Phase Autocorrelation Research Articles

A coarse-to-fine image registration method based on autocorrelation structural difference information

ABSTRACT The automatic registration of synthetic aperture radar (SAR) and optical images is still a challenging problem due to different imaging mechanisms. This letter proposes a coarse-to-fine image registration method that leverages self-similarity structural difference information. In the coarse registration stage, a Scale-Invariant Feature Transformation-based (SIFT-like) method is employed, complemented by an improved Fast Sample Consensus (IFSC) method to eliminate mismatched point pairs by probabilistic and geometric information. This stage ensures robustness against scale and rotational variations. In the fine registration stage, robust feature points are selected by utilizing phase and edge structural information. A descriptor which based on phase consistency and autocorrelation structural difference (ASDPC) is constructed to capture the structural variations between region blocks, and a fine search is carried out within the neighbourhood of the already matched feature points, so as to find more accurate matched feature points and obtain fine registration. The experimental results demonstrate that the proposed method provides robust and accurate registration for optical-to-SAR images.

Moho Imaging with Fiber Borehole Strainmeters Based on Ambient Noise Autocorrelation.

Moho tomography is important for studying the deep Earth structure and geodynamics, and fiber borehole strainmeters are broadband, low-noise, and attractive tools for seismic observation. Recently, many studies have shown that fiber optic seismic sensors can be used for subsurface structure imaging based on ambient noise cross-correlation, similar to conventional geophones. However, this array-dependent cross-correlation method is not suitable for fiber borehole strainmeters. Here, we developed a Moho imaging scheme for the characteristics of fiber borehole strainmeters based on ambient noise autocorrelation. S-wave reflection signals were extracted from the ambient noise through a series of processing steps, including phase autocorrelation (PAC), phase-weighted stacking (PWS), etc. Subsequently, the time-to-depth conversion crustal thickness beneath the station was calculated. We applied our scheme to continuous four-component recordings from four fiber borehole strainmeters in Lu'an, Anhui Province, China. The obtained Moho depth was consistent with the previous research results. Our work shows that this method is suitable for Moho imaging with fiber borehole strainmeters without relying on the number of stations.

Seismic ambient noise auto-correlation imaging in a CO2 storage area

Abstract Carbon capture and storage is an effective technique for achieving ‘carbon neutrality’. Seismology plays an important role in detecting and monitoring whether CO2 has been safely sealed. However, active seismic surveys are usually incapable of continuous observations. We can extract the body wave and image the subsurface interface directly and continuously via single sensor ambient noise auto-correlation. However, because of the weak body wave in the ambient noise and the multiples in the imaging results, it is challenging to improve the imaging resolution. This study provides a reference for the development of the ambient noise (phase) auto-correlation imaging method for future use in carbon storage areas. In this study, we performed numerical experiments to show that the phase auto-correlation method is better than the auto-correlation in terms of weakening artefacts and detecting subsurface thin CO2 layers. Then, we applied the phase auto-correlation method in the Ketzin (Germany) CO2 storage area. Using 223 body-wave dominated noise panels automatically selected from totally 4680 panels, we imaged two primary interfaces, which are consistent with the common midpoint stacking results obtained using active seismic surveys. We applied a multiple removal approach to the imaging results and obtained high precision results. Then, we applied the proposed workflow to three passive seismic survey lines north of the CO2 injection well. The results of the three passive surveys demonstrate the workflow is robust.

Generalized approach to compensate for low- and high-frequency errors in fast Fourier transform-based phase screen simulations

Fast Fourier transform-based phase screen simulations give accurate results only when the screen size (G) is much larger than the outer scale parameter (L0). Otherwise, they fall short in correctly predicting both the low and high frequency behaviors of turbulence-induced phase distortions. Subharmonic compensation is a commonly used technique that aids in low-frequency correction but does not solve the problem for all values of screen size to outer scale parameter ratios (G / L0). A subharmonics-based approach will lead to unequal sampling or weights calculation for subharmonics addition at the low-frequency range and patch normalization factor. We have modified the subharmonics-based approach by introducing a Gaussian phase autocorrelation matrix that compensates for these shortfalls. We show that the maximum relative error in structure function with respect to theoretical value is as small as 0.5% to 3% for (G / L0) ratio of 1/1000 even for screen sizes up to 100 m diameter.

An analysis of the time-frequency structure of several bursts from FRB 121102 detected with MeerKAT

ABSTRACT We present a detailed study of the complex time-frequency structure of a sample of previously reported bursts of FRB 121102 detected with the MeerKAT telescope in September 2019. The wide contiguous bandwidth of these observations have revealed a complex bifurcating structure in some bursts at 1250 MHz. When de-dispersed to their structure-optimized dispersion measures (DMs), two of the bursts show a clear deviation from the cold plasma dispersion relationship below 1250 MHz. We find a differential DM of ${\sim }1{-}2~{\rm pc \, cm^{-3}}$ between the lower and higher frequency regions of each burst. We investigate the possibility of plasma lensing by Gaussian lenses of ∼10 au in the host galaxy, and demonstrate that they can qualitatively produce some of the observed burst morphologies. Other possible causes for the observed frequency dependence, such as Faraday delay, are also discussed. Unresolved sub-components in the bursts, however, may have led to an incorrect DM determination. We hence advise exercising caution when considering bursts in isolation. We analyse the presence of two apparent burst pairs. One of these pairs is a potential example of upward frequency drift. The possibility that burst pairs are echoes is also discussed. The average structure-optimized DM is found to be $563.5\pm 0.2 (\text{sys}) \pm 0.8 (\text{stat})\, {\rm pc \, cm^{-3}}$ – consistent with the values reported in 2018. We use two independent methods to determine the structure-optimized DM of the bursts: the DM_phase algorithm and autocorrelation functions. The latter – originally developed for pulsar analysis – is applied to fast radio bursts for the first time in this paper.

Monitoring seismic velocity changes in the Saint Peter and Saint Paul Archipelago-Equatorial Atlantic using ambient noise interferometry

The Saint Paul Transform System (SPTS) is located in the Mid -Atlantic Ridge (MAR), Equatorial Atlantic and is formed by a multi-fault complex system, where many faults are interacting and small-to-moderate events are routinely located in the area using global seismic networks. This seismicity is challenging to charecterize since no permanent seismic stations near this area are available. As a result, the interplay between seismicity, faulting and fluid in the MAR is poorly constrained. In this paper, we quantify the seismic velocity perturbations due to small-to-moderate magnitude earthquakes in the Saint Peter Saint Paul Archipelago (SPSPA) using one seismological station installed in the region. We calculate noise auto-correlation functions using the data recorded by this station. The auto-correlograms were obtained by two different approaches: classical auto-correlation geometrically normalized (ACGN) and phase autocorrelation (PAC). We found that both approaches give very similar results and we are able to estimate seismic velocity changes due in the propagating medium to small earthquakes (between 3.0 and 4.7 ML). The changes in the medium were investigated through the joint analysis of decorrelation curves and velocity changes obtained by Moving Window Cross Spectral (MWCS) method. Our analysis shows that the seismic velocity changes are possibly associated with a hydromechanical coupling in which the observed velocity increase is driven by static stress changes and fluid-rock interaction is responsible for the observed seismic velocity drop. This behaviour is qualitatively explained by the multi-fault complex system nature of the SPTS.

Analysis and resistance of dynamic degradation of digital chaos via functional graphs

To analyze the effects of finite computational precision on the dynamical degradation of digital chaotic maps, we designed a periodic orbit detection algorithm that is based on a functional graph. The algorithm can calculate the transient length of each chaotic orbit, weak secret keys, fixed points and the period distribution of digital chaotic systems with various limited computational precisions accurately. Furthermore, an effective method based on quadratic congruential generator is proposed to counteract the performance degradation of digital chaos. Based on the method, a new chaotic model can be constructed with full cycle. Numerical experiments are carried out to evaluate the feasibility of the proposed scheme in terms of phase portrait, autocorrelation function, complexity and periodicity analysis. Finally, as an application, a pseudorandom bit generator with satisfactory performance is designed for chaotic secure communication.

The experimental analysis on safety stock effect of chaotic supply chain attractor

Supply chain mechanism is a management phenomenon developed to respond to customer demands at the right time, in the right place, and the right amount. However, unpredictability in demand and associated stocks and production amounts cause chaotic behaviour in the system. In this study, a three-dimensional supply chain mathematical model has been utilized to stabilize the chaotic system by adding a linear control parameter that increases the production amount to prevent a collapse leading to dangerous instability. Through adjusting the levels of the linear control parameter, the change in system behaviour has been examined with phase portrait, histogram, autocorrelation, and spectral plots. The experimental analysis demonstrates that when the amount of production is increased, the supply chain system's chaotic state is controlled. The Poincare section and phase portraits graphics have proven that the supply chain has moved away from the chaotic situation and has become stable with the increase in production amounts. The results also reveal that the autocorrelation between the sequential simulation values of the production quantities decreased when there is a transition from chaos towards a steady state. The decrease in the similarity of the values leads to a decrease in the error. It has been shown that including a control parameter for production quantity determination improves the effectiveness of the model by means of increased flexibility to handle uncertain demand.

Extracting Long-Period Surface Waves and Free Oscillations Using Ambient Noise Recorded by Global Distributed Superconducting Gravimeters

AbstractInversion of internal structure of the Earth using surface waves and free oscillations is a hot topic in seismological research nowadays. With the ambient noise data on seismically quiet days sourced from the gravity tidal observations of seven global distributed superconducting gravimeters (SGs) and the seismic observations for validation from three collocated STS-1 seismometers, long-period surface waves and background free oscillations are successfully extracted by the phase autocorrelation (PAC) method, respectively. Group-velocity dispersion curves at the frequency band of 2–7.5 mHz are extracted and compared with the theoretical values calculated with the preliminary reference Earth model. The comparison shows that the best observed values differ about ±2% from the corresponding theoretical results, and the extracted group velocities of the best SG are consistent with the result of the collocated STS-1 seismometer. The results indicate that reliable group-velocity dispersion curves can be measured with the ambient noise data from SGs. Furthermore, the fundamental frequency spherical free oscillations of 2–7 mHz are also clearly extracted using the same ambient noise data. The results in this study show that the SG, besides the seismometer, is proved to be another kind of instrument that can be used to observe long-period surface waves and free oscillations on seismically quiet days with a high degree of precision using the PAC method. It is worth mentioning that the PAC method is first and successfully introduced to analyze SG observations in our study.

Parameter-free image resolution estimation based on decorrelation analysis.

Super-resolution microscopy opened diverse new avenues of research by overcoming the resolution limit imposed by diffraction. Exploitation of the fluorescent emission of individual fluorophores made it possible to reveal structures beyond the diffraction limit. To accurately determine the resolution achieved during imaging is challenging with existing metrics. Here, we propose a method for assessing the resolution of individual super-resolved images based on image partial phase autocorrelation. The algorithm is model-free and does not require any user-defined parameters. We demonstrate its performance on a wide variety of imaging modalities, including diffraction-limited techniques. Finally, we show how our method can be used to optimize image acquisition and post-processing in super-resolution microscopy.

Reconstruction of sub cross-correlation cancellation technique for unambiguous acquisition of BOC(kn,n) signals

In order to solve the problem of ambiguous acquisition of BOC signals caused by its property of multiple peaks, an unambiguous acquisition algorithm named reconstruction of sub cross-correlation cancellation technique (RSCCT) for BOC(kn, n) signals is proposed. In this paper, the principle of signal decomposition is combined with the traditional acquisition algorithm structure, and then based on the method of reconstructing the correlation function. The method firstly gets the sub-pseudorandom noise (PRN) code by decomposing the local PRN code, then uses BOC(kn, n) and the sub-PRN code cross-correlation to get the sub cross-correlation function. Finally, the correlation peak with a single peak is obtained by reconstructing the sub cross-correlation function so that the ambiguities of BOC acquisition are removed. The simulation shows that RSCCT can completely eliminate the side peaks of BOC (kn, n) group signals while maintaining the narrow correlation of BOC, and its computational complexity is equivalent to sub carrier phase cancellation (SCPC) and autocorrelation side-peak cancellation technique (ASPeCT), and it reduces the computational complexity relative to BPSK-like. For BOC(n, n), the acquisition sensitivity of RSCCT is 3.25 dB, 0.81 dB and 0.25 dB higher than binary phase shift keying (BPSK)-like, SCPC and ASPeCT at the acquisition probability of 90%, respectively. The peak to average power ratio is 1.91, 3.0 and 3.7 times higher than ASPeCT, SCPC and BPSK-like at SNR = -20 dB, respectively. For BOC(2n, n), the acquisition sensitivity of RSCCT is 5.5 dB, 1.25 dB and 2.69 dB higher than BPSK-like, SCPC and ASPeCT at the acquisition probability of 90%, respectively. The peak to average power ratio is 1.02, 1.68 and 2.12 times higher than ASPeCT, SCPC and BPSK-like at SNR = -20 dB, respectively.

Detecting and Locating Precursory Signals During the 2011 El Hierro, Canary Islands, Submarine Eruption

AbstractForecasting and monitoring submarine volcanic eruptions represent a particular challenge due to the lack of direct surface observations. In the present study, we investigate the dynamics of the 2011 El Hierro submarine eruption using phase autocorrelation and cross‐correlation from 2 years of continuous seismic records. Time evolution analysis of the waveform similarity allows us to clearly identify different preeruptive phases of this new volcano, as well as three magmatic intrusions that occurred in 2012. We use probabilistic sensitivity kernels to locate the places of the highest dynamics within the magmatic accumulation zone and the extinct volcanic area of Tiñor that might have acted as stress barriers, guiding the magma from the North of El Hierro Island to the final eruption site at the South. Our results highlight the potential of ambient noise methods to monitor volcanic hazard and unrest even with sparse data sets and limited knowledge of the region.

Detection of Subtle Hydromechanical Medium Changes Caused By a Small-Magnitude Earthquake Swarm in NE Brazil

Ambient noise correlation analyses are largely used in seismology to map heterogeneities and to monitor the temporal evolution of seismic velocity changes associated mostly with stress field variations and/or fluid movements. Here we analyse a small earthquake swarm related to a main mR 3.7 intraplate earthquake in North-East of Brazil to study the corresponding post-seismic effects on the medium. So far, post-seismic effects have been observed mainly for large magnitude events. In our study, we show that we were able to detect localized structural changes even for a small earthquake swarm in an intraplate setting. Different correlation strategies are presented and their performances are also shown. We compare the classical auto-correlation with and without pre-processing, including 1-bit normalization and spectral whitening, and the phase auto-correlation. The worst results were obtained for the pre-processed data due to the loss of waveform details. The best results were achieved with the phase cross-correlation which is amplitude unbiased and sensitive to small amplitude changes as long as there exist waveform coherence superior to other unrelated signals and noise. The analysis of 6 months of data using phase auto-correlation and cross-correlation resulted in the observation of a progressive medium change after the major recorded event. The progressive medium change is likely related to the swarm activity through opening new path ways for pore fluid diffusion. We further observed for the auto-correlations a lag time frequency-dependent change which likely indicates that the medium change is localized in depth. As expected, the main change is observed along the fault.

Phase Autocorrelation Bark Wavelet Transform (PACWT) Features for Robust Speech Recognition

Abstract In this paper, a new feature-extraction method is proposed to achieve robustness of speech recognition systems. This method combines the benefits of phase autocorrelation (PAC) with bark wavelet transform. PAC uses the angle to measure correlation instead of the traditional autocorrelation measure, whereas the bark wavelet transform is a special type of wavelet transform that is particularly designed for speech signals. The extracted features from this combined method are called phase autocorrelation bark wavelet transform (PACWT) features. The speech recognition performance of the PACWT features is evaluated and compared to the conventional feature extraction method mel frequency cepstrum coefficients (MFCC) using TI-Digits database under different types of noise and noise levels. This database has been divided into male and female data. The result shows that the word recognition rate using the PACWT features for noisy male data (white noise at 0 dB SNR) is 60%, whereas it is 41.35% for the MFCC features under identical conditions

Utilization of balanced detection with optical hard-limiters in T/W OCDMA system

In this paper, we utilize optical hard-limiters to further enhance the system performance in balanced detection T/W optical CDMA system. In T/W optical CDMA systems, it had been investigated that the balanced detection scheme is not superior to the OOK scheme because of the adverse impact of beat noise. The employment of optical hard-limiter is an effective way to alleviate the deteriorating effect of beat noise. The carrier-hopping prime code is utilized as signature sequences whose out of phase autocorrelation is zero and the cross-correlation is at most one. Due to the orthogonality of signature sequence, the correlator of shifted version of carrier-hopping prime code is utilized in the receiver. The numerical results reveal that our proposed scheme can greatly reduce the error floor; also it is superior to that using OOK scheme with optical hard-limiter. Most important of all, our proposed scheme has fixed and optimum thresholds which do not vary with system parameters; and this will lead to dynamic estimation of optimal thresholds unnecessary in the receiver.

Optical CDMA system using spatial AMI coding scheme and coset representative

In this paper, the utilizations of spatial alternate mark inversion (AMI) coding scheme and coset representative are investigated in time-spreading wavelength-hopping optical code division multiple access systems. The carrier hopping prime code is utilized as signature sequence whose out of phase autocorrelation is zero and the cross-correlation is at most one. Predicated upon the zero autocorrelation sidelobes property of the carrier hopping prime code, we exploit the spatial AMI coding scheme to the trellis run-length limited code from one-dimension into two-dimension. To enhance the error correcting capability of the proposed trellis code, coset representative is imposed on the trellis to further enlarge the free distance. Since the multiple access interference and beat noise are the main deteriorating factors in system performance which will bring about the error floor effect, our proposed coding scheme with larger coding gain can further effectively alleviate the adverse impacts. Aside from the multiple access interference and beat noise, some of the detrimental effects in system performance are also taken into account, which include thermal noise, shot noise and relative intensity noise.

Fast and accurate simulation of the turbulent phase screen using fast Fourier transform

This work describes an accurate method for simulating turbulent phase screens. The phase screen is divided into a fast Fourier transform (FFT)-based screen and a tilt screen. The simulation of the FFT-based screen is different from that of the standard method. In the simulation, the discrete power spectrum of the turbulence is obtained from the discrete Fourier transform of the phase autocorrelation matrix, not from the theoretical power spectrum. This method avoids the drawbacks of the undersampling of the low frequency and high frequency components which occurs in the standard FFT-based method. The maximum error in the phase structure function can be reduced to <0.13% , and the additional execution time increases by only several percents. This method is only suitable for square screens.

Phase AutoCorrelation (PAC) features for noise robust speech recognition

In this paper, we introduce a new class of noise robust features derived from an alternative measure of autocorrelation representing the phase variation of speech signal frame over time. These features, referred to as Phase AutoCorrelation (PAC) features include PAC-spectrum and PAC-MFCC, among others. In traditional autocorrelation, correlation between two time delayed signal vectors is computed as their dot product. Whereas in PAC, angle between the vectors in the signal vector space is used to compute the correlation. PAC features are more noise robust because the angle is typically less affected by noise than the dot product. However, the use of angle as correlation estimate makes the PAC features inferior in clean speech. In this paper, we circumvent this problem by introducing another set of features where complementary information among the PAC features and the traditional features are combined adaptively to retain the best of both. An entropy based feature combination method in a multi-layer perceptron (MLP) based multi-stream framework is used to derive an adaptively combined representation of the component feature streams. An evaluation of the combined features using OGI Numbers95 database and Aurora-2 database under various noise conditions and noise levels show significant improvements in recognition accuracies in clean as well as noisy conditions.

Time-spreading wavelength-hopping optical CDMA system using EWO and TCM

In this paper, time-spreading wavelength-hopping optical CDMA system using trellis coded modulation scheme is investigated. The carrier hopping prime code and its shifted version are employed as signature sequences. Since the carrier hopping prime code is a symmetric code, the out of phase autocorrelation is zero. Applying the orthogonality of the signature sequences, the ternary transmission mechanism can be achieved. The proposed coding scheme is simple in both transmitter and receiver. As the multiple access interference and beat noise are the major deterioration of system performance, using coding scheme is an effective way to reduce the error floor. The numerical results reveal that the proposed coding scheme can significantly improve the system performance.

Phase transitions and autocorrelation times in two-dimensional Ising model with dipole interactions

The two-dimensional Ising model with nearest-neighbor ferromagnetic and long-range dipolar interactions exhibits a rich phase diagram. The presence of the dipolar interaction changes the ferromagnetic ground state expected for the pure Ising model to a series of striped phases as a function of the interaction strengths. Monte Carlo simulations and histogram reweighting techniques applied to multiple histograms are performed to identify the critical temperatures for the phase transitions taking place for stripes of width h = 2 on square lattices. In particular, we aim to study the intermediate nematic phase, which is observed for large lattice sizes only. For these lattice sizes, we calculate the critical temperatures for the striped-nematic and nematic-tetragonal transitions, critical exponents, and the bulk free-energy barrier associated with the coexisting phases. We also evaluate the long-term correlations in our time series near the finite-size critical points by studying the integrated autocorrelation time τ as a function of the lattice size. This allows us to infer how severe the critical slowing down for this system with long-range interaction and nearby thermodynamic phase transitions is.