Null Space Pursuit Research Articles

Estimation of Micro-Doppler Parameters With Combined Null Space Pursuit Methods for the Identification of LSS UAVs

Micro-Doppler (m-D) effect, induced by the rotation of rotor blades, supplies a differentiable characteristic to address the problem for the identification of low, slow and small unmanned aerial vehicles (LSS UAVs). However, the primary challenge for the estimation of m-D parameters is how to separate weak rotation signal from Doppler signal and other interferences. Theoretically, null space pursuit (NSP) is an operator-based signal decomposition approach to decompose a signal into additive subcomponents. The premise of NSP is that two separated components are orthogonal. However, due to the different modulation models, rotation signal, Doppler signal or other interferences could not satisfy the condition. Moreover, traditional multi-order differential operator is not suitable for the decomposition of m-D signal. In thi <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> s paper, back projection strategy with instantaneous orthogonal NSP (BPIO-NSP) is proposed to distill Doppler signal, and then micro-Doppler NSP (MD-NSP) is jointly developed to separate rotation signal for the identification of LSS UAVs. Firstly, the decomposed component after NSP is applied to the short-time Fourier transform (STFT) to find the segments with instantaneous non-orthogonal property. Secondly, the back projection strategy is developed in BPIO-NSP to acquire the instantaneous orthogonal data, so as to adjust the decomposed Doppler signal with high accuracy. Finally, customized operator is specially constructed in MD-NSP to achieve the required rotation signal from the residue. Simulation results verify the theoretical analysis, and measured data of the fun and UAV detection experiments suggest that the proposed methods could be served for the application of the identification of LSS UAVs.

Automatic Sleep Staging Based on Single-Channel EEG Signal Using Null Space Pursuit Decomposition Algorithm

Sleep quality is related to people’s physical and mental health, so an accurate assessment of sleep quality is key to recognizing sleep disorders and taking effective interventions. To address the shortcomings of traditional manual and automatic staging methods, such as being time-consuming and having low classification accuracy, an automatic sleep staging method based on the null space pursuit (NSP) decomposition algorithm of single-channel electroencephalographic (EEG) signals is proposed, which provides a new way for EEG signal decomposition and automatic identification of sleep stages. First, the single-channel EEG signal data from the Sleep-EDF database, DREAMS Subject database, and Sleep Heart Health Study database (SHHS), available on PhysioNet, were preprocessed, respectively. Second, the preprocessed single-channel EEG signals were decomposed by the NSP algorithm. Third, we extracted nine features in the time domain of the nonlinear dynamics and statistics from the original EEG signal and the six simple signals that were decomposed. Finally, the extreme gradient boosting (XGBOOST) algorithm was used to construct a classification model to classify and identify the 63 extracted EEG signal features for automatic sleep staging. The experimental results showed that, on the Sleep-EDF database, the accuracy of four and five categories were 93.59% and 92.89%, respectively; on the DREAMS Subject database, the accuracy rates of four and five categories were 91.32% and 90.01%, respectively; on the SHHS database, the accuracy rates of four and five categories were 90.25% and 88.37%, respectively. The experimental results show that the automatic sleep staging model proposed in this work has high classification accuracy and efficiency, as well as strong applicability and robustness.

Heart-rate analysis of healthy and insomnia groups with detrended fractal dimension feature in edge

Insomnia, whether situational or chronic, affects over a third of the general population in today's society. However, given the lack of non-contact and non-inductive quantitative evaluation approaches, most insomniacs are often unrecognized and untreated. Although Polysomnography (PSG) is considered as one of the assessment methods, it is poorly tolerated and expensive. In this paper, with the recent development of Internet-of-Things devices and edge computing techniques, we propose a detrended fractal dimension (DFD) feature for the analysis of heart-rate signals, which can be easily acquired by many wearables, of good sleepers and insomniacs. This feature was derived by calculating the fractal dimension (FD) of detrended signals. For the trend component removal, we improved the null space pursuit algorithm and proposed an adaptive trend extraction algorithm. The experimental results demonstrated the efficacy of the proposed DFD index through numerical statistics and significance testing for healthy and insomnia groups, which renders it a potential biomarker for insomnia assessment and management.

Learning-Refined Integral Null Space Pursuit Algorithm for Noncontact Multisubjects Vital Signs Measurements Using SFCW-UWB and IR-UWB Radar

Under low signal-to-noise-and-clutter ratio circumstances, non-contact multi-subjects vital sign assessment based on ultrawideband (UWB) radar is extremely difficult. It is challenging to obtain an accurate measurement since the respiratory frequency harmonics are mixed with noise during detection and are extremely near to the frequency of the heartbeat signal. We use an impulse radio ultrawideband (IR-UWB) radar and a stepped-frequency continuous-wave ultrawideband (SFCW-UWB) radar in measurement to get reliable vital signs from several participants. For adaptively extracting respiratory and heartbeat patterns, it is proposed to use the learning refined integral null space pursuit algorithm (LR-INSP), which is based on the learning refined integral null space pursuit method and optimum route learning. The refined-INSP technique aims to provide fine-grained multi-layer and multi-branch harmonic components. Then, to obtain a reliable and stable vital sign path from the multi-branch decomposition, an optimum path learning technique is presented. According to the experimental findings, the average signal accuracy assessment (SAA) of the heartbeat and respiratory frequencies for IR-UWB radar is 95.41% and 89.97%, respectively. The average SAA of the heartbeat and respiratory frequencies for SFCW-UWB radar is 94.39% and 99.48%, respectively.

Amplitude spectrum trend-based feature for excitation location classification from snore sounds

Objective: Successful surgical treatment of obstructive sleep apnea (OSA) depends on the precise location of the vibrating tissue. Snoring is the main symptom of OSA and can be utilized to detect the active location of tissues. However, existing approaches are limited, owing to their inability to capture the characteristics of snoring produced from the upper airway. This paper proposes a new approach to better distinguish different snoring sounds that are generated from four different excitation locations. Approach: First, we propose a robust null space pursuit algorithm for extracting the trend from the amplitude spectrum of snoring. Second, a new feature from this extracted amplitude spectrum trend, which outperforms the Mel-frequency cepstral coefficient (MFCC) feature, is designed. Subsequently, the newly proposed feature, namely the trend-based MFCC (TCC), is reduced in dimensionality by using principal component analysis. Finally, a support vector machine is employed for the classification task. Main results: By using the TCC, the proposed approach achieves an unweighted average recall of 87.5% on the classification of four excitation locations on the public dataset Munich Passau Snore Sound Corpus. Significance: The TCC is a promising feature for capturing the characteristics of snoring. The proposed method can effectively perform snore classification and assist in accurate OSA diagnosis.

A Detection Method for Bearing Faults Using Complex-Valued Null Space Pursuit and 1.5-Dimensional Teager Energy Spectrum

Because of the nonlinear and unsteady characteristics of bearing vibration signals, the fault diagnosis of the rolling bearing in complex environments has become a challenging task. This paper deals with the bearing fault diagnosis method of vibration signals based on the complex-valued null space pursuit algorithm (NSP-CD) combined with the 1.5-dimensional Teager energy spectrum (1.5DTES). In the proposed algorithm, the bearing fault signals are decomposed by NSP-CD that is deduced by using partial differential equations and alternating direction method of multipliers, and several components that conform to the vibration signal mode are obtained. Then, the component containing the principal fault characteristic is selected according to the kurtosis value of each component. Finally, in order to accurately track the variation of amplitude and reduce noise interference, the 1.5DTES of the selected component is used to demonstrate the fault frequency of the bearing vibration signal. Experiments on vibration signals collected from electro-discharge machining with inner and outer ring faults demonstrate that the proposed method is more efficient and robust than other bearing diagnosis methods.

Local null space pursuit for real-time moving object detection in aerial surveillance

Recently, accurate detection of moving objects has achieved via principal component pursuit (PCP). However, in the case of aerial imagery, existing PCP-based detection methods suffer from low accuracy and/or high computational loads. This paper presents a novel S-PCP method, called local null space pursuit (LNSP), which achieves a high detection accuracy and real-time performance on aerial images. LNSP models the background as a subspace that lies in a low-dimensional subspace, while the moving objects are modelled as sparse. Based on these two models, LNSP proposes a new formulation for the detection problem by using multiple local null spaces and $$\ell _1$$-norm. The performance of LNSP is evaluated on challenging aerial datasets and then compared the results with relevant current state-of-the-art methods.

An Accelerated Sequential PCP-Based Method for Ground-Moving Objects Detection From Aerial Videos.

The detection of ground-moving objects in aerial videos has evolved over the years to handle more challenges such as large camera motion, the small size of the objects, and occlusion. Recently, aerial detection has been attempted using principal component pursuit (PCP) due to its superiority in detecting small moving objects. However, PCP-based detection methods generally suffer from high-false detections as well as high-computational loads. This paper presents a novel PCP-based detection method called kinematic regularization with local null space pursuit (KRLNSP) that drastically reduces false detections and the computational loads. KRLNSP models the background in an aerial video as a subspace that spans a low-dimension subspace while it models the moving objects as moving sparse. Accordingly, the detection is achieved by using multiple local null spaces and enhanced kinematic regularization. The multiple local null spaces allow real-time execution to nullify the background while preserving the moving objects unchanged. The kinematic regularization penalizes these moving objects to filter out false detections. The extensive evaluation of KRLNSP and relevant current state-of-the-art methods prove that the KRLNSP outperforms these methods (the true positive rate of KRLNSP is 98% and its false positive rate is 0.4%) and significantly reduces the computational loads (KRLNSP execution time is 0.3 s/frame).

Complex-valued differential operator-based method for multi-component signal separation

The null space pursuit (NSP) algorithm is an operator-based signal separation approach which separates a signal into a set of additive subcomponents using adaptively estimated operators and parameters. In this paper, a new operator termed complex-valued differential (CD) operator is proposed. Combining with the CD operator, this paper proposes NSP-CD algorithm to solve the CD operator-based signal separation problem. The NSP-CD algorithm can separate the multi-component signal into sum of amplitude-modulated and frequency-modulated (AM–FM) signals in the form of A(t)exp(j)(ϕ(t)). The proposed NSP-CD algorithm has many advantages. Firstly, the proposed CD operator can ensure that the AM–FM signal totally lies in the null space of the operator rather than close to the null space that the original used operator may reach. Secondly, compared with the original NSP algorithm, our algorithm provides a more reasonable strategy to update the regularization parameter λ and the leakage factor γ. Finally, we have proved that the proposed algorithm has quadric convergence theoretically. Experiments on both synthetic and real-life signals demonstrate that the NSP-CD algorithm is more robust and effective than other state-of-the-art methods.

Adaptive Integral Operators for Signal Separation

The operator-based signal separation approach uses an adaptive operator to separate a signal into a set of additive subcomponents. In this paper, we show that differential operators and their initial and boundary values can be exploited to derive corresponding integral operators. Although the differential operators and the integral operators have the same null space, the latter are more robust to noisy signals. Moreover, after expanding the kernels of Frequency Modulated (FM) signals via eigen-decomposition, the operator-based approach with the integral operator can be regarded as the matched filter approach that uses eigen-functions as the matched filters. We then incorporate the integral operator into the Null Space Pursuit (NSP) algorithm to estimate the kernel and extract the subcomponent of a signal. To demonstrate the robustness and efficacy of the proposed algorithm, we compare it with several state-of-the-art approaches in separating multiple-component synthesized signals and real-life signals.

Diagnosis of Roller Bearings Compound Fault Using Underdetermined Blind Source Separation Algorithm Based on Null-Space Pursuit

In order to solve the problem of underdetermined blind source separation (BSS) in the diagnosis of compound fault of roller bearings, an underdetermined BSS algorithm based on null-space pursuit (NSP) was proposed. In this algorithm, the signal model of faulty roller bearing is firstly used to construct an appropriate differential operator in null space. With the constructed differential operator, the mixed signals collected by the vibration sensor are decomposed into a series of stacks of narrow band signal containing the characteristics of faulty bearing. Finally, the underdetermined problem is transformed to an overdetermined problem by combining the narrow band signals and the original mixed signals into a new group of observed signals. In this way, the separation of the mixed signals can be realized. Experiments and engineering data analyses show that the problem of underdetermined BSS can be solved effectively by this approach, and then the compound fault of the roller bearing can be separated.

Research on Voltage Fluctuation and Flicker Extraction Method Based on Null Space Pursuit Algorithm

In order to obtain more accurate and rapid voltage fluctuations and flicker signal and provide fast and accurate data for power quality analysis and improvement, this paper proposes the improvement measures of null space pursuit algorithm based on the analysis of the principle of null space pursuit algorithm, which improves the value of practical application. By the simulation analysis, it proves that the combined null space pursuit algorithm not only has the same advantage of high precision extraction and decent noise reduction capabilities as original algorithm but also improves its computing speed and enhances its practical value.

A denoising method based on null space pursuit for infrared spectrum

The reduction of noise in infrared spectrum is of vital importance, as the infrared signal is often buried in excessive noise. In this paper, a novel denoising method based on null space pursuit (NSP) is proposed to eliminate noise in the infrared signal. The NSP is an adaptive operator-based signal separation approach, which can decompose signal into subband components and residue according to their characteristics. The residue is processed by mean filter because it contains very little useful information. Then, the subband components and the filtered residue are used to reconstruct the noise-free signal. Experimental results show that the proposed denoising method is effective in suppressing noise while retaining signal characteristics.

A detection method for bearing faults using null space pursuit and S transform

In this paper, a novel measurement method based on null space pursuit and S transform is presented to detect the faults of the bearing vibration signal. Since the features of bearing faults in the vibration signal may be submerged by machine-borne vibration and the high intensity of noise, it is very difficult to detect the bearing faults directly. The proposed method is a hybrid of null space pursuit and S transform. As a signal separation approach, the null space pursuit based on operator can extract the fault components from the vibration signal efficiently. Then, S transform is introduced to represent a “Magnitude-Frequency” and a “Time-Frequency” contour of the extracted fault components. Finally, several real vibration signals containing bearing fault signature are investigated to verify the effectiveness of the proposed method.

ECG Baseline Wander Removal by Null Space Pursuit

ECG Baseline Wander Removal by Null Space Pursuit

Multicomponent AM-FM signal separation and demodulation with null space pursuit

The operator-based signal separation approach, which formulates signal separation as an optimization problem, uses an adaptive operator to separate a signal into additive subcomponents. Furthermore, it is possible to design different operators to fit different signal models. In this paper, we propose a new kind of differential operator to separate multicomponent AM-FM signals. We then use the estimated operators to calculate each sub-component’s envelope and instantaneous frequency. To demonstrate the efficacy of the proposed method, we compare the decomposition and AM-FM demodulation results of several signals, including real-life signals.

Null Space Pursuit: An Operator-based Approach to Adaptive Signal Separation

The operator-based signal separation approach uses an adaptive operator to separate a signal into additive subcomponents. The approach can be formulated as an optimization problem whose optimal solution can be derived analytically. However, the following issues must still be resolved: estimating the robustness of the operator's parameters and the Lagrangian multipliers, and determining how much of the information in the null space of the operator should be retained in the residual signal. To address these problems, we propose a novel optimization formula for operator-based signal separation and show that the parameters of the problem can be estimated adaptively. We demonstrate the effectiveness of the proposed method by processing several signals, including real-life signals.