Signal Reconstruction Method Research Articles

EWT-ASG: Empirical Wavelet Transform With Adaptive Savitzky–Golay Filtering for TDLAS

Inspired by the empirical mode decomposition (EMD)-enhanced gas detection work, this paper develops a further improved signal reconstruction method (namely EWT-ASG) for the demodulated harmonics of tunable diode laser absorption spectroscopy (TDLAS), which is mainly based on empirical wavelet transform (EWT) and Savitzky-Golay (S-G) filtering. First, the imported EWT performs better on the decomposition precision as it successfully bypasses the mode aliasing problem of EMD resulting by the lack of mathematical basis. Second, the improved S-G filter effectively suppresses the noisy components of the wavelet coefficients by updating its one key parameter (i.e., window size w) dynamically according to the correlation coefficients between the raw signals and the decomposed wavelet coefficients. The EWT-ASG scheme was first applied on the oxygen concentration detection for pharmaceutical glass vials. The preliminary experimental results indicate that the EWT-ASG method performs better than recent state-of-the-arts, with an average correct discrimination rate of 98.14% when the normalized SNR is 1. Even when the normalized SNR is degenerated from 1 to 0.85, our detection system still survived well, with a highest average correct discrimination rate of 90.45%. The detection system precision is also improved to a large extent, with a minimal Allan deviation of 0.856@(117s).

A signal reconstruction method of wireless sensor network based on compressed sensing

Compressed sensing (CS) is a new theory for sampling and recovering signal-based sparse transformation. This theory could help us to acquire complete signal at low cost. Therefore, it also satisfies the requirement of low-cost sampling since bandwidth and capability of sampling is not sufficient. However, wireless sensor network is an open scene, and signal is easily affected by noise in the open environment. Specially, CS theory indicates a method of sub-Nyquist sampling which is effective to reduce cost in the process of data acquirement. However, the sampling is “imperfect”, and the corresponding data is more sensitive to noise. Consequently, it is urgently requisited for robust and antinoise reconstruction algorithms which can ensure the accuracy of signal reconstruction. In the article, we present a proximal gradient algorithm (PRG) to reconstruct sub-Nyquist sampling signal in the noise environment. This algorithm iteratively uses a straightforward shrinkage step to find the optimum solution of constrained formula, and then restores the original signal. Finally, in the experiment, PRG shows excellent performance comparing to OMP, BP, and SP while signal is corrupted by noise.

Signal Selection for Oscillation Monitoring With Guarantees on Data Recovery Under Corruption

Insights are developed into grouping PMU signals for guaranteeing data recovery under sparse corruption. Analytical relations are derived to express the denseness of the subspace spanned by a measurement window in terms of the modal observabilities of its constituent signals. It is shown that grouping signals by minimizing variation in phase angles and amplitudes of observabilities for each poorly-damped mode minimizes the numerical-rank of the measurement window, enhances denseness of the subspace, and helps in attaining the sufficiency condition guaranteeing exact recovery using Robust Principal Component Analysis-based signal reconstruction methods. These insights are structured into lemmas and propositions for signal selection and are validated on synthetic data from IEEE test systems, as well as field PMU data from a US utility.

ℓ1 − αℓ2 minimization methods for signal and image reconstruction with impulsive noise removal

In this paper, we study ℓ1 − αℓ2 (0 < α ⩽ 1) minimization methods for signal and image reconstruction with impulsive noise removal. The data fitting term is based on ℓ1 fidelity between the reconstruction output and the observational data, and the regularization term is based on ℓ1 − αℓ2 nonconvex minimization of the reconstruction output or its total variation. Theoretically, we show that under the generalized restricted isometry property that the underlying signal or image can be recovered exactly. Numerical algorithms are also developed to solve the resulting optimization problems. Experimental results have shown that the proposed models and algorithms can recover signal or images under impulsive noise degradation, and their performance is better than that of the existing methods.

Estimation of Thermal Resistance Field in Layered Materials by Analytical Asymptotic Method

In this paper, the problem of the quantitative characterization of thermal resistance fields in a multilayer sample is addressed by using the classical front face flash method as the thermal excitation and infrared thermography (IRT) as the monitoring sensor. In this challenging problem, the complete inverse processing of a multilayer analytical model is difficult due to the lack of sensitivity of some parameters (layer thickness, depth of thermal resistance, etc.) and the expansive computational iterative processing. For these reasons, the proposed strategy is to use a simple multilayer problem where only one resistive layer is estimated. Moreover, to simplify the inverse processing often based on iterative methods, an asymptotic development method is proposed here. Regarding the thermal signal reconstruction (TSR) methods, the drawback of these methods is the inability to be quantitative. To overcome this problem, the method incorporates a calibration process originating from the complete analytical quadrupole solution to the thermal problem. This analytical knowledge allows self-calibration of the asymptotic method. From this calibration, the quantitative thermal resistance field of a sample can be retrieved with a reasonable accuracy lower than 5%.

Robust signal recovery using Bayesian compressed sensing based on Lomax prior

Recently published research shows that Lomax distribution exhibits compressibility in Lorentz curves. In this paper, we address the problem of signal reconstruction in the high noise level and phase error environments in a Bayesian framework of Lomax prior distribution. Furthermore, from the perspective of improving sparsity and compressibility of the signal constraints, a novel reconstruction model deducted from Lomax-prior-based Bayesian compressed sensing (LomaxCS) is proposed. The LomaxCS improves the accuracy of existing Bayesian compressed sensing signal reconstruction methods and enhances the robustness against Gauss noise and phase errors. Compared with the conventional models, the proposed LomaxCS model still reveals the general profile of the signal in the worst conditions. The experimental results demonstrate that the proposed algorithm can achieve substantial improvements in terms of recovering signal quality and robustness; meanwhile, it brings an evident application prospect.

Development of a generative-adversarial-network-based signal reconstruction method for nuclear power plants

In nuclear power plants (NPPs), the reliability of instrumentation signals is crucial for making appropriate decisions. Multiple signals can become faulty simultaneously and become unavailable under harsh conditions, and this could lead to improper decisions being made, which could result in catastrophic failure. The authors proposed a new signal reconstruction method based on a generative adversarial network (GAN) that can be applied to reconstruct multiple missing signals. In the method, a GAN model is first trained to generate realistic signal sets from random latent vectors and then used to find the optimal latent vector for the reconstruction of a damaged signal set. The signal set is reconstructed by replacing its missing parts with the corresponding parts of the signal set generated from the optimal latent vector. Experiments were conducted to verify the applicability of the proposed method to the reconstruction of multiple missing signals under various NPP emergency situations.

Minimum phase properties of systems with a new signal reconstruction method

The Minimum Phase (MP) properties of linear control systems can be reflected by its zero stability. The stability of zeros affects the system control performance. When a continuous-time system is discretized to a discrete-time system, the discretization process may render continuous-time system models have nonminimum phase. This paper analyses the MP properties of system and deduces a new stable condition of the zeros when continuous-time system is discretized by Forward Triangle Sample and Hold (FTSH) for sufficiently small sampling periods. Finally, two numerical examples have verified our results.

CEEMD: A New Method to Identify Mine Water Inrush Based on the Signal Processing and Laser-Induced Fluorescence

The rapid and accurate identification of water source types in mine water inrush has been achieved by combining laser-induced fluorescence technology (LIF) with artificial intelligence algorithms. However, these algorithms solely rely on data and image processing analysis to identify different kinds of water samples. To address this issue, we analyzed the fluorescence spectrum and the types of mine water inrush sources from the signal point of view. Firstly, a LIF water inrush spectral analysis system was built to collect spectral data and exhibit fluorescence spectra. Different methods of spectral signal decomposition and reconstruction were compared. The complementary ensemble empirical mode decomposition (CEEMD) algorithm with a better signal evaluation index was selected to preprocess raw spectral signals. Then, the multi-class support vector machine of the cuckoo search optimization (CS-MSVM) model was implemented to the reconstructed spectral signals in different stages. The classification accuracy of the reconstructed signals in the fifth stage was 100%. Compared with raw spectra, other signal processing methods, and other different classifiers, the proposed method has the highest classification accuracy. Finally, the reliability of the algorithm was validated by using the LIF spectral signals of different edible oils and the classification accuracy was 100%. The experimental results show that the CEEMD signal processing method combined with LIF spectroscopy is effective for the accurate identification of mine water inrush source, and it also provides a theoretical basis for the spectral analysis technology that can be used for the identification of other substances.

High-Resolution Signal Reconstruction Method Based on Sparse Structure Preservation

Given the problem that the low sampling period of the servo controller cannot provide high-frequency information for high-precision servo control system state recognition, this paper proposes a high-resolution signal reconstruction method based on sparse structure preservation. The servo system status data is reconstructed to obtain high sampling rate data equivalent to direct measurement, which provides support for extracting system features and status recognition. The main research content of this paper includes verifying the sparseness of the servo control signal, analyzing the consistency of the sparse structure of different sampling rates signals; extracting characteristics based on the combination of empirical mode decomposition (EMD) and principal component analysis (PCA) method. An adaptive sparse dictionary for servo control signals is trained by K-SVD. An objective function is constructed for high-resolution signal reconstruction based on the sparse structure retention properties. It is proved by simulations and experiments that the high-resolution reconstructed signal can be obtained, which is consistent with the high-resolution signal obtained by direct measurement. The method can be used as a reference for the analysis of low-sampling signals of servo control systems of industrial robots and similar equipment and has certain engineering application value.

TDLAS/WMS Embedded System for Oxygen Concentration Detection of Glass Vials with Variational Mode Decomposition

Whether the oxygen content for medical glass vials can be measured accurately affects greatly the ingredient stability of sterile pharmaceuticals. Tunable diode laser absorption spectroscopy (TDLAS/WMS) based on wavelength modulation has the remarkable advantages of non-contact, low cost, high sensitivity, real-time response, which shows great potential in the field of in-site oxygen concentration detection. Due to the short optical path and various environmental disturbances, it is challenging to measure the headspace oxygen concentration in open-path optical environment. Targeting this challenge, this paper designs a TDLAS/WMS-based gas concentration sensing architecture and turns it into an embedded detection system. Then, a robust signal reconstruction method based on variational mode decomposition (VMD) is established to suppress the random noise of the demodulated harmonic signal. Hence, the oxygen concentration can be reliably inversed from the peak-to-peak values (Vp-p) of the 2nd harmonic signal. This detection framework is abbreviated as WMS+VDM+Vp-p. Encouragingly, the preliminary application on a glass vial encapsulation line demonstrate that the proposed method performs promising results with an absolute detection error of within ±1.5% and a minimal Allan deviation of 0.0010@(100s), which provides a good start for the on-site headspace oxygen concentration measurement for pharmaceutical glass vials.

ECG Signal Reconstruction via Doppler Sensor by Hybrid Deep Learning Model With CNN and LSTM

An Electrocardiogram (ECG) is a typical method used to detect heartbeat, and an ECG signal analysis enables the detection of some heart diseases. However, the ECG-based heartbeat detection requires device attachment, which is not preferred for daily use. A Doppler sensor could be a device used to enable the non-contact heartbeat detection. In this paper, we propose a Doppler sensor-based ECG signal reconstruction method by a hybrid deep learning model with Convolutional Neural Network (CNN) and Long Short-Term Memory (LSTM). An ECG signal can be reconstructed by relating features of a heartbeat signal obtained by a Doppler sensor to those of the ECG signal. Thus, we construct the deep learning model that extracts the spatial and temporal features from the heartbeat signal by CNN and LSTM. Based on the extracted features, the ECG signal is reconstructed. We conducted experiments to observe heartbeat against 9 healthy subjects without heart disease. The experimental results showed that our method performed ECG signal reconstruction with a correlation coefficient of 0.86 between the reconstructed and actual ECG signals, even without attaching devices. The results indicate that it is possible to remotely reconstruct an ECG signal from a heartbeat signal via a Doppler sensor.

Source localization in reverberation environment based on improved equivalent sound source near-field acoustic holography algorithm

The compressive-equivalent source method near-field acoustic holography (C-ESM) is disturbed by reverberation in the enclosed space such as room and cabin, which leads to large reconstruction error and disturbs the judgment of sound source position. In order to solve this problem, an improved C-ESM algorithm based on room impulse response (RIR) is proposed to filter out reverberation interference in this paper. Different from the original equivalent source method, the improved algorithm constructs the transfer function through the room impulse response to establish the relationship between the equivalent source and the sound pressure on any plane in space, and the sparse signal reconstruction method of the compressive sensing technology is used to obtain the strength of the equivalent source. Then the transfer function to any plane of space is established according to the free field Green’s function, to eliminate the interference of reverberation and improve the effect of sound source location. The accuracy and effectiveness of the improved method are verified by preliminary numerical simulation. And the results show that compared with the original algorithm, this method has obvious advantages in sound source localization in a reverberant field.

Backtracking based Joint-Sparse Signal Recovery for Distributed Compressive Sensing

In Distributed Compressive Sensing (DCS), the Joint Sparsity Model (JSM) refers to an ensemble of signals being jointly sparse. In [4], a joint reconstruction scheme was proposed using a single linear program. However, for reconstruction of any individual sparse signal using that scheme, the computational complexity is high. In this paper, we propose a dual-sparse signal reconstruction method. In the proposed method, if one signal is known apriori, then any other signal in the ensemble can be efficiently estimated using the proposed method, exploiting the dual-sparsity. Simulation results show that the proposed method provides fast and efficient recovery.

Headspace Oxygen Concentration Measurement for Pharmaceutical Glass Bottles in Open-Path Optical Environment Using TDLAS/WMS

Accurate measurement of oxygen concentration for pharmaceutical glass bottles is of great significance to ensure the asepsis of medicine and stability of ingredients. With merits of high sensitivity, low cost, noncontact, and real-time response, the wavelength-modulation-based tunable diode laser absorption spectroscopy (TDLAS/WMS) technology shows great potential to achieve in-site oxygen concentration detection by the single-line spectrum measurement. This article focuses on headspace oxygen concentration measurement in the open-path optical environment, which is extremely challenging due to the short light path length and random ambient noises. First, a signal reconstruction method is established based on the discrete wavelet packet transform (DWPT), where random noise suppression is implicitly achieved. Then, oxygen concentration is inversed among the data between two adjacent valley values of the demodulated second-harmonic signal by multiple linear regression (MLR), and the linear discriminant analysis (LDA) is imported to enhance the information sparsity of second-harmonic signal matrix and to address the multicollinearity problem. Simulation results prove that our proposed method achieved considerable detection accuracy with the average absolute error of 0.05%. This article also designed a TDLAS/WMS prototype, and the experimental results aiming at glass bottles with different oxygen concentration of 0%, 5%, 10%, and 21% in open-path optical environment indicate our method has achieved an encouraging average absolute error of 0.54% and can survive well when the normalized signal-to-noise ratio (SNR) is within 0.85–1. These results promise that the proposed methodology can be widely applied in in-site automatic optic inspection (AOI) instrumentation of headspace oxygen concentration measurement for glass vials.

Performance comparison based on single-pixel imaging methods in the time domain

In this paper, different signal reconstruction methods are combined with temporal ghost imaging. The different methods are verified by the data collected from the system of temporal ghost imaging with the chaotic light. Simulated results suggest that the method of total variance minimization gives high-quality reconstruction of the imaging object with less time consumption compared with other methods. The different performances among these reconstruction techniques are also analyzed. The result thus provides valuable information for temporal ghost imaging with the advantages of high security, fast speed imaging and high quality of reconstructed signal in the area of optical cryptography applications.

Quantized compressive sensing with RIP matrices: the benefit of dithering

Abstract Quantized compressive sensing deals with the problem of coding compressive measurements of low-complexity signals with quantized, finite precision representations, i.e., a mandatory process involved in any practical sensing model. While the resolution of this quantization impacts the quality of signal reconstruction, there exist incompatible combinations of quantization functions and sensing matrices that proscribe arbitrarily low reconstruction error when the number of measurements increases. This work shows that a large class of random matrix constructions known to respect the restricted isometry property (RIP) is ‘compatible’ with a simple scalar and uniform quantization if a uniform random vector, or a random dither, is added to the compressive signal measurements before quantization. In the context of estimating low-complexity signals (e.g., sparse or compressible signals, low-rank matrices) from their quantized observations, this compatibility is demonstrated by the existence of (at least) one signal reconstruction method, the projected back projection, whose reconstruction error decays when the number of measurements increases. Interestingly, given one RIP matrix and a single realization of the dither, a small reconstruction error can be proved to hold uniformly for all signals in the considered low-complexity set. We confirm these observations numerically in several scenarios involving sparse signals, low-rank matrices and compressible signals, with various RIP matrix constructions such as sub-Gaussian random matrices and random partial discrete cosine transform matrices.

Gravity anomaly reconstruction based on nonequispaced Fourier transform

Irregular sampled gravity data are often interpolated into regular grid data for convenience of data processing and interpretation. The compressed sensing theory provides a signal reconstruction method that can recover a sparse signal from far fewer samples. We have introduced a gravity data reconstruction method based on the nonequispaced Fourier transform (NFT) in the framework of compressed sensing theory. We have developed a sparsity analysis and a reconstruction algorithm with an iterative cooling thresholding method and applied to the gravity data of the Bishop model. For 2D data reconstruction, we use two methods to build the weighting factors: the Gaussian function and the Voronoi method. Both have good reconstruction results from the 2D data tests. The 2D reconstruction tests from different sampling rates and comparison with the minimum curvature and the kriging methods indicate that the reconstruction method based on the NFT has a good reconstruction result even with few sampling data.

Block rank sparsity-aware DOA estimation with large-scale arrays in the presence of unknown mutual coupling

With the development of massive multiple-input mutiple-output (MIMO) technique, high-resolution direction-of-arrival (DOA) estimation has attracted great attention. A novel sparse signal reconstruction method based on the inherent block rank sparsity of the sub-matrix is proposed for high resolution DOA estimation with large-scale arrays under the condition of unknown mutual coupling. In the proposed method, by taking advantage of the banded symmetric Toeplitz structure of the mutual coupling matrix (MCM), a novel block representation model is firstly formulated by parameterizing the steering vector. Then, exploiting the inherent block sparsity characteristics of the sub-matrix, a reweighted nuclear norm minimization algorithm is proposed to reconstruct the sparse matrix, in which the weighted matrix is designed by using the spectrum of MUSIC-Like algorithm. Finally, the DOAs are achieved by searching the non-zeros blocks of the recovered matrix. The proposed method not only makes full use of the block rank sparsity characteristics of the sub-matrix and weighted matrix for enhancing the sparse solution, but also avoids the array aperture loss. Thus, the proposed method has superior estimation performance than the state-of-the-art algorithms under the condition of unknown mutual coupling. Especially, in the case of large-scale antennas, the advantage of the proposed method is more obvious. Some computer simulation results are performed to verify the advantage of our proposed method.

A Lamb wave signal reconstruction method for high-resolution damage imaging

In Lamb wave-based Structural Health Monitoring (SHM), a high-enough spatial resolution is highly required for Lamb wave signals to ensure the resolution and accuracy of damage detection. However, besides the dispersion characteristic, the signal spatial resolution is also largely restricted by the space duration of excitation waveforms, i.e., the Initial Spatial Resolution (ISR) for the signals before travelling. To resolve the problem of inferior signal spatial resolution of Lamb waves, a Lamb Wave Signal Reconstruction (LWSR) method is presented and applied for high-resolution damage imaging in this paper. In LWSR, not only a new linearly-dispersive signal is reconstructed from an original Lamb wave signal, but also the group velocity at the central frequency is sufficiently decreased. Then, both dispersion compensation and ISR improvement can be realized to achieve a satisfying signal spatial resolution. After the frequency domain sensing model and spatial resolution of Lamb wave signals are firstly analyzed, the basic idea and numerical realization of LWSR are discussed. Numerical simulations are also implemented to preliminarily validate LWSR. Subsequently, LWSR-based high-resolution damage imaging is developed. An experiment of adjacent multiple damage identification is finally conducted to demonstrate the efficiency of LWSR and LWSR-based imaging methods.