Fourier Filtering Research Articles

Fast & adaptive fault location technique for three-terminal lines

This paper presents a fast and adaptive method to locate faults in three-terminal transmission lines, based on the synchronized measurements within the half-cycle data window. First, the voltage and current data are processed by two sets of half-cycle Fourier filters at three terminals in order to extract the main component of the voltage and current phasors quickly and with a high accuracy using a novel method. The proposed algorithm uses the calculated phasors and works without any need to transmission line’s data or the Thevenin equivalent of the system at each terminal. For making sure of considering the real operation conditions of the network, transmission line’s parameters are determined adaptively using the calculated phasors. The voltage at the tapping point is calculated separately using three-terminal data and consequently the faulty section is identified and then, the precise location of fault in the faulty section is accurately calculated using the nodal current unbalance method. Performance of the proposed algorithm is evaluated under different fault conditions. The simulation results show the high convergence speed and the excellent accuracy of the proposed method under various operating conditions and various fault types.

Fast-modulation imaging with the self-coherent camera

Context. Direct detection of exoplanets requires imaging in a highly dynamic range and exquisite image quality and stability. Wavefront error (atmospheric errors, manufacturing errors on optics, cophasing residuals, temperature variations, etc.) will limit the efficiency of this endeavor by creating various flavors of speckles that evolve with different timescales. Active wavefront-error correction using a deformable mirror requires measuring the wavefront aberrations in the science image with high accuracy and in a shorter time than the duration of the dominant speckle lifetime. Aims. The self-coherent camera (SCC) is a focal plane wavefront sensor exploiting the coherence of light to generate Fizeau fringes in the image plane to spatially encode speckles. The SCC combines a coronagraph and a modified Lyot stop to which a reference channel is added. The conventional SCC is restricted to long-exposure measurements because the light transmitted through the reference channel is limited. The SCC can correct quasi-static aberrations but precludes short-lived atmospheric aberrations from the measurement. Methods. I propose an alternative to the conventional SCC that I call the fast-modulated SCC. It uses a simplified Lyot stop design and an adequate Fourier filtering algorithm. The theory is established and confirmed by means of numerical simulations. Results. The SCC theory dictates that the separation between the classical Lyot stop and the reference channel must be larger than 1.5 times the Lyot stop diameter. The fast-modulated SCC allows for the reference channel to be placed anywhere, in particular in the vicinity of the pupil where the maximum of diffracted light is found. This alternative represents a complete game changer for the sensor: full compatibility with any type of coronagraph, easy installation in existing instruments, and versatility by accessing short- and long-time exposure measurements. Conclusions. While the conventional SCC can almost not be implemented in existing instruments because the optical beam footprint in the instrument must be wide enough to illuminate the reference channel, which is often seen as a significant shortcoming, the fast-modulated SCC does not require any constraint on this. The fast-modulated SCC also relaxes the high sampling requirement to resolve the fringes, which is usually incompatible with the observation of fainter targets because the fringes are larger. The fast-modulated SCC simultaneously counteracts the two original shortcomings of the SCC concept.

Mapping the strain distribution within embedded nanoparticles via geometrical phase analysis

Strain variation within a nanoparticle plays a crucial role in tuning its properties. Geometrical phase analysis (GPA) is typically a powerful tool to investigate the strain in high-resolution transmission electron microscopy (HRTEM) images. It is known that the traditional GPA method measuring the displacement of lattice fringes directly in an HRTEM image is inapplicable to strain measurements on nanoparticles embedded in a matrix, where lattice fringes of nanoparticles are invisible, instead Moiré fringes are present. Furthermore, considering the small size of embedded nanoparticles, generally a few nanometers, no reference region can be chosen and utilized to calculate the relative displacement by GPA. Hence advanced methods need to be developed to break through the barriers of invisible lattice fringes and lack of a reference region. In this work, using α-Fe nanoparticles embedded in sapphire as a test object, we illustrate a GPA method dedicated to embedded nanoparticles. Both the Fourier filter method and the inverse Moiré fringes method were used to reconstruct the invisible lattice fringes of α-Fe nanoparticles. Then a computer-generated image corresponding to an unstrained α-Fe lattice was used as the reference during GPA. The GPA results indicate that there exists a compressive strain in the range of 1.5˜2% within the α-Fe nanoparticles. Our work presents an effective approach to revealing the strain distributions within embedded nanoparticles.

Objective Center-Finding Algorithm for Tropical Cyclones in Numerical Models

Precise center-detection of tropical cyclones (TCs) is critical for dynamic analysis in high resolution model data. The existence of both smaller scale perturbations and larger scale circulations could reduce the accuracy of center positioning. In this study, an objective center-finding algorithm is developed based on a two-dimensional Fourier filter and a vorticity centroid algorithm. This proposed algorithm is able to automatically adjust its parameters according to the scale of the target vortex instead of using artificially prescribed parameters in previous research. What’s more, this new algorithm has been optimized and validated by a hundred idealized vortexes with different sizes and small-scale perturbations. A high-resolution simulation of Typhoon Soudelor (2015) was used to evaluate the performance of the new algorithm, and the proposed objective center-finding algorithm was found able to detect a precise and reliable center.

Space Vector Taylor–Fourier Models for Synchrophasor, Frequency, and ROCOF Measurements in Three-Phase Systems

Taylor–Fourier (TF) filters represent a powerful tool to design phasor measurement unit (PMU) algorithms able to estimate synchrophasor, frequency, and rate of change of frequency (ROCOF). The resulting techniques are based on dynamic representations of the synchrophasor, and hence, they are particularly suitable to track the evolution of its parameters during time-varying conditions. Electrical quantities in power systems are typically three-phase and weakly unbalanced, but most PMU measurement techniques are developed by considering them as a set of three single-phase signals; on the contrary, this peculiarity can be favorably exploited to improve accuracy and reduce the computational cost. In this respect, this paper proposes to directly perform the TF expansion of the space vector (SV) samples obtained from three-phase measurements. A new paradigm allows to independently estimate positive and negative sequence synchrophasors along with system frequency and ROCOF, leveraging the three-phase characteristics. The performance of the proposed technique is assessed by using test signals inspired by the standard IEEE C37.118.1-2011, including noise as well as magnitude and phase unbalance. Achieved results highlight the flexibility of the enhanced SV-based approach, which is capable to combine excellent dynamic performance together with an accurate estimation of both positive and negative sequence components.

Hopf bifurcation in diffusive model of nonlinear optical system with matrix fourier filtering

We consider a new formulation of the Fourier filtering problem based on the use of matrix filters instead of conventional filters-multiplicators in the framework of the periodic boundary value problem for a quasilinear diffusion equation of nonlinear optics. Our attention is mostly focused on studying the capabilities of matrix Fourier filtering as an efficient tool for constructing periodic solutions with prescribed spatial-temporal dynamics. To this end, we analyze the spectrum of the linearized operator and the possibility to localize it by choosing a matrix Fourier filter that provides the existence of the Hopf bifurcation. We also describe the structure of bifurcation solution for two important classes of filters: finite filters-multiplicators and matrix filters. We theoretically and numerically show that along with rotating waves, typical for the Hopf bifurcation with conventional filters-multiplicators, there exist waves with new nontrivial dynamics (rotating waves with nodes and pulsating structures). These waves excite as a result of the Hopf bifurcation under an appropriate choice of nondiagonal matrix Fourier filters.

Three methods for determining the type of LPSO-phase in an Mg–Zn–Y alloy by transmission electron microscopy

ABSTRACTThree methods for determining the type of LPSO-phases in an Mg–Zn–Y alloy are described: electron diffraction and two methods based on high-resolution image analysis. The diffraction method consists in counting the diffraction spot between (000)Mg and (00.1)Mg reflections; comparison with the calculated diffraction patterns allows determining the mixed types of LPSO-phase. The routine operations with high-resolution imaging using Fourier filtering and building intensity profiles in Digital Micrograph are described in detail. Recommendations on the preferred orientation of the sample for each method are given. The procedure for identifying (00.2)Mg layers using template figures and a simplified search for stacking faults in an image using a Fourier mask for reflection is described. The advantages, possibilities and limitations of each method are discussed.

Removal of ‘strip noise’ in radio-echo sounding data using combined wavelet and 2-D DFT filtering

ABSTRACTRadio-echo sounding (RES) can be used to understand ice-sheet processes, englacial flow structures and bed properties, making it one of the most popular tools in glaciological exploration. However, RES data are often subject to ‘strip noise’, caused by internal instrument noise and interference, and/or external environmental interference, which can hamper measurement and interpretation. For example, strip noise can result in reduced power from the bed, affecting the quality of ice thickness measurements and the characterization of subglacial conditions. Here, we present a method for removing strip noise based on combined wavelet and two-dimensional (2-D) Fourier filtering. First, we implement discrete wavelet decomposition on RES data to obtain multi-scale wavelet components. Then, 2-D discrete Fourier transform (DFT) spectral analysis is performed on components containing the noise. In the Fourier domain, the 2-D DFT spectrum of strip noise keeps its linear features and can be removed with a ‘targeted masking’ operation. Finally, inverse wavelet transforms are performed on all wavelet components, including strip-removed components, to restore the data with enhanced fidelity. Model tests and field-data processing demonstrate the method removes strip noise well and, incidentally, can remove the strong first reflector from the ice surface, thus improving the general quality of radar data.

Toward Phase and Catalysis Control: Tracking the Formation of Intermetallic Nanoparticles at Atomic Scale

Summary Intermetallic nanoparticles (iNPs) have yielded enormous successes in catalytic applications by the formation of ordered phases. However, atomic-level understanding of the alloying mechanism, which plays a pivotal role in controlling intermetallic phases and tailoring their catalytic properties, is still elusive. In this study, we discovered a consecutive formation of ordered Pt3Sn and PtSn phases during the growth of Pt-Sn iNP inside a well-defined nano-reactor at elevated temperature by using in situ scanning transmission electron microscopy. We found that the surface-mediated diffusion of Sn controls overall dynamics of the reaction, while the unique coherent interfacial structure is determinative for the PtSn transformation. We then further controlled the phase selection of Pt-Sn iNPs and demonstrated their distinguishable catalytic behaviors. Our findings not only provide detailed experimental evidence on the alloying mechanism in intermetallic nanoscale systems but also pave the way for mechanistic control of synthesis and catalytic properties of iNPs.

Single-pixel imaging with Fourier filtering: application to vision through scattering media.

We present a novel approach for imaging through scattering media that combines the principles of Fourier spatial filtering and single-pixel imaging. We compare the performance of our single-pixel imaging setup with that of a conventional system. First, we show that a single-pixel camera does not reduce the frequency content of the object, when a small pinhole is used as a low-pass filter at the detection side. Second, we show that the introduction of Fourier gating improves the contrast of imaging through scattering media in both optical systems. We conclude that single-pixel imaging fits better than conventional imaging on imaging through scattering media by the Fourier gating.

A decision support tool for early detection of knee OsteoArthritis using X-ray imaging and machine learning: Data from the OsteoArthritis Initiative

This paper presents a fully developed computer aided diagnosis (CAD) system for early knee OsteoArthritis (OA) detection using knee X-ray imaging and machine learning algorithms. The X-ray images are first preprocessed in the Fourier domain using a circular Fourier filter. Then, a novel normalization method based on predictive modeling using multivariate linear regression (MLR) is applied to the data in order to reduce the variability between OA and healthy subjects. At the feature selection/extraction stage, an independent component analysis (ICA) approach is used in order to reduce the dimensionality. Finally, Naive Bayes and random forest classifiers are used for the classification task. This novel image-based approach is applied on 1024 knee X-ray images from the public database OsteoArthritis Initiative (OAI). The results show that the proposed system has a good predictive classification rate for OA detection (82.98% for accuracy, 87.15% for sensitivity and up to 80.65% for specificity).

Quantification of amplitude modulation in wall-bounded turbulence

Many recent investigations on the scale interactions in wall-bounded turbulent flows focus on describing so-called amplitude modulation, the phenomenon that deals with the influence of large scales in the outer region on the amplitude of the small-scale fluctuations in the near-wall region. The present study revisits this phenomenon regarding two aspects, namely the method for decomposing the scales and the quantification of the modulation. First, the paper presents a summary of the literature that has dealt with either or both aspects. Second, for decomposing the scales, different spectral filters (temporal, spatial or both) and empirical mode decomposition (EMD) are evaluated and compared. The common data set is a well-resolved large-eddy simulation that offers a wide range of Reynolds numbers spanning Reθ = 880–8200. The quantification of the amplitude modulation is discussed for the resulting scale components. Particular focus is given to evaluate the efficacy of the various filters to separate scales for the range of Reynolds numbers of interest. Different to previous studies, the different methods have been evaluated using the same data set, thereby allowing a fair comparison between the various approaches. It is observed that using a spectral filter in the spanwise direction is an effective approach to separate the small and large scales in the flow, even at comparably low Reynolds numbers, whereas filtering in time should be approached with caution in the low-to-moderate Re range. Additionally, using filters in both spanwise and time directions, which would separate both wide and long-living structures from the small and fast scales, gives a cleaner image for the small-scales although the contribution to the scales interaction from that filter implementation has been found negligible. Applying EMD to decompose the scales gives similar results to Fourier filters for the energy content of the scales and thereby for the quantification of the amplitude modulation using the decomposed scales. No direct advantage of EMD over classical Fourier filters could be seen. Potential issues regarding different decomposition methods and different definitions of the amplitude modulation are also discussed.

Thermal anomalies detection before earthquake using three filters (Fourier, Wavelet and Logarithmic Differential Filter), A Case study of two earthquakes in Iran

Earthquake is one of the most destructive natural phenomena which has human and financial losses. The existence of an efficient prediction system and early warning system will be useful for reducing effects of destroying earthquake. In this paper by applying three filters (Fourier, Wavelet and Difference Logarithmic Filter (LDF)) on soil temperature time-series, anomaly behavior before the major earthquakes was studied. Aforementioned methods were performed of the Bam (2003), and Zarand (2005) earthquakes in Iran. The results indicate thermal anomalies were detected before earthquake occurrence. Furthermore, the LDF filter detects thermal anomaly as well as the Fourier and Wavelet filters. For validation of the results, the soil temperature data of the Bam earthquake were considered from the Bam meteorological station and also from the Joroft meteorological stations that located in effective radius (Dobrolsky radius) and the same results was obtained. It states that there is a relation between temperature anomaly behavior and the major earthquakes.

Interference Information Processing Technology for Defects of Aluminum Honeycomb Structure in Aircraft

In order to get the interference information extraction aircraft aluminum honeycomb structure defect extraction, reliability of testing. This paper uses image processing technology to find a method about image processing composite, with the help of laser shearography detection method detecting detection. The flaw speckle results show that, after Fourier filtering, unpacking of step by step, linear trend processing of the image, gray scale processing method can extract powder composite suited interference information, effectively improve the reliability of detection of the scattered laser displacement suited, provides a new image processing program to help speckle image processing.

Bayesian random Fourier filters for Gaussian noises

Bayesian random Fourier filters for Gaussian noises

SURE-Fuse WFF: A Multi-Resolution Windowed Fourier Analysis for Interferometric Phase Denoising

Interferometric phase (InPhase) imaging is an important part of many present-day coherent imaging technologies. Often in such imaging techniques, the acquired images, known as interferograms, suffer from two major degradations: 1) phase wrapping caused by the fact that the sensing mechanism can only measure sinusoidal $2\pi$-periodic functions of the actual phase, and 2) noise introduced by the acquisition process or the system. This work focusses on InPhase denoising which is a fundamental restoration step to many posterior applications of InPhase, namely to phase unwrapping. The presence of sharp fringes that arises from phase wrapping makes InPhase denoising a hard-inverse problem. Motivated by the fact that the InPhase images are often locally sparse in Fourier domain, we propose a multi-resolution windowed Fourier filtering (WFF) analysis that fuses WFF estimates with different resolutions, thus overcoming the WFF fixed resolution limitation. The proposed fusion relies on an unbiased estimate of the mean square error derived using the Stein's lemma adapted to complex-valued signals. This estimate, known as SURE, is minimized using an optimization framework to obtain the fusion weights. Strong experimental evidence, using synthetic and real (InSAR & MRI) data, that the developed algorithm, termed as SURE-fuse WFF, outperforms the best hand-tuned fixed resolution WFF as well as other state-of-the-art InPhase denoising algorithms, is provided.

DC Offset Removal Algorithm for Improving Location Estimates of Momentary Faults

Fault location algorithms require the input of voltage and current phasors when estimating the distance to a fault. In the case of momentary faults, phasor calculations are often complicated by the presence of an exponentially decaying dc offset. Fourier filters and cosine filters, popularly used by most phasor estimation algorithms in relays, are successful in filtering out most, but not all, of the exponentially decaying dc offset. This dc offset affects the accuracy of voltage and current phasors and may result in a significant error in location estimates. Therefore, this paper presents a dc offset removal algorithm to improve the fault location estimates of momentary faults. The algorithm uses the rms-wavelet method for fault detection and estimates voltage and current phasors using non-linear least squares methods. The proposed method uses variable window size in calculating phasors and estimates a single, but more accurate fault location than multiple locations estimated by the Fourier and cosine filters. The method is validated using simulated and actual field data. The location estimates are shown to be accurate within 5.6% in all cases.

Quantitative phase imaging with increased spatial coherence based on Fourier filtering.

This Letter reports a method for tuning the degree of spatial coherence in an optical microscope. The method employs an amplitude spatial light modulator (aSLM) placed in the Fourier plane of the microscope. The aSLM displays a set of binary filters that blocks specific frequencies of the Fourier spectrum of the complex object field. It is shown that numerical processing of these filtered fields provides a final intensity with increased spatial coherence. Coherence tuning is used in a new hybrid phase reconstruction algorithm that employs the transport of intensity equation and an iterative phase retrieval technique. It is validated experimentally that this hybrid approach is able to retrieve the phase information with high resolution, and effective artifact noise suppression when employing at minimum two symmetrical defocused intensities and large sources.

Assessment of despeckle filtering algorithms for segmentation of breast tumours from ultrasound images

In the present work, the performance assessment of despeckle filtering algorithms has been carried out for (a) noise reduction in breast ultrasound images and (b) segmentation of benign and malignant tumours from breast ultrasound images. The despeckle filtering algorithms are broadly classified into eight categories namely local statistics based filters, fuzzy filters, Fourier filters, multiscale filters, non-linear iterative filters, total variation filters, non-local mean filters and hybrid filters. Total 100 breast ultrasound images (40 benign and 60 malignant) are processed using 42 despeckle filtering algorithms. A despeckling filter is considered to be appropriate if it preserves edges and features/structures of the image. Edge preservation capability of a despeckling filter is measured by beta metric (β) and feature/structure preservation capability is quantified using image quality index (IQI). It is observed that out of 42 filters, six filters namely Lee Sigma, FI, FB, HFB, BayesShrink and DPAD yield more clinically acceptable images in terms of edge and feature/structure preservation. The qualitative assessment of these images has been done on the basis of grades provided by the experienced participating radiologist. The pre-processed images are then fed to a segmentation module for segmenting the benign or malignant tumours from ultrasound images. The performance assessment of segmentation algorithm has been done quantitatively using the Jaccard index. The results of both quantitative and qualitative assessment by the radiologist indicate that the DPAD despeckle filtering algorithm yields more clinically acceptable images and results in better segmentation of benign and malignant tumours from breast ultrasound images.

Random Fourier Filters Under Maximum Correntropy Criterion

Random Fourier adaptive filters (RFAFs) project the original data into a high-dimensional random Fourier feature space (RFFS) such that the network structure of filters is fixed while achieving similar performance with kernel adaptive filters. The commonly used error criterion in RFAFs is the well-known minimum mean-square error (MMSE) criterion, which is optimal only under the Gaussian noise assumption. However, the MMSE criterion suffers from instability and performance deterioration in the presence of non-Gaussian noises. To improve the robustness of RFAFs against large outliers, the maximum correntropy criterion (MCC) is applied to RFFS, generating a novel robust random Fourier filter under maximum correntropy (RFFMC). To further improve the filtering accuracy, a random-batch RFFMC (RB-RFFMC) is also presented. In addition, a theoretical analysis on the convergence characteristics and steady-state excess mean-square error of RFFMC and RB-RFFMC is provided to validate their superior performance. Simulation results illustrate that RFFMC and its extension provide desirable filtering performance from the aspects of filtering accuracy and robustness, especially in the presence of impulsive noises.