Compressive Sensing Theory Research Articles

Compressive sensing based parameter estimation for free-space continuous-variable quantum key distribution.

In satellite-based free-space continuous-variable QKD (CV-QKD), the parameter estimation for the atmospheric channel fluctuations due to the turbulence effects and attenuation is crucial for analyzing and improving the protocol performance. However, the partial key data usually need to be sacrificed for the parameter estimation leading to the secret key reduction and the possible information leakage, especially when the channel is varying. In this paper, compressive sensing (CS) theory is applied to free-space CV-QKD to achieve the channel parameter estimation with small amount of key data sacrifice and low computational complexity. According to CS theory, the possibility of the sparse representation for free-space channel is analyzed and the two types of sparse reconstruction models for the channel parameters are constructed combining with the stability of the sub-channels. The most part of key data for parameter estimation is saved by using the model constructed by the variables in the quantum signals, while all the key data can be saved and be used to generate the secret key by using the model constructed by the second-order statistics of the variables. Thus, the methods can generate more secret key, improve the secret key rate, and be well adapted for the cases with the limited communication time since fewer or no key data (variables) is sacrificed for parameter estimation. Finally, simulation results are given to verify the effectiveness of the proposed methods.

A novel pipeline leak detection and localization method based on the FBG pipe-fixture sensor array and compressed sensing theory

Low localization accuracy and instability have always been two primary problems for the pipeline leak detection and localization method based on the negative pressure wave (NPW) technique. In this paper, based on compressed sensing (CS) theory, a novel pipeline leak detection and localization method is proposed to replace the solutions of the arrival time difference of NPW knee points. In addition, based on the presented method, the localization accuracy can be improved without increasing the number of sensors. To validate the localization accuracy and stability of the presented method, a pipeline leak simulation test under flow conditions is conducted on a steel pipe leak test platform. The fiber Bragg grating (FBG) pipe-fixture sensor array is developed and applied to detect pipeline leakage and measure the pressure variations in the NPW signals, which provides the data basis for pipeline leak localization based on CS theory. A concept of the relative localization coefficient bCS is proposed, and the test results indicate that when bCS is 0.5, all localization errors of different leakage points with different leakage rates are 2 m.

Joint sparse recovery for direction of arrival based on the generalized MUSIC criterion

The core of compressed sensing (CS) is to recover a set of sparse signals from incomplete measurements. In this paper, to solve the coherent direction-of-arrival (DOA) estimation problem, it is formulated as a joint-sparse recovery problem by exploiting the signal sparsity in the spatial domain. When the sparsity level of the signals satisfies certain conditions, the signals are recoverable even in the case of coherent sources. By further considering the structure of the sparse signals, a more general condition for the recoverability is theoretically derived. Then a method is proposed based on the CS theory and the generalized MUSIC criterion. This criterion improves on MUSIC so that the support is reliably recovered under the case of rank-defect. In our method, we modify the criterion to make it applicable for continuous dictionaries. When the partial DOAs has been estimated, the modified criterion can estimate the remaining DOAs with higher accuracy. By alternately using the modified criterion, the proposed method achieves super-resolution. Simulation results demonstrate that the proposed method has satisfactory performance even in the case of coherent sources.

Data-Driven Time-Frequency Method and Its Application in Detection of Free Gas Beneath a Gas Hydrate Deposit

The time-frequency (TF) analysis method plays a significant role in the detection of natural gas hydrates. As a data-driven method, compressed sensing (CS) has been widely used in the TF methods due to the sparsity of the TF representation. This study proposes a data-driven TF method based on the CS theory and a non-convex regularization. In the implementation, a continuous wavelet transform (CWT) with a generalized beta wavelet (GBW) is formulated as an inverse problem based on the CS theory. The selection of appropriate parameters enables the GBW to match the seismic wavelets better than the widely used Morlet wavelet. The GBW can constitute a tight frame to reduce calculation time, particularly for large-scale field data processing. Additionally, the proposed TF method introduces the generalized minimax concave (GMC) penalty function as a non-convex regularization term. Compared with the classical sparse approximation method with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{1} $ </tex-math></inline-formula> regularization, the GMC regularization term can enhance the sparsity in sparse inverse problems and ensure the convexity of sparse inversions. This article also presents an exponentially decreasing threshold scheme to adaptively select the regularization parameters. Three synthetic examples are investigated to demonstrate the performance of the proposed sparse TF representation with GMC regularization. Finally, the proposed TF method’s performance in detecting free gas of gas hydrates is validated using field seismic data obtained from the Blake Ridge.

Void Fraction Measurement of C Apacitively C Oupled E Lectrical R Esistance T Omography System Based on Compressive Sensing Theory

Void Fraction Measurement of C Apacitively C Oupled E Lectrical R Esistance T Omography System Based on Compressive Sensing Theory

Dynamic Compressive Data Gathering using Angle-based Random Walk in Hybrid WSNs

This paper addresses the problems of energy consumption, load-balancing, and Compressive Sensing (CS) recovery performance in hybrid proactive-reactive wireless sensor network, where sensors are categorized into two representative and relay nodes. We jointly consider the dynamic compressive data gathering, angle-based random walk, and spatial correlation to propose an efficient method named “Dynamic Compressive Data Gathering using Angle-based Random Walk (DCDG-ARW)”. The proposed scheme uses the CS theory along with the angle-based random walks to transmit CS measurements from sensors to the sink node. To select a starting node for each random walk path, a heuristic mechanism called Distance-and Correlation-aware Node Selection (DCNS) is presented. Furthermore, a transition probability is defined for the proposed angle-based random walks to jointly investigate dynamic changes of the network, increasing load-balancing, and improving the quality of the measurement matrix. The effectiveness of DCDG-ARW is evaluated in terms of energy consumption, load variance, network’s lifetime, and reconstruction error. Based on the simulation results, the proposed DCDG-ARW algorithm illustrates significant performance improvements in comparison to its counterparts across all the aforementioned aspects.

Image Reconstruction for ECT under Compressed Sensing Framework Based on an Overcomplete Dictionary

Electrical capacitance tomography (ECT) has great application potential in multiphase process monitoring, and its visualization results are of great significance for studying the changes in two-phase flow in closed environments. In this paper, compressed sensing (CS) theory based on dictionary learning is introduced to the inverse problem of ECT, and the K-SVD algorithm is used to learn the overcomplete dictionary to establish a nonlinear mapping between observed capacitance and sparse space. Because the trained overcomplete dictionary has the property to match few features of interest in the reconstructed image of ECT, it is not necessary to rely on the sparsity of coefficient vector to solve the nonlinear mapping as most algorithms based on CS theory. Two-phase flow distribution in a cylindrical pipe was modeled and simulated, and three variations without sparse constraint based on Landweber, Tikhonov, and Newton-Raphson algorithms were used to rapidly reconstruct a 2-D image.

Clustered sparsity and Poisson-gap sampling

Non-uniform sampling (NUS) is a popular way of reducing the amount of time taken by multidimensional NMR experiments. Among the various non-uniform sampling schemes that exist, the Poisson-gap (PG) schedules are particularly popular, especially when combined with compressed-sensing (CS) reconstruction of missing data points. However, the use of PG is based mainly on practical experience and has not, as yet, been explained in terms of CS theory. Moreover, an apparent contradiction exists between the reported effectiveness of PG and CS theory, which states that a “flat” pseudo-random generator is the best way to generate sampling schedules in order to reconstruct sparse spectra. In this paper we explain how, and in what situations, PG reveals its superior features in NMR spectroscopy. We support our theoretical considerations with simulations and analyses of experimental data from the Biological Magnetic Resonance Bank (BMRB). Our analyses reveal a previously unnoticed feature of many NMR spectra that explains the success of ”blue-noise” schedules, such as PG. We call this feature “clustered sparsity”. This refers to the fact that the peaks in NMR spectra are not just sparse but often form clusters in the indirect dimension, and PG is particularly suited to deal with such situations. Additionally, we discuss why denser sampling in the initial and final parts of the clustered signal may be useful.

Adaptive Cluster Structured Sparse Bayesian Learning with Application to Compressive Reconstruction for Chirp Signals

Compressive sensing (CS) is a promising framework to achieve efficient sampling for wide-band chirp signals due to its significance in reducing the sampling rate and power consumption. Under the CS theory, this paper studies the compressive reconstruction problem for chirp signals whose sparse matrix shows unknown cluster structures. To investigate the structure information to improve the reconstruction performance, existing methods require the prior knowledge on the cluster structure and suffer from the model mismatch problem. In this paper, an adaptive cluster structured sparse Bayesian learning algorithm is proposed to alleviate the requirements on the prior knowledge by exploiting and incorporating the local structure of the sparse matrix into the reconstruction model. To avoid the model mismatch problem, we apply an adaptive mechanism in variable estimation so that the reconstruction for one coefficient can selectively use the statistical information of its neighbors. The proposed algorithm is verified on both the simulated and the real chirp datasets. Numerical experimental results show that the proposed algorithm outperforms other state-of-art reconstruction algorithms in both noiseless and noisy environments. The proposed method is also found to further reduce the total sampling rate of the compressive sampling system.

Compressed Sensing of Extracellular Neurophysiology Signals: A Review.

This article presents a comprehensive survey of literature on the compressed sensing (CS) of neurophysiology signals. CS is a promising technique to achieve high-fidelity, low-rate, and hardware-efficient neural signal compression tasks for wireless streaming of massively parallel neural recording channels in next-generation neural interface technologies. The main objective is to provide a timely retrospective on applying the CS theory to the extracellular brain signals in the past decade. We will present a comprehensive review on the CS-based neural recording system architecture, the CS encoder hardware exploration and implementation, the sparse representation of neural signals, and the signal reconstruction algorithms. Deep learning-based CS methods are also discussed and compared with the traditional CS-based approaches. We will also extend our discussion to cover the technical challenges and prospects in this emerging field.

Sar compressed sensing based on Gaussian process regression

ABSTRACT Synthetic Aperture Radar systems are capable of acquiring high-resolution images by modulating and transmitting waves in high frequency levels towards the ground. Synthetic Aperture Radar (SAR) images are generated by demodulating and processing the backscattered waves by the targets. New SAR systems produce high-resolution images by raising the modulation frequency. The sampling time becomes shorter and a large number of samples are generated, which costs for processing and storage. Compressed Sensing (CS) is a compression technique capable of reconstructing a sparse signal from a small number of samples inferior to the conventional sampling. The representation basis, that projects a signal to a sparse form is the key of the application of CS. CS becomes unusable in the acquisition of heterogeneous scenes that present many scatterings types because the representation matrices are unknown and require intensive computing to generate them. In the literature, most proposed researches in the CS field apply CS on simulated sparse scenes, where only a few number of strong scatters are present to avoid the representation matrix computing. The purpose of this paper is to apply CS on non-sparse images and to avoid heavy computation to generate a representation matrix at the same time by combining the CS with the Gaussian Process regression (GPR). A small number of backscattered signals are acquired and sampled with respect to the Nyquist theory, sparsified and used as a feature vector for the training of the GPR model. The remaining signals are processed by the CS theory. After reconstruction, the zero values of the image are predicted using the model generated by the GPR algorithm. Five strategies are proposed in this paper and several evaluations are performed. These methods reconstruct an exploitable image from of samples.

Low-Frequency Expansion Approach for Seismic Data Based on Compressed Sensing in Low SNR

Low-frequency information can reflect the basic trend of a formation, enhance the accuracy of velocity analysis and improve the imaging accuracy of deep structures in seismic exploration. However, the low-frequency information obtained by the conventional seismic acquisition method is seriously polluted by noise, which will be further lost in processing. Compressed sensing (CS) theory is used to exploit the sparsity of the reflection coefficient in the frequency domain to expand the low-frequency components reasonably, thus improving the data quality. However, the conventional CS method is greatly affected by noise, and the effective expansion of low-frequency information can only be realized in the case of a high signal-to-noise ratio (SNR). In this paper, well information is introduced into the objective function to constrain the inversion process of the estimated reflection coefficient, and then, the low-frequency component of the original data is expanded by extracting the low-frequency information of the reflection coefficient. It has been proved by model tests and actual data processing results that the objective function of estimating the reflection coefficient constrained by well logging data based on CS theory can improve the anti-noise interference ability of the inversion process and expand the low-frequency information well in the case of a low SNR.

Fast 3D time-domain airborne EM forward modeling using random under-sampling

The high sampling rate of airborne electromagnetic (AEM) systems can create huge data volumes, causing major challenges for three-dimensional (3D) electromagnetic modeling and inversions and constraining the practical applicability of AEM. Rapid and accurate forward modeling is the key to efficient 3D inversion. Here a new strategy for improving the efficiency of 3D time-domain AEM forward modeling is presented, based on compressed-sensing theory combined with the finite-volume method. A Poisson disk random under-sampling method was used to obtain random survey stations and to calculate AEM responses via the finite-volume method at these sampling stations. Coefficients from the curvelet transform with anisotropic characteristics for sparse expression were used to analyze the sparsity of AEM data, with the AEM responses of all survey stations being obtained by reconstruction. Key factors influencing the accuracy of the reconstruction are also discussed, including the sampling method and rate, the sparse transformation, and the noise. To test the effectiveness of the method, reconstructed results were compared with those from traditional schemes for forward modeling using all stations. Results indicate that the new strategy requires only 20% ~ 50% of samples to achieve high-precision reconstruction of the AEM signal even for complex geoelectrical structures, and the efficiency of 3D forward modeling can be enhanced by a factor of two to five, laying a foundation for fast AEM inversions of large datasets and complex models.

3-D Through-the-Wall Radar Imaging Using Compressed Sensing

The compressed sensing (CS) technique is applied to the diffraction tomography (DT) method for through-the-wall radar imaging (TWRI), which leads to significantly decreasing the number of measurements and, consequently, reducing the data acquisition time. A large amount of required measurements is a real difficulty in TWRI, which is addressed in our work, due to the CS theory. In addition, the nonuniform fast Fourier transform (NUFFT) is also employed in the DT algorithm to accelerate the image reconstruction processing time. By exploiting the advantages of both the CS and NUFFT, the imaging speed is noticeably increased. As a proof of concept, in a sample scenario, our experiments show that, by using only 10% of the measurements used in the conventional DT algorithm, the imaging time is reduced by around 1/4 (with respect to the conventional DT method) while maintaining the quality of the reconstructed images.

Joint User Activity Identification and Channel Estimation for Grant-Free NOMA: A Spatial–Temporal Structure-Enhanced Approach

Exploiting the sparse nature of user activity, compressed sensing (CS) has been a powerful technique to realize efficient user detection in grant-free nonorthogonal multiple access (NOMA). However, most of the existing CS-based multiuser detection schemes merely independently incorporate the temporal correlation in frame-based transmission or spatial correlation induced by multiantenna reception, leading to unsatisfactory user detection performance. Driven by the observation in the CS theory that the signal recovery performance could be enhanced by an increased number of sparse vectors with a common support set, in this article, we propose a novel joint user activity identification and channel estimation (JUICE) framework by integrating the temporal correlation of active user sets with multiantenna reception, which could achieve superior user detection performance. Specifically, we first formulate the JUICE as a Kronecker CS (KCS) problem to model the CS measurement process, by fully extracting the spatial-temporal structure of user activity. Then, based on the mined spatial-temporal structure of user activity, an adaptive subspace pursuit algorithm is developed, i.e., spatial-temporal structure enhanced adaptive subspace pursuit (STS-ASP), which could realize efficient multiuser detection. A distinct advantage of the proposed algorithm is that it does not require any prior knowledge (e.g., the number of active users and the noise level), by adaptively acquiring the number of active users and employing the cross-validation technique to appropriately terminate the iterative procedures. Extensive experimental evaluation is conducted, and the results corroborate the superiority of the proposed framework compared with the existing CS-based multiuser detection methods.

Matrix Element-Based Theory of Compressive Sensing and Its Application to Electromagnetic Imaging

We present a simple and general theory of compressive sensing (CS) that relies on elements of the sensing matrix rather than on the number of measurements. We prove the exact recovery using a dual certificate by showing that the sensing matrix satisfies an incoherence property and isotropy property if the sparsity level is kept lower than the reciprocal of the largest element of a matrix created from the sensing matrix. Unlike the CS literature, this unconventional approach does not require a linear relationship between the sparsity and the number of measurements and at the same time, can easily be evaluated. This adaptability captures anisotropic measurements appropriately as with anisotropic measurements, adding more measurements does not really imply that a signal with more nonzero elements will be recovered exactly. As an illustration, we demonstrate the theory’s ability to accurately handle the anisotropic (Green’s function-based sensing matrix) measurements and also its similarity to the existing CS literature for isotropic (Fourier) measurements. Further, we show the usefulness of the theory in comparing different sensing matrices and in generating dielectric images. The dielectric images are perfectly recovered even when there is only a single transmitter.

L(1/2) Regularization for ISAR Imaging and Target Enhancement of Complex Image

Synthetic aperture radar (SAR) and inverse synthetic aperture radar (ISAR) imaging technology are powerful tools to acquire high-resolution radar image, which is an important basis for further automatic target recognition (ATR). For ISAR, if the radar frequency is high enough, signals that the radar received usually have strong sparsity when the radar data convert to Fourier domain, and they can be downsampled and restored by compressed sensing (CS). As for the regularization method in CS theory, while L₁ regularization is popular, the Lq(0 < q < 1) regularization is proved to be a sparse regularization framework and could achieve well performance. In this work, inspired by the L₁-based complex approximated message passing (CAMP) method and the L(1/2) regularization framework, we extend the CAMP method into an L(1/2)-based iterative thresholding method in ISAR imaging under the downsampling rate of the scattered fields. The matched filtering (MF) method is widely used to generate the SAR image, where targets are usually overwhelmed by noise and scene background. In order to make the target enhanced to further improve recognition, regularization is adopted in recovering sparse solution and the clutter reduction of MF image. This work implements the L(1/2)-based regularization into the SAR image target enhancement and the scene-noise reduction via CAMP. The SAR image is generated by ideal point scatterers and the real measurement data of RADARSAT-1. Given the sparsity estimated, the experiment results show the advantage of L(1/2) regularization compared with the L₁ regularization.

Compressive sensing theory and neighborhood spatial‐temporal information for frame rate improvement of dynamic ultrasonic imaging

AbstractThe frame rate improvement is an essential issue in dynamic ultrasonic imaging for better displaying rapid heart movements. In this study, a new technique using the compressive sensing (CS) theory was introduced for the frame rate improvement of two‐dimensional (2D) and three‐dimensional (3D) dynamic ultrasonic imaging. In the suggested procedure, a fewer radio frequency (RF) lines were received. Subsequently, the CS theory by the recommended approach was used to reconstruct the nonacquired RF lines. The suggested process uses the temporal and spatial information in the neighborhood samples of the desired sample in RF frame sequences. We utilized the dictionary learning technique to construct the sparsifying over‐complete dictionary. Here, we used the 2D in vivo carotid artery data and the 3D simulated echocardiography for the quality assessment of the suggested approach. According to the qualitative and quantitative results, reconstructions in the suggested approach are more precise, and the reconstruction errors are much lower than the conventional techniques. The tissues' structure in reconstructed videos by the suggested approach is preserved to be applicable for medical diagnosis goals. The frame rate can be improved by a factor of 10 with suitable quality for medical diagnosis goals. The implementation of the suggested approach does not require any more hardware or alternation in the devices' available hardware. The frame rate can be improved by only implementing effective programming on the ultrasound systems.

A Compressed Sensing Network for Acquiring Human Pressure Information

In this article, sparse autoencoder in deep learning is integrated into the compressed sensing (CS) theory, and a reconstruction algorithm is designed based on the biological mechanism of human brain synaptic connections. The compressive sampling process is modeled as a neural network model. Then a biological mechanism-inspired stacked long short-term memory (LSTM) network model is proposed as a reconstruction algorithm of CS theory. Consequently, a CS network (ComsensNet) model is introduced, by integrating the compressive sampling process and reconstruction algorithm. ComsensNet can provide a bridge between sparse autoencoder in deep learning, synapses in human brain neurons and the CS theory. A deep neural network is designed based on the synaptic biological mechanism of human brain neurons, and then combine with the theory of CS. The effectiveness of ComsensNet is investigated by using acquired pressure data from the human body model. The experimental results demonstrate that the biological mechanism-inspired stacked LSTM network in ComsensNet can improve the reconstruction accuracy compared to other reconstruction algorithms.

Fault diagnosis of bearing vibration signals based on a reconstruction algorithm with multiple side Information and CEEMDAN method

When bearing vibration of instruments is monitored, a large number of data are produced. This requires a massive capacity of storage and high bandwidth of data transmission whereby costs and complex installation are concerned. In this study, we aim to propose an effective framework to address such the amount of bearing signals to which only meaningful information is extracted. Based on the compressed sensing (CS) theory. We proposed a reconstruction algorithm based on the multiple side information signal (RAMSI) with a purpose to effectively obtain important information from recorded bearing signals. In the process of sparse optimization, the RAMSI algorithm was implemented to solve the n-11 minimization problem with the weighting adaptive multiple side information signals. Wavelet basis and Hartley matrix were applied for the reconstruction process, for which the effective sparse optimization processing of bearing signals was able to adaptively computed. The performance of our RAMSI-based CS theory was compared with the basis pursuit (BP) which is based on the alternating direction method of multiplier (ADMM) and orthogonal matching pursuit (OMP). The error indices of the reconstruction algorithms were evaluated. This proves that the performance of the sparse optimization algorithm from our proposed framework is superior to the BP based on the ADMM and OMP algorithm. After recovering vibration signals, some strong noise caused by the incipient fault characteristic of the bearing. The complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN) method was performed to extract the bearing fault component from such noise. In terms of performance, the CEEMDAN method was compared to the standard ensemble empirical mode decomposition (EEMD) method. The results show that the CEEMDAN method yields a better decomposition performance and is able to extract meaningful information of bearing fault characteristic.