Space-frequency Domain Research Articles

CSF-GTNet: A Novel Multi-Dimensional Feature Fusion Network Based on Convnext-GeLU- BiLSTM for EEG-Signals-Enabled Fatigue Driving Detection.

Electroencephalography (EEG) signal has been recognized as an effective fatigue detection method, which can intuitively reflect the drivers' mental state. However, the research on multi-dimensional features in existing work could be much better. The instability and complexity of EEG signals will increase the difficulty of extracting data features. More importantly, most current work only treats deep learning models as classifiers. They ignored the features of different subjects learned by the model. Aiming at the above problems, this paper proposes a novel multi-dimensional feature fusion network, CSF-GTNet, based on time and space-frequency domains for fatigue detection. Specifically, it comprises Gaussian Time Domain Network (GTNet) and Pure Convolutional Spatial Frequency Domain Network (CSFNet). The experimental results show that the proposed method effectively distinguishes between alert and fatigue states. The accuracy rates are 85.16% and 81.48% on the self-made and SEED-VIG datasets, respectively, which are higher than the state-of-the-art methods. Moreover, we analyze the contribution of each brain region for fatigue detection through the brain topology map. In addition, we explore the changing trend of each frequency band and the significance between different subjects in the alert state and fatigue state through the heat map. Our research can provide new ideas in brain fatigue research and play a specific role in promoting the development of this field.

Efficient preconditioned least-squares wave-equation migration

Since the appearance of wave-equation migration (WEM), many have tried to improve the resolution and effectiveness of this technology. Least-squares wave-equation migration is one of those attempts that try to fill the gap between migration assumptions and reality in an iterative manner. However, these iterations do not come cheap. A proven solution to limit the number of least-squares iterations is to correct the gradient direction within each iteration via the action of a preconditioner that approximates the inverse Hessian. However, the Hessian computation, or even the Hessian approximation computation, in large-scale seismic imaging problems involves an expensive computational bottleneck, making it unfeasible. Therefore, we develop an efficient computation of the Hessian approximation operator in the context of one-way WEM in the space-frequency domain. We build the Hessian approximation operator depth by depth, considerably reducing the operator size each time it is calculated. We prove the validity of our method with two numerical examples. We then extend our proposal to the framework of full-wavefield migration, which is based on WEM principles but includes interbed multiples. Finally, this efficient preconditioned least-squares full-wavefield migration is successfully applied to a data set with strong interbed multiple scattering.

Large-region image inpainting using adaptive Fourier Neural Network and space-frequency domain structural analysis

Large-region image inpainting using adaptive Fourier Neural Network and space-frequency domain structural analysis

TFCSRec: Time–frequency consistency based contrastive learning for sequential recommendation

Sequential recommendation aims to predict future user interactions by analyzing dynamic patterns within their historical behavior sequences. Deep neural networks have recently become popular for learning representations of these sequences in the time domain. However, representing users’ intentions in the time domain faces challenges such as noise in interactions and sparsity of data. Contrastive learning and representation learning in the frequency domain can mitigate these issues from different perspectives. In this paper, to fully integrate time-domain sequence representations, frequency-domain sequence representations and contrastive learning based on them, we propose a model called Time–Frequency Consistency based contrastive learning for Sequential Recommendation (TFCSRec). TFCSRec utilizes a time-domain encoder with a fully connected network and a filter network to extract high-order features and catch pure sequential patterns. Then, a learnable frequency-domain encoder with a recurrent neural network is designed to capture sequential characteristics in the frequency-domain space. Finally, TFCSRec combines a recommendation task and two contrastive learning tasks to optimize the two user representation encoders. Its contrastive learning is designed to minimize a contrastive regularization loss and a time–frequency consistency loss, which for the first time is constructed directly on the time-domain sequence representation and the frequency-domain sequence representation. Experiments on five benchmark datasets show that the proposed TFCSRec model outperforms other sequential recommendation models based on deep neural networks.

Multi-feature fusion based face forgery detection with local and global characteristics.

The malicious use of deepfake videos seriously affects information security and brings great harm to society. Currently, deepfake videos are mainly generated based on deep learning methods, which are difficult to be recognized by the naked eye, therefore, it is of great significance to study accurate and efficient deepfake video detection techniques. Most of the existing detection methods focus on analyzing the discriminative information in a specific feature domain for classification from a local or global perspective. Such detection methods based on a single type feature have certain limitations in practical applications. In this paper, we propose a deepfake detection method with the ability to comprehensively analyze the forgery face features, which integrates features in the space domain, noise domain, and frequency domain, and uses the Inception Transformer to learn the mix of global and local information dynamically. We evaluate the proposed method on the DFDC, Celeb-DF, and FaceForensic++ benchmark datasets. Extensive experiments verify the effectiveness and good generalization of the proposed method. Compared with the optimal model, the proposed method with a small number of parameters does not use pre-training, distillation, or assembly, but still achieves competitive performance. The ablation experiments evaluate the role of each component.

Channel Estimation for LEO Satellite Massive MIMO OFDM Communications

In this paper, we investigate the massive multiple-input multiple-output orthogonal frequency division multiplexing channel estimation for low-earth-orbit satellite communication systems. First, we use the angle-delay domain channel to characterize the space-frequency domain channel. Then, we show that the asymptotic minimum mean square error (MMSE) of the channel estimation can be minimized if the array response vectors of the user terminals (UTs) that use the same pilot are orthogonal. Inspired by this, we design an efficient graph-based pilot allocation strategy to enhance the channel estimation performance. In addition, we devise a novel two-stage channel estimation (TSCE) approach, in which the received signals at the satellite are manipulated with per-subcarrier space domain processing followed by per-user frequency domain processing. Moreover, the space domain processing of each UT is shown to be identical for all the subcarriers, and an asymptotically optimal vector for the per-subcarrier space domain linear processing is derived. The frequency domain processing can be efficiently implemented by means of the fast Toeplitz system solver. Simulation results show that the proposed TSCE approach can achieve a near performance to the MMSE estimation with much lower complexity.

SOC Algorithm-Based Framework for Spectrum Occupancy Completion

This paper investigates the completion of continuous spectrum occupancy in space-frequency domain. Most of the existing studies adopt the traditional scheme, namely field strength completion followed by feature extraction. However, the existence of non-ideal sampling data challenges the recovery of spectrum occupancy array in accuracy. In this paper, we first develop a spectrum occupancy completion framework that implements feature extraction and spectrum occupancy completion sequentially, which reduces the impact of non-ideal data on completion. Then, to further improve the completion accuracy, a semantic-optional-based completion (SOC) algorithm is proposed, which divides the continuous spectrum occupancy data into discrete and multi-class spectrum semantic data according to the spectrum occupancy level. Specifically, the completion of spectrum occupancy is realized by specific semantic extraction, spectrum semantic completion and spectrum semantic recovery. Further, the real-world measured data are simulated to demonstrate the effectiveness of our proposed framework and SOC. The experimental results show that, compared with the low-rank completion algorithm and spatial interpolation algorithm, the proposed SOC has higher completion accuracy at more than 93% frequency points.

A novel knee-guided algorithm based on frequency analysis for non-cyclic dynamic multiobjective optimization problems

In real life, many dynamic multiobjective optimization problems (DMOPs) have both time-varying and non-cyclic properties. Their non-cyclic nature differentiates the dynamics of the problem from all previous moments, and the changes become increasingly complex over time. Therefore, geometric changes in the Pareto-optimal front (PF) are more difficult to track. A novel knee-guided algorithm based on frequency analysis (NKGFA) is designed to solve non-cyclic DMOPs. To identify sufficient feature points to describe the change in PF, a knee-guided prediction strategy based on frequency analysis is proposed. From the perspective of frequency-domain analysis, almost all concave and convex knee points that contain critical feature information on the PF are identified. By predicting the frequency-domain information of the knees, the population’s evolutionary trend is obtained in the frequency-domain space. An interpolation strategy based on approximate frontier manifold construction is proposed to ensure that the population is uniformly distributed on the PF. This strategy established an approximate PF between concave and convex knee points. Moreover, it adaptively interpolated the new individuals in the approximate PF. A non-cyclic dynamic (NCD) benchmark test suite is designed, including PFs with increasingly complex geometric features. The effectiveness of the NKGFA is verified by comparing it with four algorithms in the NCD test suite. The NKGFA performed best on 26, 23, and 29 of the 39 test problems on Inverted Generational Distance (IGD), Schott’s Spacing Metric (SP), and Hypervolume Difference (HVD), respectively.

Efficient representation of head-related transfer functions in continuous space–frequency domains

Utilizing spherical harmonic (SH) domain has been established as the default method of obtaining continuity over space in head-related transfer functions (HRTFs). This paper concerns different variants of extending this solution by replacing SHs with four-dimensional (4D) continuous functional models in which frequency is imagined as another physical dimension. Recently developed hyperspherical harmonic (HSH) representation is compared with models defined in spherindrical coordinate system by merging SHs with one-dimensional basis functions. The efficiency of both approaches is evaluated based on the reproduction errors for individual HRTFs from HUTUBS database, including detailed analysis of its dependency on chosen orders of approximation in frequency and space. Employing continuous functional models defined in 4D coordinate systems allows HRTF magnitude spectra to be expressed as a small set of coefficients which can be decoded back into values at any direction and frequency. The best performance was noted for HSHs and SHs merged with reverse Fourier–Bessel series, with the former featuring better compression abilities, achieving slightly higher accuracy for low number of coefficients. The presented models can serve multiple purposes, such as interpolation, compression or parametrization for machine learning applications, and can be applied not only to HRTFs but also to other types of directivity functions, e.g. sound source directivity.

High-Resolution and Wide-Swath SAR Imaging with Space–Time Coding Array

To achieve high-resolution and wide-swath (HRWS) synthetic aperture radar (SAR) images, this paper focuses on resolving the problem of separating range-ambiguous echoes with the space–time coding (STC) array. At the modeling stage, the transmit elements and pulses of the STC array are configured with time delay and phase coding modulation, which introduces extra degrees of freedom (DOFs) in the transmit domain. To separate the echoes corresponding to different range-ambiguity regions, the equivalent transmit beamforming is performed in the two-dimensional space–frequency domain. Moreover, in order to compensate for the loss of range resolution during the beamforming progress, the frequency splicing method is proposed. At the analysis stage, the distributed target simulation is provided to demonstrate the effectiveness of obtaining HRWS SAR images in the STC radar. Additionally, the performance of resolving range ambiguity is compared with the traditional radar in terms of the range-ambiguity-to-signal ratio (RASR).

A stochastic volume approach based on tailored Green’s functions for airfoil noise prediction at low Mach number

The presence of boundary surfaces in a turbulent flow can result in the enhancement of the radiated acoustic field especially for eddies close to any geometrical singularity. At low Mach number, the best suited prediction methods consist in using an acoustic analogy solved with an integral formulation. In the present study, we focus on the Lighthill’s wave equation combined with a tailored Green’s function and a new semi-analytical model for the turbulence statistics in the space-frequency domain to extend acoustic analogies to geometries of arbitrary shapes. To validate the model predictions for the leading edge noise and the trailing edge noise, a NACA 0012 airfoil at zero angle of attack is considered and predictions are compared to experimental data. The volume integral approach introduced in this study allows us to study the spatial distribution of the noise sources inside the turbulence volume. In addition, the direct noise radiation associated with the turbulent boundary layer is investigated.

Generation of cross-spectrally pure electromagnetic fields using a pair of moving diffusers.

In this paper, we demonstrate that the vector light field is cross-spectrally pure if it passes through two diffusers (having similar correlation properties) moving with identical linear speeds in opposite directions. To determine the spatio-temporal coherence function of cross-spectrally pure light, a double slit is placed just after the second diffuser. We show that the normalized space-time coherence Stokes parameters of emerging light can be described in the form of a reduction formula, whereas the absolute values of the normalized space-frequency coherence Stokes parameters are the same for every frequency component of the light field. These are the conditions of cross-spectral purity of Stokes parameters. We further prove that at zero time delay, the condition of strict cross-spectral purity is validated. Furthermore, we establish the conditions for cross-spectral purity for a vector light field passing through the aforesaid diffusers, when they rotate with identical angular speeds in opposite directions, offering a possibility to optimize the scheme using only a single diffuser. For the first time, to our knowledge, an additional condition for equality of the degree of cross-polarization in space-time and space-frequency domains for strict cross-spectrally pure light beams is also introduced.

A Study on Electromagnetic Scattering Characteristics of 4-D Antenna Arrays

A theoretical study on electromagnetic scattering mechanism of 4-D antenna arrays is performed for the first time. First, the scattering fields of one antenna element within an infinite 4-D array are derived under periodic boundary conditions. In order to estimate the scattering performances of 4-D antenna arrays, numerical models of the scattering fields are then established based on the traditional scattering pattern multiplication theory. Moreover, an effective time-domain full-wave approach is proposed for the scattering cross section (SCS) simulation of 4-D arrays. Finally, to verify the feasibility for SCS reduction through 4-D arrays, the differential evolution (DE) algorithm is adopted to synthesize a 14-element microstrip patch antenna array for the optimization of radiation and scattering performances. Numerical results show that 4-D arrays are capable of scattering the incident waves in both space domain and frequency domain simultaneously, thus accomplishing remarkable in-band SCS reduction.

Low-Altitude Windshear Estimation Method Based on Four-Dimensional Frequency Domain Compensation for Fuselage Frustum Conformal Array

In this paper, a low-altitude wind speed estimation method based on the fuselage frustum conformal array system is proposed. Firstly, based on the signal model of the fuselage conformal array radar, the four-dimensional joint phase compensation of the echo data in the Doppler domain and three-dimensional space-frequency domain is performed by using the four-dimensional frequency domain compensation method. Secondly, the clutter covariance matrix is estimated by the compensated echo data, and a space-time Adaptive Processing (STAP) processor suitable for low-altitude windshear target is constructed to suppress clutter. Finally, the maximum Doppler value of each distance cell is extracted, and the wind velocity is estimated. Simulation results show that the proposed method can effectively suppress clutter and accurately estimate wind speed.

Measurement of spatial coherence of light [Invited

The most frequently used experimental techniques for measuring the spatial coherence properties of classical light fields in the space-frequency and space-time domains are reviewed and compared, with some attention to polarization effects. In addition to Young's classical two-pinhole experiment and several of its variations, we discuss methods that allow the determination of spatial coherence at higher data acquisition rates and also permit the characterization of lower-intensity light fields. These advantages are offered, in particular, by interferometric schemes that employ only beam splitters and reflective elements, and thereby also facilitate spatial coherence measurements of broadband fields.

The spatial frequency domain designated watermarking framework uses linear blind source separation for intelligent visual signal processing.

This paper develops a digital watermarking algorithm using an informed watermark retrieval architecture. The developed method uses the fractional Fourier transform to embed the watermark in the space-frequency domain and extracts the watermark using blind source separation techniques. The watermark embedding is further enhanced using a heuristic algorithm to increase the strength of the watermarking system. We use genetic algorithm to find the optimal fractional domain by minimizing the coefficient of RMSE between the input image and the watermarked image. The algorithm's performance against various common attacks, e.g., JPEG compression and Gaussian noise, is presented to estimate the algorithm's robustness.

Spectral coherence of white LEDs

We address space–frequency domain coherence properties of broadband light-emitting diodes (white LEDs) and fields radiated by them. Inverse-source techniques are employed to determine the spectral degree of spatial coherence of an effective planar source representing a real LED, and coherent elementary fields associated with it. By fitting with experimental measurements, we formulate simple analytical coherence models that can be used as a basis for theoretical and experimental studies of the coherence of polychromatic stationary light in free space and in various optical systems. In particular, we find that radiation from white LEDs follows closely Wolf’s scaling law for spectral invariance [Phys. Rev. Lett. 56, 1370 (1986)PRLTAO0031-900710.1103/PhysRevLett.56.1370] in the blue and the phosphor-generated parts of the spectrum separately, but not across the entire white-light spectrum.

Generalized partially coherent power-exponent-phase vortex beams

We propose a generalized partially coherent power-exponent-phase vortex beam, and study its generation and propagation characteristics in space-frequency domain. A complete transmission theory suitable for all generalized power-exponent-phase vortex beams is established and then demonstrated by experiments. The results show that generalized partially coherent power-exponent-phase vortex beams have their own characteristics in fan-shaped intensity distribution, intensity distribution of main lobes and side lobes and phase singularities. By combining theory and experiments, we summarize these characteristics, and put forward some potential application prospects.

Single-shot ultrafast multiplexed coherent diffraction imaging

Classic interferometry was commonly adopted to realize ultrafast phase imaging using pulsed lasers; however, the reference beam required makes the optical structure of the imaging system very complex, and high temporal resolution was reached by sacrificing spatial resolution. This study presents a type of single-shot ultrafast multiplexed coherent diffraction imaging technique to realize ultrafast phase imaging with both high spatial and temporal resolutions using a simple optical setup, and temporal resolution of nanosecond to femtosecond scale can be realized using lasers of different pulse durations. This technique applies a multiplexed algorithm to avoid the data division in space domain or frequency domain and greatly improves the spatial resolution. The advantages of this proposed technique on both the simple optical structure and high image quality were demonstrated by imaging the generation and evaluating the laser-induced damage and accompanying phenomenon of laser filament and shock wave at a spatial resolution better than 6.96 μm and a temporal resolution better than 10 ns.

SparNet: A Convolutional Neural Network for EEG Space-Frequency Feature Learning and Depression Discrimination.

Depression affects many people around the world today and is considered a global problem. Electroencephalogram (EEG) measurement is an appropriate way to understand the underlying mechanisms of major depressive disorder (MDD) to distinguish depression from normal control. With the development of deep learning methods, many researchers have adopted deep learning models to improve the classification accuracy of depression recognition. However, there are few studies on designing convolution filters for spatial and frequency domain feature learning in different brain regions. In this study, SparNet, a convolutional neural network composed of five parallel convolutional filters and the SENet, is proposed to learn EEG space-frequency domain characteristics and distinguish between depressive and normal control. The model is trained and tested by the cross-validation method of subject division. The results show that SparNet achieves a sensitivity of 95.07%, a specificity of 93.66%, and an accuracy of 94.37% in classification. Therefore, our results can conclude that the proposed SparNet model is effective in detecting depression using EEG signals. It also indicates that the combination of spatial information and frequency domain information is an effective way to identify patients with depression.