Subspace Projection Algorithm Research Articles

Automatic Estimation of the Interference Subspace Dimension Threshold in the Subspace Projection Algorithms of Magnetoencephalography Based on Evoked State Data.

A class of algorithms based on subspace projection is widely used in the denoising of magnetoencephalography (MEG) signals. Setting the dimension of the interference (external) subspace matrix of these algorithms is the key to balancing the denoising effect and the degree of signal distortion. However, most current methods for estimating the dimension threshold rely on experience, such as observing the signal waveforms and spectrum, which may render the results too subjective and lacking in quantitative accuracy. Therefore, this study proposes a method to automatically estimate a suitable threshold. Time-frequency transformations are performed on the evoked state data to obtain the neural signal of interest and the noise signal in a specific time-frequency band, which are then used to construct the objective function describing the degree of noise suppression and signal distortion. The optimal value of the threshold in the selected range is obtained using the weighted-sum method. Our method was tested on two classical subspace projection algorithms using simulation and two sensory stimulation experiments. The thresholds estimated by the proposed method enabled the algorithms to achieve the best waveform recovery and source location error. Therefore, the threshold selected in this method enables subspace projection algorithms to achieve the best balance between noise removal and neural signal preservation in subsequent MEG analyses.

Music Curriculum Research Using a Large Language Model, Cloud Computing and Data Mining Technologies

This paper presents a method to enhance the scientific nature of the music curriculum model by integrating a large language model, cloud computing and data mining technology for the analysis of the music teaching curriculum model. To maintain the integrity of the mixing matrix while employing the frequency hopping frequency, the paper suggests dividing the mixing matrix into a series of sub-matrices along the vertical time axis. This approach transforms wideband music signal processing into a narrowband processing problem. Additionally, two hybrid matrix estimation algorithms are proposed in this paper using underdetermined conditions. Furthermore, utilizing the estimated mixing matrix and the detected time-frequency support domain, the paper employs the subspace projection algorithm for underdetermined blind separation of music signals in the time-frequency domain. This procedure, along with the integration of the estimated direction of arrival (DoA), enables the completion of frequency-hopping network station music signal sorting. Extensive simulation teaching demonstrates that the music curriculum model proposed in this paper, based on a large language model, cloud computing and data mining technologies, significantly enhances the quality of modern music teaching.

Simulation of RFI Cancellation Using Subspace Projection Algorithm for PAF Receiver

The simulation of radio frequency interference (RFI) cancellation by applying a spatial filtering technique for phased array feed (PAF) is presented. In order to better reflect the characteristics of PAF, a new signal model is to add the coupling coefficient among elements of PAF to the conventional array signal model. Then the subspace projection (SP) algorithm is used to cancel RFI from the correlation matrix of the signal, and finally, the 2D power image is drawn. The power variation of signal-of-interest direction and RFI direction before and after using the SP algorithm is analyzed. The new signal model and simulation strategy can be used to test and verify the beamformer.

Performance analysis of subspace projection algorithm with respect to projection length for GNSS jamming mitigation

Non-stationary jamming signals broadcast by jammers severely threaten the reliability of global navigation satellite systems (GNSS). The instantaneous frequency (IF) based subspace projection algorithm is an attractive solution for GNSS jamming mitigation. However, its theoretical performance analysis is rare and not well discussed. To better apply subspace projection, we develop the theoretical post-correlation signal-to-interference-plus-noise power ratio (SINR) of receivers incorporating subspace projection to facilitate performance analysis. Different from existing work, this paper assumes that IF errors are independent and identically distributed instead of instantaneous phase errors, which is more reasonable. Numerical simulation results validate the derived theoretical SINR. The results show that the performance of subspace projection highly depends on the selection of projection length. Subspace projection with a well-designed projection length can perform much better than a conventional long projection length. Utilizing the theoretical SINR, the jamming mitigation performance of subspace projection with different projection lengths can be quickly evaluated, which provides an important theoretical guidance for the application of the algorithm.

Monopulse Parameter Estimation for FDA-MIMO Radar under Mainlobe Deception Jamming

Multiple input multiple output with frequency diversity array (FDA-MIMO) radar has unique advantages in mainlobe deception jamming suppression and target location. However, if the training sample contains the target signal, it will lead to poor jamming suppression performance and large target measurement error. To deal with the problem, a method of coarse target location in the time domain is proposed based on the cumulative sampling analysis. Taking full advantages of the strongest correlation characteristic between the expected steering vector and the true target, the feature vector and feature value corresponding to the true target are found after feature decomposition. The time domain location of the target is roughly estimated during the cumulative sampling analysis from near to far. Then, a pure jamming training sample can be obtained by avoiding the location. Noise subspace projection algorithm is used to measure the angle and range of the target while suppressing mainlobe jamming. The simulation results show that the proposed method can roughly estimate the target location in the time domain when the mainlobe deception jamming completely covers the target. Compared with conventional methods, the performance of jamming suppression and target localization error are closer to the performance of ideal sampling.

Subspace projection algorithms with robustness to IF errors for GNSS jamming mitigation

Subspace projection algorithms with robustness to IF errors for GNSS jamming mitigation

Interpolation-Based Subspace Projection for Sparsely Sampled Non-Stationary Jamming Mitigation

Non-stationary jamming signals broadcasted by jammers seriously affect the reliability of Global Navigation Satellite Systems (GNSS). What is worse, GNSS signals may be sparsely sampled or missing some samples in some situations. In this context, applying conventional anti-jam methods can lead to interference leakage. This letter proposes an interpolation-based subspace projection algorithm for non-stationary jamming mitigation in the presence of missing samples. To reduce interference leakage caused by missing samples, we propose to perform interpolation before applying subspace projection. The effectiveness of the algorithm is analyzed briefly. Numerical simulations show that the proposed algorithm can suppress interference very well in the presence of missing samples.

Supervised dimensionality reduction technology of generalized discriminant component analysis and its kernelization forms

Supervised subspace projection technology is a major method for dimensionality reduction in pattern recognition. At present, most supervised subspace projection algorithms are derived from the multi-dimensional extended version of Fisher linear discriminant analysis (FDA), also known as Multi-dimensional Fisher discriminant analysis (MD-FDA). However, MD-FDA needs to be improved further because the projection vectors in the noise-subspace cannot be sorted and the ill-condition of the within-class scatter matrix may cause severe numerical instabilities. Generalized discriminant component analysis (GDCA), the generalization of MD-FDA, together with its kernelization forms are proposed and correspondingly rigorous mathematical proofs are detailed in this paper. By virtue of 5 validation data sets derived from UCI Machine Learning Repository and our laboratory, the theoretical validity and technical advantages of GDCA as well as its kernelization forms are verified, and the effectiveness of the newly proposed method is demonstrated in comparison with 36 kinds of state-of-the-art dimensionality reduction algorithms.

Three-dimensional transient electromagnetic response of multiple grounded-wire sources

Multiple grounded-wire sources combination are proposed to improve the signal strength and resolution of the transient electromagnetic method. Multi-source excitation from the different direction was executed to identify the conductive body in the subsurface and achieve refined detection of the target body. The vector finite element method based on the rational Krylov subspace projection algorithm was used to calculate transient response of the target bodies. The voltage response calculated by our algorithm was compared with that calculated by the integral equation method and the results agreed well with them. We designed different grounded-wire combinations, including a single source, pairs of sources, and groups of three and four sources, and analyzed induced EMF and the secondary field response of one conductive body. It indicates that multi-source transient method can obtain stronger signals, which is beneficial to the discovery of deep weak anomalies. Finally, we established two adjacent conductive block bodies and compared their electromagnetic response for the different source combination. The results showed that multiple-source transient electromagnetic response anomaly amplitude and lateral resolution are superior to those of a single source. Multi-channel diagram for multiple sources have two obvious peaks, especially for three sources and four sources, but the induced EMF from a single source does not differentiate between the two conductive bodies in the horizontal direction. Multiple grounded-wire source combinations are used not only for the surface transient electromagnetic method but can also be extended to the grounded electrical-source airborne transient electromagnetic survey.

Unsupervised Identification of Targeted Spectra Applying Rank1-NMF and FCC Algorithms in Long-Wave Hyperspectral Infrared Imagery

Clustering methods unequivocally show considerable influence on many recent algorithms and play an important role in hyperspectral data analysis. Here, we challenge the clustering for mineral identification using two different strategies in hyperspectral long wave infrared (LWIR, 7.7–11.8 μm). For that, we compare two algorithms to perform the mineral identification in a unique dataset. The first algorithm uses spectral comparison techniques for all the pixel-spectra and creates RGB false color composites (FCC). Then, a color based clustering is used to group the regions (called FCC-clustering). The second algorithm clusters all the pixel-spectra to directly group the spectra. Then, the first rank of non-negative matrix factorization (NMF) extracts the representative of each cluster and compares results with the spectral library of JPL/NASA. These techniques give the comparison values as features which convert into RGB-FCC as the results (called clustering rank1-NMF). We applied K-means as clustering approach, which can be modified in any other similar clustering approach. The results of the clustering-rank1-NMF algorithm indicate significant computational efficiency (more than 20 times faster than the previous approach) and promising performance for mineral identification having up to 75.8% and 84.8% average accuracies for FCC-clustering and clustering-rank1 NMF algorithms (using spectral angle mapper (SAM)), respectively. Furthermore, several spectral comparison techniques are used also such as adaptive matched subspace detector (AMSD), orthogonal subspace projection (OSP) algorithm, principal component analysis (PCA), local matched filter (PLMF), SAM, and normalized cross correlation (NCC) for both algorithms and most of them show a similar range in accuracy. However, SAM and NCC are preferred due to their computational simplicity. Our algorithms strive to identify eleven different mineral grains (biotite, diopside, epidote, goethite, kyanite, scheelite, smithsonite, tourmaline, pyrope, olivine, and quartz).

Recognition and Mitigation of Micro-Doppler Clutter in Radar Systems via Support Vector Machine

The Micro-Doppler effect is a special manifestation of the signatures and motion states of the target. It plays an important role in the target classification and recognition. However, the micro-Doppler effects of many objects in the environment, such as wind turbines, tower cranes, and air conditionings, etc., act as time-varying clutter to radar systems, causing false alarms and missed detections. In this paper, we investigate the recognition and mitigation problems of the micro-Doppler clutter (MDC) in radar systems. Firstly, the recognition model of the MDC is obtained using the support vector machine (SVM). Through this recognition model, we are able to know the distribution of the MDC in range-Doppler (RD) maps. Then, a spatial subspace projection algorithm is used to mitigate the MDC along the Doppler dimension in the RD map. The proposed algorithm is verified by both simulated and measured data.

Resolution Threshold Analysis of the Microwave Radar Coincidence Imaging

The resolution of the microwave radar coincidence imaging (MRCI) can break the diffraction limit, which has been validated by experiments. However, there is still no theoretical analysis. In this article, the resolution of the MRCI is theoretically analyzed using the orthogonal subspace projection algorithm based on the space spanned by the discrete reference radiation mode. First, a target location estimate (TLE) method using the data from the nonfocusing radar array of the MRCI system is proposed to estimate the target position assisted by the equivalent detection method. The estimation precision of the TLE method is approximately equal to the 3-dB beamwidth of the coherent transmitting radar array with the same aperture; hence, the imaging plane can be obtained. Then, the equivalent internal noise (generated by the error of the target distance estimation, i.e., the location of the imaging plane) is theoretically analyzed. Finally, the imaging resolution threshold of the MRCI system is theoretically analyzed. The relationship between the resolution threshold and the factors (such as the deployment of the transmitting radar array, the distance between the target and the radar array, and the signal-to-noise ratio of the imaging system) is summarized. The proposed estimation method and the analyses of the MRCI system are validated through a set of simulations and experiments.

Evaluation of a dual signal subspace projection algorithm in magnetoencephalographic recordings from patients with intractable epilepsy and vagus nerve stimulators

Magnetoencephalography (MEG) data is subject to many sources of environmental noise, and interference rejection is a necessary step in the processing of MEG data. Large amplitude interference caused by sources near the brain have been common in clinical settings and are difficult to reject. Artifact from vagal nerve stimulators (VNS) is a prototypical example. In this study, we describe a novel MEG interference rejection algorithm called dual signal subspace projection (DSSP), and evaluate its performance in clinical MEG data from people with epilepsy and implanted VNS. The performance of DSSP was evaluated in a retrospective cohort study of patients with epilepsy and VNS who had MEG scans for source localization of interictal epileptiform discharges. DSSP was applied to the MEG data and compared with benchmark for performance. We evaluated the clinical impact of interference rejection based on human expert detection and estimation of the location and time-course of interictal spikes, using an empirical Bayesian source reconstruction algorithm (Champagne). Clinical recordings, after DSSP processing, became more readable and a greater number of interictal epileptic spikes could be clearly identified. Source localization results of interictal spikes also significantly improved from those achieved before DSSP processing, including meaningful estimates of activity time courses. Therefore, DSSP is a valuable novel interference rejection algorithm that can be successfully deployed for the removal of strong artifacts and interferences in MEG.

When collaborative representation meets subspace projection: A novel supervised framework of graph construction augmented by anti-collaborative representation

Abstract Collaborative representation (CR) offers an appealing way for similarity graph construction in subspace projection (SP) methods. However, the dissimilarities between samples from different classes under the CR framework have been far less investigated. In this paper, we try to integrate the full-length CR with graph embedding based SP, and gradually arrive at the following findings: (1) The methods involving both CR and SP can be formulated as a two-stage framework, where CR servers as a feature extraction step while SP further constructs the similarity graph for feature embedding. This uncovers the essence of this type of methods, as well as their limitations due to the unsupervised property of CR. (2) A novel concept of anti-collaborative representation (Anti-CR), as a counterpart of CR, is introduced to characterize the coding ability of each sample by the samples from different classes. In this way, the label information could be fully exploited to capture the sample-by-sample dissimilarities derived from Anti-CR at the first stage. (3) At the second stage, the above two representations are incorporated into the construction of within-class and between-class graphs, respectively, so that in the projected subspace, the collaborative relationship of the samples in the same class could be strengthened while the collaborative relationship of the samples from different classes would be largely inhibited. Straightforwardly, the above analysis leads to a novel SP method, coined Complete Representation based supervised Feature Extraction and Embedding (CRFEE), as well as its accelerated version (CRFEE-A). Extensive experiments on benchmark image datasets show that the proposed methods outperform several state-of-the-art SP and CR algorithms in terms of discriminant power, indicating the benefits of exploring the anti-collaborative representation for feature description and projection.

Harmonics extraction based speech recovery for underdetermined mixing systems

It is an intractable task to achieve high-efficiency and high-quality speech recovery for the existing underdetermined systems. To solve this problem, this paper proposes a harmonics extraction based underdetermined speech recovery algorithm, which consists of 4 stages. In the 1st stage, spectrum correction technique is adopted to extract the harmonic components from the mixtures’ short time Fourier transform (STFT); In the 2nd stage, a phase-coherence criterion is applied on these harmonic components to identify the single source components; In the 3rd stage, these single source patterns are further categorized into multiple groups by means of the adaptive k-means clustering, from which the mixing matrix is estimated; In the last stage, this estimated matrix is further combined with the subspace projection algorithm, which resultantly yields the final source recovery. The high efficiency lies in that the harmonics extraction is properly combined with single source component identification. The speech recovery experiment demonstrated that, compared to the original subspace projection algorithm, the proposed method can acquire a higher recovery quality, which presents a potential application in other harmonic related fields.

Joint Estimation of Frequency Offset and Doppler Shift in High Mobility Environments Based on Orthogonal Angle Domain Subspace Projection

Conventional frequency preshift technology cannot distinguish between the large Doppler shift and the frequency offset aroused by crystal oscillator, which significantly hinders the system performance improvement in high mobility environments when the frequency offset is present. In this paper, a joint frequency offset and Doppler shift estimation algorithm in high mobility environment based on orthogonal angle domain subspace projection is proposed, which can track the fast time-varying Doppler shift and separate the Doppler shift from the frequency offset. First, an orthogonal angle domain subspace projection algorithm is proposed to project the Doppler spread caused by high mobility into equivalent Doppler shifts in each orthogonal subspace. Second, it utilizes equivalent Doppler shift of all orthogonal subspaces to jointly estimate the maximal Doppler shift and frequency offset. Finally, the estimates are used to compensate the frequency error in the received signal. Moreover, the maximum Doppler shift estimation, together with the projection vectors and the received power on each orthogonal subspace, is fed back and exploited in the subsequent transmitted signal. Simulation results show that the proposed method can estimate the two parameters accurately and eliminate almost all the errors on the Doppler rapidly changing area when SNR is up to 15 dB. Compared with the conventional receiver with automatic frequency control, the receiver with our proposed method achieves better system performance even on the Doppler rapidly changing area.

Mapping alteration mineral zones and lithological units in Antarctic regions using spectral bands of ASTER remote sensing data

Geological mapping is one of the primary tasks of remote sensing. Remote sensing applications are especially useful when extreme environmental conditions inhibit direct survey such as in Antarctica. In this investigation, a satellite-based remote sensing approach was used for mapping alteration mineral zones and lithological units using Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) data in the Oscar II coast area, north-eastern Graham Land, Antarctic Peninsula. Specialized band ratios and band combinations were developed using visible and near infrared, shortwave infrared (SWIR) and thermal infrared spectral bands of ASTER for detecting alteration mineral assemblages and lithological units in Antarctic environments. Constrained Energy Minimization, Orthogonal Subspace Projection and Adaptive Coherence Estimator algorithms were tested to ASTER SWIR bands for detecting sub-pixels’ abundance of spectral features related to muscovite, kaolinite, illite, montmorillonite, epidote, chlorite and biotite. Results indicate valuable applicability of ASTER data for Antarctic geological mapping.

Tensor-Based Efficient Multi-Interferer RFI Excision Algorithms for SIMO Systems

Radio frequency interference (RFI) is causing performance loss in microwave radiometry, radio astronomy, and satellite communications. As the number of interferers increases, the performance loss gets more severe and RFI excision becomes more difficult. In this regard, this paper introduces the multilinear algebra framework to the multi-interferer RFI (MI-RFI) excision research by proposing a multi-linear subspace estimation and projection (MLSEP) algorithm for single-input multiple-output (SIMO) systems suffering from MI-RFI. Having employed smoothed observation windows, a smoothed MLSEP (s-MLSEP) algorithm, which enhances MLSEP, is also proposed. MLSEP and s-MLSEP require the knowledge of the number of interferers and their respective channel order. Accordingly, a novel smoothed matrix-based joint number of interferers and channel order enumerator is proposed. Performance analyses corroborate that both MLSEP and s-MLSEP can excise all interferers when the perturbations get infinitesimally small. For such perturbations, the analyses also attest that s-MLSEP exhibit a faster convergence to a zero excision error than MLSEP which, in turn converges faster than a subspace projection algorithm. Despite its slight complexity, simulations and performance assessment on real-world data demonstrate that MLSEP outperforms projection-based RFI excision algorithms. Simulations also corroborate that s-MLSEP outperforms MLSEP as the smoothing factor gets smaller.

Improved algorithm for hyperspectral data dimension determination

The correlation between adjacent bands of hyperspectral image data is relatively strong. However, signal coexists with noise and the HySime (hyperspectral signal identification by minimum error) algorithm which is based on the principle of least squares is designed to calculate the estimated noise value and the estimated signal correlation matrix value. The algorithm is effective with accurate noise value but ineffective with estimated noise value obtained from spectral dimension reduction and de-correlation process. This paper proposes an improved HySime algorithm based on noise whitening process. It carries out the noise whitening, instead of removing noise pixel by pixel, process on the original data first, obtains the noise covariance matrix estimated value accurately, and uses the HySime algorithm to calculate the signal correlation matrix value in order to improve the precision of results. With simulated as well as real data experiments in this paper, results show that: firstly, the improved HySime algorithm are more accurate and stable than the original HySime algorithm; secondly, the improved HySime algorithm results have better consistency under the different conditions compared with the classic noise subspace projection algorithm (NSP); finally, the improved HySime algorithm improves the adaptability of non-white image noise with noise whitening process.

Clutter suppression for hypersonic vehicle-borne radar with frequency diverse array

The seriously range-ambiguous clutter is one of the main problems in clutter suppression for hypersonic vehicle-borne forward-looking radar. An approach based on the frequency diverse array (FDA) technique is proposed to mitigate the range-ambiguous clutter. The frequency increment is designed to distinguish the clutter at ambiguous ranges and suppress the clutter by using a subspace projection algorithm. On the platform with high altitude or limited array antennas, the proposed method performs better for its independence of the elevation degrees-of-freedom (DOF). Finally, simulation results verify the effectiveness of the proposed method.