware overhead of the temperature reconstruction unit can be reduced significantly. Compared with the conventional approaches, we can reduce 24%–87% area overhead and improve 50%–220% hardware efficiency.

A novel fault diagnosis method of wind turbine bearings based on compressed sensing and AlexNet

The bearing is the core component which ensures the normal operation of the wind turbine. The vibration signal based on fault diagnosis is non-linear, non-stationary and causes serious noise pollution. Conventional methods are difficult to demodulate, and the operation is complex. With the increasing capacity of wind turbine assemblers, the signal samples based on Shannon sampling theorem are also increasing, which brings great pressure to data transmission and storage. Deep learning based on big data-driven for wind turbine running condition monitoring plays an effective role in the field of fault diagnosis. However, data training depends on a large amount of data and takes a long time. Therefore, a novel fault diagnosis method based on compressed sensing (CS) and AlexNet is proposed. This method used small sample data. Firstly, the signal is sparsely processed by stagewise orthogonal matching pursuit algorithm, so that the sparse signal is convenient for signal transmission and can alleviate the pressure of signal storage. Secondly, the CS theory is used to restore the signal and reduce the noise of the signal. Thirdly, a fault-free signal is selected and compared with the fault signal with the same phase to obtain the characteristic residual signal. Next, they are subjected to continuous wavelet transform to obtain the wavelet spectrum of the signal. Finally, it is constructed into a pseudo-trichromatic graph and put into the improved AlexNet network to obtain the effect of fault diagnosis. Compared with other methods, experiment shows that the proposed method has higher accuracy in wind turbine fault diagnosis

Energy Aware Talented Clustering with Compressive Sensing (TCCS) for Wireless Sensor Networks

Wireless sensor networks (WSNs) are networks of sensor nodes that interact wirelessly to gather information about the surrounding environment. Nodes are often low-powered and dispersed in an ad hoc, decentralized manner. Although WSNs have gained in popularity, they still have several serious shortcomings, like limited battery life and bandwidth. In this paper, the cluster head (CH) selection, the Compressive Sensing (CS) theory, the Connection-based Decentralized Clustering (CDC), the relay node selection, and the Multi Objective Genetic Algorithm (MOGA)are all taken into account The initial stage provided a theoretical revision to the concepts of network construction, compressive sensing, and MOGA, which impacted the improvement of network lifetime. In the second stage developed a novel model such as Energy Aware Talented Clustering with Compressive Sensing (TCCS) for the sensor network. This approach considers increasing longevity but also raises the network's overall quality of service (QoS). In the analysis, the TCCS model is applied to both the centralized and distributed networks and compared with the existing methods. When compared to the previous methods, the simulation results show that the proposed work performs better in terms of the calculation of maximum packet delivery ratio of 93.93 percent, minimum energy consumption of 8.04J, maximum energy efficiency of 91.04 percent, maximum network throughput of 465.51kbps, minimum packet loss of 282 packets, and minimum delay of 63.82 msec.

Separable compressed coded aperture imaging via singular value decomposition

Compressed Sensing (CS) encodes a signal or image into a relatively small number of incoherent linear measurements. Compressed Imaging (CI), as the application and promotion of CS theory in imaging, which exploits the sparsity of most images in nature and is expected to overcome some shortcomings of existing imaging theories. However, one of the main difficulties in implementing CI is that it involves a large amount of data, which has a profound impact on the complexity of optical design, calibration, data storage requirements, and computational burden. Compressed Coded Aperture Imaging (CCAI) is a practical CI method, which can reconstruct the true image from a single, low-resolution, noisy measurements, obtained under the convolution with a coded aperture and sampling operation. However, the key problem that existed in CCAI is the huge requirements for the storage of the measurement matrix and the computation burden for algorithm to recover the original image. As a result, CCAI is only limited to relatively small-size images. In this paper, separable compressed sensing (SCS) is introduced into CCAI, and the only separable compressed coded aperture imaging (SCCAI) method is proposed. The singular value decomposition (SVD) of the two separated measurement matrices are performed, and the measurement matrices and measurements are both optimized, which is the SCCAI-SVD method proposed in this paper. Our method has the advantages of optical implementation and computational feasibility. Numerical results demonstrate the superiority of our proposed method.

Modification of reconstruction threshold algorithm in two-dimensional LFMCW compressive radar

Nowadays, the Compressive Sensing theory has an important effect on many communication system’s performances, and one of these applications is the radar system. Applying CS in the radar such as Linear Frequency Modulation Continuous Wave (LFMCW) radar signals has many advantages but suffers from the processing time in the two-dimensional processing. The performance of the LFMCW radar signals is achieved by using both conventional Complex Approximate Message Passing (CAMP) and adaptive recovery algorithms using a suitable reduction factor in both range and Doppler directions. In this paper, a modification is made to the adaptive CAMP algorithm to enhance the radar detection performance compared to both the conventional and adaptive algorithms under the same conditions. One of the main problems in radar detection is off-pin targets, which can be overcome using a certain filter in both range and Doppler directions. A comparison is achieved among these algorithms concerning detection performance using Receiver Operating Characteristic curves and the resolution performance in both range and Doppler directions. During the system analysis, it was found that an enhancement was achieved using the modified algorithm in the radar performance without any degradation in both range and Doppler resolution compared with the other algorithms.

SEPCS: Prolonging Stability Period of Wireless Sensor Networks using Compressive Sensing

Compressive sensing (CS) is an emerging theory thatis based on the fact that a small number of linear projections of asparse data contains enough information for reconstruction. CScan break through the asymmetry between the data acquisitionand information processing that makes a great challenge to therestriction energy and computation consumption of the sensornodes. In this paper, we propose a routing protocol called SEPCSfor clustered wireless sensor networks (WSNs) using CS. SEPCScombines a new clustering strategy with CS theory for prolongingstability period and network lifetime in WSNs. Our simulationresults show that the proposed protocol can effectively prolongthe stability period and network lifetime compared with existingprotocols.

An Anti-Jamming Method against Interrupted Sampling Repeater Jamming Based on Compressed Sensing.

Interrupted sampling repeater jamming (ISRJ) is an attracted coherent jamming method to inverse synthetic aperture radar (ISAR) in the past decades. By means of different jamming parameters settings, realistic dense false targets can be formed around the true target. This paper proposed an adaptive anti-jamming method against ISRJ by adjusting the number of measurements based on compressed sensing (CS). The jamming signal is energy concentrated and segmented sparse in the frequency domain. The measurements number of the reconstructed target signal and the jamming signal is different. According to the restricted isometry property (RIP) condition of CS theory, signal reconstructing performance depends on the number of measurements that varies with the sparsity of the vector. Thus, the jamming signal is suppressed, and the true target signal is retained by altering the measurements number of echo signals. Besides, the two-dimensional (2D) anti-jamming method is derived in detail. The anti-jamming effect is analyzed with different signal-to-noise ratios (SNR), sampling rates, and jam-to-signal ratios (JSR). Simulations prove the effectiveness of the proposed anti-jamming method.

Developing a Deep Neural Network for Driver Fatigue Detection Using EEG Signals Based on Compressed Sensing

In recent years, driver fatigue has become one of the main causes of road accidents. As a result, fatigue detection systems have been developed to warn drivers, and, among the available methods, EEG signal analysis is recognized as the most reliable method for detecting driver fatigue. This study presents an automated system for a two-stage classification of driver fatigue, using a combination of compressed sensing (CS) theory and deep neural networks (DNNs), that is based on EEG signals. First, CS theory is used to compress the recorded EEG data in order to reduce the computational load. Then, the compressed EEG data is fed into the proposed deep convolutional neural network for automatic feature extraction/selection and classification purposes. The proposed network architecture includes seven convolutional layers together with three long short-term memory (LSTM) layers. For compression rates of 40, 50, 60, 70, 80, and 90, the simulation results for a single-channel recording show accuracies of 95, 94.8, 94.6, 94.4, 94.4, and 92%, respectively. Furthermore, by comparing the results to previous methods, the accuracy of the proposed method for the two-stage classification of driver fatigue has been improved and can be used to effectively detect driver fatigue.

A Study on Dictionary Selection in Compressive Sensing for ECG Signals Compression and Classification.

The paper proposes a comparative analysis of the projection matrices and dictionaries used for compressive sensing (CS) of electrocardiographic signals (ECG), highlighting the compromises between the complexity of preprocessing and the accuracy of reconstruction. Starting from the basic notions of CS theory, this paper proposes the construction of dictionaries (constructed directly by cardiac patterns with R-waves, centered or not-centered) specific to the application and the results of their testing. Several types of projection matrices are also analyzed and discussed. The reconstructed signals are analyzed quantitatively and qualitatively by standard distortion measures and by the classification of the reconstructed signals. We used a k-nearest neighbors (KNN) classifier to evaluate the reconstructed models. The KNN module was trained with the models from the mega-dictionary used in the classification block and tested with the models reconstructed with class-specific dictionaries. In addition to the KNN classifier, a neural network was used to test the reconstructed signals. The neural network was a multilayer perceptron (MLP). Moreover, the results are compared with those obtained with other compression methods, and ours proved to be superior.