Fourier Phase Research Articles

Biometric Identification From ECG Signals Using Fourier Decomposition and Machine Learning

This paper investigates biometric identification systems based on ECG signals and their intra-subject and intrasession validity. We develop an efficient algorithm using Fourier decomposition method (FDM) and phase transform. Firstly, the ECG signal is divided into frames consisting of one or more beats. These frames capture both inter-beat and intra-beat variations. They are decomposed into a set of Fourier intrinsic band functions using FDM and relevant features are extracted from them. In addition to this, phase transform has been employed to highlight the intrinsic information hidden in the phase of ECG signals. The effects of variations in size of the frame, the decomposition levels, and the number of sessions used for training and testing, on the performance of the algorithm are analyzed. Random forest, ensemble subspace discriminant and support vector machine are applied as classifiers to evaluate the performance on three datasets, MIT-BIH, ECG-ID and CYBHi, where MIT-BIH is acquired in an on-the-person setting and the other two are off-the-person datasets. The proposed method achieved identification accuracies of 91.07% for CYBHi dataset, 97.92% for MIT-BIH dataset and 98.45% for ECG-ID dataset, which are better than most of the existing state-of-the-art algorithms.

Celestial Spectrum Velocimetry With Non-Linear Fourier Phase Shift and Its CRLB

To solve the problem of the non-linear Fourier phase shift caused by the wavelength shift in the celestial spectrum velocimetry, a celestial spectrum velocimetry method based on non-uniform discrete Fourier transform and compressed sensing is proposed. First, according to the properties of the non-uniform discrete Fourier transform with non-periodic celestial spectra, the non-linear relationship between the spectral wavelength shift and the Fourier phase shift is deduced theoretically. And then, the discrete cosine transform is used to decompose and reconstruct the spectrum to construct the phase dictionary of the non-periodic spectrum. In this dictionary, the spectral wavelength shift has a non-linear relationship with the Fourier phase shift. Finally, the non-uniform Fourier transform matrix is used as the measurement matrix. And the Doppler wavelength shift is estimated by using a non-linear and super-resolution matching algorithm to estimate the velocimetry. Experimental results show that when the spacecraft’s velocity is high, the celestial spectrum velocimetry method with non-linear Fourier phase shift (CSV-NFPS) can effectively measure the velocity from the spectrum, and its accuracy approaches the theoretical Cramer-Rao lower bounds (CRLB). Compared with the traditional Taylor method, the CSV-NFPS has an average accuracy improvement of 16.18% and a computational complexity reduction of 25.07%. In short, our method eliminate the non-linear bias in the celestial spectrum velocimetry and reduce a certain computational complexity.

Key Frame Extraction Algorithm of Surveillance Video Based on Quaternion Fourier Significance Detection

With the improvement of people's security awareness, numerous monitoring equipment has been put into use, resulting in the explosive growth of surveillance video data. Key frame extraction technology is a paramount technology for improving video storage efficiency and enhancing the accuracy of video retrieval. It can extract key frame sets that can express video content from massive videos. However, the existing key frame extraction algorithms of surveillance video still have deficiencies, such as the destruction of image information integrity and the inability to extract key frames accurately. To this end, this paper proposes a key frame extraction algorithm of surveillance video based on quaternion Fourier saliency detection. Firstly, the algorithm used colors, and intensity features to perform quaternion Fourier transform on surveillance video sequences. Next, the phase spectrum of the quaternion Fourier transformed image was obtained, and he image visual saliency map was obtained according to the quaternion Fourier phase spectrum. Then, the image visual saliency map of two adjacent frames is used to characterize the change of target motion state. Finally, the frames that can accurately express the motion state of the target are selected as key frames. The experimental results show that the method proposed in this paper can accurately capture the changes of the local motion state of the target while maintaining the integrity of the image information.

An Efficient Short-Time Discrete Cosine Transform and Attentive MultiResUNet Framework for Music Source Separation

The music source separation problem, where the task at hand is to estimate the audio components that are present in a mixture, has been at the centre of research activity for a long time. In more recent frameworks, the problem is tackled by creating deep learning models, which attempt to extract information from each component by using Short-Time Fourier Transform (STFT) spectrograms as input. Most approaches assume that one source is present at each time-frequency point, which allows to allocate this point from the mixture to the desired source. Since this assumption is very strong and is reported not to hold in practice, there is a problem that arises from the use of the magnitude of the STFT as input to these networks, which is the absence of the Fourier phase information during the separated source reconstruction. The recovery of the Fourier phase information is neither easily tractable, nor computationally efficient to estimate. In this paper, we propose a novel Attentive MultiResUNet architecture, that uses real-valued Short-Time Discrete Cosine Transform data as inputs. This step avoids the phase recovery problem, by estimating the appropriate values within the network itself, rather than employing complex estimation or post-processing algorithms. The proposed novel network features a U-Net type structure with residual skip connections and an attention mechanism that correlates the skip connection and the decoder output at the previous level. The proposed network is used for the first time in source separation and is more computationally efficient than state-of-the-art separation networks and features favourable performance compared to the state-of-the-art with a fraction of the computational cost.

High Accuracy Motion Detection Algorithm via ISM Band FMCW Radar

The conventional frequency modulated continuous wave (FMCW) radar accuracy range detection algorithm is based on the frequency estimation and additional phase evaluation which contains Fourier transform and frequency refining analysis in each chirp, so it has the disadvantages of being computationally expensive, and not being suitable for real-time motion measurement. In addition, if there are other objects near the target, the spectra of the clutter and the target will be adjacent and affect each other, making it more challenging to estimate the frequency of the target. In this paper, the analytical expression of the Fourier transform of the beat signal is presented and it can be seen that spectrum leakage makes the phase of Fourier transform no longer consistent with the real phase of signal. The change regularities of real and imaginary parts of Fourier transform are studied, and the corrected phase of ellipse approximation is given in the industrial, scientific, and medical (ISM) band. Accurate displacement can be obtained by accurate phase. The algorithm can filter the direct current (DC) offset which is mainly caused by stationary objects. The performance of the algorithm is evaluated by a radar system whose center frequency is 24.075 GHz and the bandwidth is 0.15 GHz; the measurement accuracy of displacement is 0.087 mm and the accuracy of distance is 0.043 m.

High-Performance Polymeric Surfactant of Sodium Lignosulfonate-Polyethylene Glycol 4000 (SLS-PEG) for Enhanced Oil Recovery (EOR) Process

Recently, the increase in fuel oil demand was not supported by petroleum production due to the low productivity of old wells. Furthermore, an appropriate technology, such as Enhanced Oil Recovery (EOR) technology, is needed to maximize the productivity of the old well. Therefore, the purpose of this study was to synthesize a polymeric surfactant for the EOR process from sodium lignosulfonate (SLS) and polyethylene glycol (PEG) in various SLS to PEG ratios, namely 1:1 (PS1), 1:0.8 (PS2), and 1:0.5 (PS3). The surfactants were characterized using several methods, such as Fourier Transform-Infrared spectroscopy (FT-IR), compatibility, stability, viscosity, and phase behavior tests. The performance of the surfactants for the EOR process in different brine solution concentrations (16,000 ppm and 20,000 ppm) was also studied. The result showed that the introduction of the PEG molecule to the surfactant had been successfully conducted as FT-IR analysis confirmed. The surfactant's hydrophilicity increased with the introduction of PEG due to the increase of the ether group. A Winsor Type I or lower phase microemulsion was formed due to the high hydrophilicity. The highest oil yield (79 %) was obtained by PS1 surfactant, which has the highest PEG dosage, in a brine solution of 1,600 ppm. Therefore, it was concluded that the introduction of PEG could increase the hydrophilicity, viscosity, and EOR performance.

Exploring different textures of a nematic liquid crystal for quantitative Fourier phase contrast microscopy

Quantitative phase microscopy (QPM) has emerged as a viable technique for investigating biological and biomedical samples in its natural environment. Contrary to well established phase microscopes, QPM provides phase map of the optical path length delays introduced by the specimen. Building on our prior technology of the Fourier phase contrast microscopy (FPCM) technique, we present a low-cost and robust quantitative Fourier phase contrast microscopy system that can easily be attached to most commercial brightfield microscopes. This is derived by merging the FPCM technique with phase shifting interferometry. By applying voltages across a nematic liquid crystal cell with various anchoring properties, Stokes’ parameters are obtained to unwrap the object information quantitatively. Further three different nematic textures were considered to improve the utility of the phase unwrapping: planar, twisted, and hybrid. Our results indicate that the hybrid nematic film presents the best phase contrast filter.

Methods of Projecting Mode Amplitude Changes on the Wavelength Axis in Order to Determine the Bending Radius on the Basis of TFBG Grating Spectra.

Tilted fibre Bragg grating (TFBG) are used as sensors to determine many quantities such as refractive index, temperature, stress, rotation and bending. The TFBG spectrum contains a lot of information and various algorithms are used for its analysis. However, most of these algorithms are dedicated to the analysis of spectral changes under the influence of the refractive index. The most popular algorithm used for this purpose is to calculate the area occupied by cladding modes. Among the remaining algorithms, there are those that use the determination of the cut-off wavelength as a surrounding refractive index (SRI) indicator. Projection on the wavelength axis can also be used to calculate the bending radius of the fibre. However, this is a more difficult task than with SRI, because the mode decay in bending is not so easy to catch. In this article, we propose a multi-step algorithm that allows to determine the impact of bending on mode leakage. At the same time, the place on the wavelength from the side of the Bragg mode and the ghost mode is determined, which represents the cladding mode radiated from the cladding under the influence of bending. The developed algorithm consists of the following operations carried out on the transmission spectrum: Fourier filtering, calculation of the cumulative value of the spectral length, low-pass filtering of the cumulative curve or its corresponding polynomial approximation, determination of the first and second derivative of the approximated curve, and projection of the second derivative of the curve on the wavelength axis. The shift of the wavelength determined in this way indirectly indicates the bending radius of the optical fibre. Based on multiple measurements, we prove that the presented algorithm provides better results when determining the bending radius compared to other algorithms adopted for this purpose and proposed for SRI measurements. Additionally, we analyse the method of determining the shift of a fragment of the spectrum using the phase of the discrete Fourier transform.

Automated design of pulse sequences for magnetic resonance fingerprinting using physics-inspired optimization

Magnetic resonance fingerprinting (MRF) is a method to extract quantitative tissue properties such as [Formula: see text] and [Formula: see text] relaxation rates from arbitrary pulse sequences using conventional MRI hardware. MRF pulse sequences have thousands of tunable parameters, which can be chosen to maximize precision and minimize scan time. Here, we perform de novo automated design of MRF pulse sequences by applying physics-inspired optimization heuristics. Our experimental data suggest that systematic errors dominate over random errors in MRF scans under clinically relevant conditions of high undersampling. Thus, in contrast to prior optimization efforts, which focused on statistical error models, we use a cost function based on explicit first-principles simulation of systematic errors arising from Fourier undersampling and phase variation. The resulting pulse sequences display features qualitatively different from previously used MRF pulse sequences and achieve fourfold shorter scan time than prior human-designed sequences of equivalent precision in [Formula: see text] and [Formula: see text] Furthermore, the optimization algorithm has discovered the existence of MRF pulse sequences with intrinsic robustness against shading artifacts due to phase variation.

Orthogonal sampling moiré method and its application in microscale deformation field measurement

Sampling moiré (SM) method is one of the modern deformation measurement methods in photomechanics. This method realizes the visualization measurement of deformation field by a sparse sampling of grating images, showing the advantages of high efficiency and strong robustness. However, in the traditional sampling moiré method, the unidirectional sampling mode is used with the result that the two-dimensional deformation cannot be acquired at the same time. In this paper, by combining the orthogonal sampling and Fourier phase analysis techniques, an orthogonal sampling moiré (OSM) method is proposed with which the two-directional moiré phase of specimen grating can be separated synchronously. The accuracy of the OSM method for the deformation measurement is verified by numerical experiments and PMMA uniaxial tensile tests. As an application, in a scanning electron microscope (SEM), the deformation field near the crack tip of small fatigue cracks is measured, based on which the crack opening displacement (COD) and the stress intensity factors (K) are obtained. Furthermore, the crack closure effects at different temperatures are characterized. The experimental results show that the crack closure significantly affects the process of small crack growth at both room temperature and high temperature, and the crack opening load at high temperature is greater than that at room temperature, which indicates that small cracks are easier to close at high temperature.

Asteroseismology of RRab variable star EZ Cnc from K2 photometry and LAMOST spectroscopy

ABSTRACT EZ Cnc, or EPIC 212182292, is a non-Blažko RRab variable star located in the field of K2 Campaign 16. Its atmospheric parameters (Teff, log g, [M/H]) and radial velocities are measured from the 55 high-quality LAMOST medium-resolution spectra. The fundamental frequency of pulsation is derived as f = 1.8323(17) d−1 from the K2 light curves. The amplitude ratios R21 = 0.5115(15), 0.490(8), R31 = 0.3249(20), 0.279(7) and Fourier phase differences φ21 = 2.7550(20), 2.764(16), φ31 = 5.7194(25), 5.719(31) are determined from the Fourier decomposition of K2 light curve and LAMOST radial velocity curve, respectively. Through the constraints of the parameters, four optimal models are obtained in a time-dependent turbulent convection model survey for EPIC 212182292. The parameters of EPIC 212182292 are derived as M = 0.48 ± 0.03 M⊙, L = 42 ± 2 L⊙, Teff = 6846 ± 50 K, log g = 2.79 ± 0.01 dex, and Z = 0.006 ± 0.002, respectively. The precisely determined parameters for RRab variable stars like EPIC 212180092 might help to better understand the period–luminosity relationship of RR Lyrae stars.

4.7 THz asymmetric beam multiplexer for GUSTO.

A full demonstration of the Fourier phase grating used as 4.7 THz local oscillator (LO) multiplexer for Galactic/Extragalactic ULDB Spectroscopic Terahertz Observatory (GUSTO) is presented in this paper, including its design, modeling, tolerance analysis, and experimental characterizations of the angular and intensity distributions among 2 × 4 output beams and the power efficiency. A quantum cascade laser (QCL) is used to generate the input beam for evaluation of the grating performance in its all relevant aspects with an accuracy level never reported before, where good agreements with modeling results are found. This is the first asymmetric-profile grating fully modelled and characterized at a THz frequency, that further confirms the versatility of this technology for providing an intermediate optical element for feeding multiple array detectors with a single radiation source at such a scientifically interesting frequency regime.

Optimizing Synchronization of Tennis Professional League Live Broadcast Based on Wireless Network Planning

The live broadcast of the common league mainly adopts the design of streaming media data block by block. The secondary processing of streaming data is carried out on the server-side. It results in a higher delay during a live broadcast. The higher delay has numerous disadvantages during broadcasting for delay-sensitive applications. We have to solve the delay problems during a live broadcast. Therefore, in this paper, we optimize the synchronization of the tennis professional league live broadcast based on wireless network planning. In the proposed scheme, the 3D detection target model is first constructed, and the background is extracted from the moving video image. The extraction is performed using the interframe difference elimination algorithm, and the target motion trajectory is predicted. Then the phase difference characteristics of the image foreground trajectory are analyzed by the Hilbert transform to detect target missing points. By observing the vertex structure of the target missing point, the phase Fourier transform frame is constructed. Finally, the synchronization of the league live broadcast is encoded and decoded. Based on the timestamp, the synchronization optimization of the tennis professional league live broadcast is completed. The experimental results show that the synchronization optimization method has good synchronization, high resolution, short reaction time, and good detection effect.

Characterizing defects in materials with fusion of thermography and shearography

Thermography and shearography are optical techniques for detecting and characterizing subsurface defects in structures. Both techniques possess unique advantages and abilities, as well as limitations, based on their distinct mechanisms. In this study, the feasibility in fusion of thermography and shearography is explored. Thermal excitation is selected to induce temperature variation and out-of-plane deformation on the object surface, acquiring the shearography phase maps and thermography image sequence simultaneously. Infrared images are dealt with by the Fourier phase analysis incorporate with an edge-aware filter. Fusion of the detecting images is obtained by performing a projective transform between each pair of the thermography and shearography images. Subsequently, both thermography and shearography images are separated into detail and background images. The fused image is reconstructed from the detail and background images by applying a weighting function. Experiments have indicated that the proposed method is effective in identifying defects by combining two image-based NDT methods.

Automatic Sub-Pixel Co-Registration of Remote Sensing Images Using Phase Correlation and Harris Detector

In this paper, we propose a new approach for sub-pixel co-registration based on Fourier phase correlation combined with the Harris detector. Due to the limitation of the standard phase correlation method to achieve only pixel-level accuracy, another approach is required to reach sub-pixel matching precision. We first applied the Harris corner detector to extract corners from both references and sensed images. Then, we identified their corresponding points using phase correlation between the image pairs. To achieve sub-pixel registration accuracy, two optimization algorithms were used. The effectiveness of the proposed method was tested with very high-resolution (VHR) remote sensing images, including Pleiades satellite images and aerial imagery. Compared with the speeded-up robust features (SURF)-based method, phase correlation with the Blackman window function produced 91% more matches with high reliability. Moreover, the results of the optimization analysis have revealed that Nelder–Mead algorithm performs better than the two-point step size gradient algorithm regarding localization accuracy and computation time. The proposed approach achieves better accuracy than 0.5 pixels and outperforms the speeded-up robust features (SURF)-based method. It can achieve sub-pixel accuracy in the presence of noise and produces large numbers of correct matching points.

Spectral features of cortical auditory evoked potentials inform hearing threshold and intensity percepts in acoustic and electric hearing

Objective. Stimulus-elicited changes in electroencephalography (EEG) recordings can be represented using Fourier magnitude and phase features (Makeig et al (2004 Trends Cogn. Sci. 8 204–10)). The present study aimed to quantify how much information about hearing responses are contained in the magnitude, quantified by event-related spectral perturbations (ERSPs); and the phase, quantified by inter-trial coherence (ITC). By testing if one feature contained more information and whether this information was mutually exclusive to the features, we aimed to relate specific EEG magnitude and phase features to hearing perception. Approach. EEG responses were recorded from 20 adults who were presented with acoustic stimuli, and 20 adult cochlear implant users with electrical stimuli. Both groups were presented with short, 50 ms stimuli at varying intensity levels relative to their hearing thresholds. Extracted ERSP and ITC features were inputs for a linear discriminant analysis classifier (Wong et al (2016 J. Neural. Eng. 13 036003)). The classifier then predicted whether the EEG signal contained information about the sound stimuli based on the input features. Classifier decoding accuracy was quantified with the mutual information measure (Cottaris and Elfar (2009 J. Neural. Eng. 6 026007), Hawellek et al (2016 Proc. Natl Acad. Sci. 113 13492–7)), and compared across the two feature sets, and to when both feature sets were combined. Main results. We found that classifiers using either ITC or ERSP feature sets were both able to decode hearing perception, but ITC-feature classifiers were able to decode responses to a lower but still audible stimulation intensity, making ITC more useful than ERSP for hearing threshold estimation. We also found that combining the information from both feature sets did not improve decoding significantly, implying that ERSP brain dynamics has a limited contribution to the EEG response, possibly due to the stimuli used in this study. Significance. We successfully related hearing perception to an EEG measure, which does not require behavioral feedback from the listener; an objective measure is important in both neuroscience research and clinical audiology.

Fourier horizontal parallax only computer and digital holography of large size.

Registration and reconstruction of high-quality digital holograms with a large view angle are intensive computer tasks since they require the space-bandwidth product (SBP) of the order of tens of gigapixels or more. This massive use of SBP severely affects the storing and manipulation of digital holograms. In order to reduce the computer burden, this work focuses on the generation and reconstruction of very large horizontal parallax only digital holograms (HPO-DHs). It is shown that these types of holograms can preserve high quality and large view angle in x direction while keeping a low use of SBP. This work first proposes a numerical technique that allows calculating very large HPO-DHs with large pixel size by merging the Fourier holography and phase added stereogram algorithm. The generated Fourier HPO-DHs enable accurate storing of holographic data from 3D objects. To decode the information contained in these Fourier HPO-DHs (FHPO-DHs), a novel angular spectrum (AS) technique that provides an efficient use of the SBP for reconstruction is proposed. Our reconstruction technique, which is called compact space bandwidth AS (CSW-AS), makes use of cylindrical parabolic waves that solve sampling issues of FHPO-DHs and AS. Moreover, the CSW-AS allows for implementing zero-padding for accurate wavefield reconstructions. Hence, suppression of aliased components and high spatial resolution is possible. Notably, the imaging chain of Fourier HPO-DH enables efficient calculation, reconstruction and storing of HPO holograms of large size. Finally, the accuracy and utility of the developed technique is proved by both numerical and optical reconstructions.

Development of terahertz two-dimensional phase gratings for multiple beam generation based on a high-accuracy phase retrieval algorithm.

High efficiency and accuracy phase gratings are of crucial importance for large format heterodyne array receivers at terahertz frequencies. Here, by developing a design approach that can create gratings with arbitrary two-dimensional diffraction distributions, we have realized a reflective metallic phase grating that generates 2×2 diffraction beams at 0.85 THz. The measured total power efficiency of the diffraction beam pattern is 81.9%, which demonstrates at least 17% improvement in efficiency compared with the standard pseudo-2D Fourier phase grating. In addition, we report the realization of up to 10×10 diffraction beam two-dimensional phase grating designs at terahertz wavelengths, using an adaptation of the Gerchberg-Saxton (GS) scheme known as the Mixed-Region-Amplitude-Freedom algorithm. Rigorous full wave simulation proves the efficiency and accuracy of the design, which overcomes the inaccurate intensity of the beam distribution drawbacks originated from the standard GS algorithm. The results pave the way for the development of large-pixel terahertz multi-beam heterodyne receivers.

I3T: Intensity Interferometry Imaging Telescope

ABSTRACT We propose a new approach, based on the Hanbury Brown and Twiss intensity interferometry, to transform a Cherenkov telescope to its equivalent optical telescope. We show that, based on the use of photonics components borrowed from quantum-optical applications, we can recover spatial details of the observed source down to the diffraction limit of the Cherenkov telescope, set by its diameter at the mean wavelength of observation. For this, we propose to apply aperture synthesis techniques from pairwise and triple correlation of sub-pupil intensities, in order to reconstruct the image of a celestial source from its Fourier moduli and phase information, despite atmospheric turbulence. We examine the sensitivity of the method, i.e. limiting magnitude, and its implementation on existing or future high energy arrays of Cherenkov telescopes. We show that despite its poor optical quality compared to extremely large optical telescopes under construction, a Cherenkov telescope can provide diffraction limited imaging of celestial sources, in particular at the visible, down to violet wavelengths.

Sky Image Prediction Model Based on Convolutional Auto-Encoder for Minutely Solar PV Power Forecasting

The precise minute time scale forecasting of an individual PV power station output relies on accurate prediction of cloud distribution, which can lead to dramatic fluctuation of PV power generation. Precise cloud distribution information is mainly achieved by ground-based total sky imager, then the future cloud distribution can also be achieved by sky image prediction. In previous studies, traditional digital image processing technology (DIPT) has been widely used in predicting sky images. However, DIPT has two deficiencies: relatively limited input spatiotemporal information and linear extrapolation of images. The first deficiency makes the input spatiotemporal information not rich enough, while the second creates the prediction error from the beginning. To avoid these two deficiencies, convolutional autoencoder (CAE) based sky image prediction models are proposed due to the spatiotemporal feature extraction ability of two-dimensional (2-D) CAEs and 3-D CAEs. For 2-D CAEs and 3-D CAEs, four architectures are given respectively. To verify the effectiveness of the proposed models, two typical DIPT methods, including particle image velocimetry and Fourier phase correlation theory are introduced to build the benchmark models. Besides, five different scenarios are also set and the results show that the proposed models outperform the benchmark models in all scenarios.