Estimators for instantaneous phase

A robust algorithm for the simultaneous estimation of dip, azimuth and curvature in the depth migrated domain is developed. The algorithm makes use of instantaneous‐attribute beamforming in small windows aligned with locally coherent migrated events. This is the following two‐step procedure: inline and cross‐line linear beam stacks to compute the two local dips at image points; 360‐degree azimuthal parabolic beamforming to estimate azimuthally dependent curvatures with respect to the plane tangent to the instantaneous‐phase surface at the image point. Amplitude and phase content of migrated traces are processed independently using complex trace analysis in order to facilitate this procedure. The instantaneous phase is of central importance since it describes the lateral continuity of events and defines instantaneous dips corresponding to instantaneous apparent phase velocity and group velocity. This attribute is used to compute the instantaneous frequency that defines the beam wavelet at the peak of waveform envelope. The instantaneous amplitude or envelope represents an input to model‐based wavefield (Born‐Kirchhoff) de‐remigration of picked events, useful for dip QC. The QC analysis involves thresholding of modeled migrated amplitudes predicted by Kirchhoff remigration of the Born demigrated wavefield. This also includes simple thresholding of the instantaneous frequency. The analysis is shown to be capable of eliminating undesired events. The algorithm was tested using a 3‐D marine streamer dataset with high noise. The success with field migrated data demonstrates that the algorithm is particularly useful for slope‐limited tomographic velocity updates and structural interpretation when the signal‐to‐noise ratio (SNR) is low.

Borehole Radar (BHR) uses ultra-wideband electromagnetic (EM) waves to image discontinuities in formations. It has been a major bottleneck to extend BHR applications to obtain a clear and high-resolution radar profile in a complex and noisy environment, which increases ambiguity in the geology interpretation. To avoid this increased ambiguity in the geology interpretation, we proposed a scheme based on the empirical mode decomposition (EMD) and complex signal analysis theory to process the BHR data with low signal to noise ratio (SNR). The scheme includes four steps. First, the original radar profile is pre-processed to avoid mode confusion and noise interference to the radar echo. Next, the EMD method is used to process a single-channel radar dataset and to analyze the frequency components of the radar signal. Various intrinsic modes of the pre-processing radar profile are also obtained by using EMD. Finally, we reconstruct the intrinsic mode profile, which contains information about the formation, calculate the complex signals of the reconstructed radar profile using the Hilbert transform, extract the three instantaneous attributes (instantaneous amplitude, instantaneous phase, and instantaneous frequency), and draw the separate instantaneous attributes profiles. This processing scheme provides both the conventional time-distance profile also in addition to the three instantaneous attributes. The additional attributes reduce ambiguity when evaluating the original radar profile and avoid the deviation relying solely on a conventional time-distance profile. An actual radar profile, which was obtained by a BHR system in a limestone fracture zone, is used to verify the effectiveness of instantaneous attributes for improving interpretation accuracy. The results demonstrate that the EMD method is superior in processing the BHR signal under a low SNR and has the capability to separate the high-low components of the radar echo effectively.

A method for automatically determining first-motion polarities is developed, with a view to its application to the focal mechanism analysis of massive microseismic events caused by hydraulic fracturing. The method is based on two assumptions: the existence of a point source, which has negligible effects of fault finiteness and rupture directivity; and a laterally homogeneous structure, which has azimuthally isotropic propagation characteristics. Under these assumptions, the event waveforms recorded at each station share a common source time function shape, with varying amplitudes, that is dependent on the radiation pattern from the source. With respect to the reference waveform with the highest signal-to-noise ratio (SNR) among all the waveforms at each station for an event, the relative polarities of waveforms at other stations are estimated using cross correlation analysis. The absolute polarities of each waveform are then defined using the reference waveform, whose SNR can be further enhanced using the stacked waveforms after corrections of relative polarities and time lags between the reference and target waveforms have been made. Then, a grid-search algorithm can be incorporated to invert focal mechanisms using the automatically measured polarities for a given event. Since the procedure requires only the evaluation of a cross-correlation coefficient, it can be incorporated into an automated algorithm. The method is applied to determine the focal mechanism solutions of microseismic events occurring in a shale gas play where commercial production is ongoing. Two types of focal mechanism solutions are found to be dominant: vertical dip-slip, and strike-slip. The strike-slip events occur due to re-activation of natural fractures connecting cracks opened by hydraulic fracturing. For the vertical dip-slip events, it was observed that their strikes are consistent with the direction of maximum horizontal stress, which supports the theory that slips occur on the horizontal bedding planes due to the opening of vertical cracks generated by hydraulic fracturing.

This work presents a phase unwrapping (PU) algorithm for SAR interferometry based on an approximate grid-based filter (GbF). This PU algorithm, which makes use of state space techniques, performs simultaneously noise filtering and phase unwrapping. The formulation of this technique provides independence from noise statistics and is not constrained by the non-linearity of the problem. Results obtained with synthetic and real data show a significant improvement with respect to conventional PU algorithms in some situations.

In order to accurately identify the distribution of the karst water conduction channel after water inrush, the ground penetrating radar (GPR) is used for fine detection of development of karst water conduction in front of the heading surface after water inrush, and the instantaneous amplitude, instantaneous phase and instantaneous frequency are extracted from the radar signal by Hilbert transform. Then, the three instantaneous properties are combined for multi-parameter comprehensive analysis of the karst water conduction channel. As shown in the study results, the instantaneous amplitude can better show the boundary characteristics and morphological size of the karst water conduction channel. The instantaneous phase can clearly show the heterogeneous characteristics inside the karst water conduction channel. The instantaneous frequency can reflect the water richness of the karst water conduction channel from the angle of energy decay. The combination of the three instantaneous attributes can avoid the explanatory bias due to the analysis of single waveform characteristics, and effectively improve the resolution and accuracy of the detection of the karst water conduction channel.

ALTIS: A new algorithm for adaptive long-term SNR estimation in multi-talker babble

The Tuaheni Landslide Complex, located on the upper slope of the northern Hikurangi Margin in New Zealand, is a unique place to research on slow slip creep-like deformation and seabed failure, as well as their possible relationship with the presence of gas hydrates, cold seeps, and fluid migration. Based on the visual interpretation of seismic data, it is sometimes very difficult to identify various subsurface structures and tectonic features. We study certain seismic attributes, namely the reflection strength, instantaneous frequency, instantaneous phase, and the Hilbert transform, in the Tuaheni Landslide Complex and observe that these attributes play a very important role in identifying and interpreting various subsurface geological features and bed boundaries that are not clearly visible in the seismic sections. In general, these seismic attributes are studied to identify hydrocarbons such as oil and gas. However, in this present study these seismic attributes nicely illustrate the fluid migration pathways, the decollement of the sediment slide, the base of the debris flow, the base of the deformed sediment and gas migration, etc., along two perpendicular seismic profiles crossing the Site U1517 of IODP Expedition 372. The instantaneous phase and Hilbert transform attribute depict the bed boundaries and discontinuities, whereas the reflection strength and instantaneous frequency attributes characterize the various strata in terms of whether they are associated with fluid at their bases. The possible role of tectonic activity and seafloor slope failure due to gas hydrate dissociation and vice versa is clearly visible through fluid-filled weak zones in the seismic attribute volumes. Gas hydrates are dissociating and BSRs are abruptly pinching out towards the seafloor due to the movement of hot fluid and free gas, enhancing seafloor sliding and local tectonic activities together.

We consider the task of estimating the randomly fluctuating phase of a continuous-wave beam of light. Using the theory of quantum parameter estimation, we show that this can be done more accurately when feedback is used (adaptive phase estimation) than by any scheme not involving feedback (non-adaptive phase estimation) in which the beam is measured as it arrives at the detector. Such schemes not involving feedback include all those based on heterodyne detection or instantaneous canonical phase measurements. We also demonstrate that the superior accuracy adaptive phase estimation is present in a regime conducive to observing it experimentally.

Intravoxel incoherent motion (IVIM) modeling offers the parameters f, D and D* as biomarkers for different lesion types and cancer stages from diffusion MR signals. Challenges with the available optimization algorithms in fitting the model to the signals motive new studies for improved parameter estimations. In this study, one thousand value sets of f, D, D* for human breast are assembled and used to generate five thousand diffusion MR signals considering noise-free and noisy situations exhibiting signal-to-noise ratios (SNR) of 20, 40, 60 and 80. The estimates of f, D, D* are obtained using Levenberg-Marquardt (LM), trust-region (TR) and particle swarm (PS) algorithms. On average, the algorithms provide the highest fitting performance for the noise-free signals (R2adj=1.000) and great fitting performances on the noisy signals with SNR>20 (R2adj>0.988). TR algorithm performs slightly better for SNR=20 (R2adj=0.947). TR and PS algorithms achieve the highest parameter estimation performance for all the parameters while LM algorithm reveals the highest performance for f and D only on the noise-free signals (r=1.00). For the noisy signals, performances increase while SNR increases. All algorithms accomplish poor performances for D* (r=0.01-0.20) while TR and PS algorithms perform same for f (r=0.48-0.97) and D (r=0.85-0.99) but remarkably better than LM algorithm for f (r=0.08-0.97) and D (r=0.53-0.99). Overall, TR and PS algorithms demonstrate better but indistinguishable performances. Without requiring any user-given initial value, PS algorithm may facilitate improved estimation of IVIM parameters of the human breast tissue. Further studies are needed to determine its benefit in clinical practice.

The kalman filtering phase unwrapping is a state estimation problem. It can realize phase unwrapping and noise elimination at the same time, and calculate the real phase by establishing the state space model and vector observation model. In the steep terrain, the conventional kalman filtering algorithm unwrapping results are often not accurate, easy to cause the error transfer. Aiming at this problem, the weighted kalman filter phase unwrapping algorithm based on the phase derivative variance map is proposed. The values of the phase derivative variance maps are applied to determine the noise variance in the observation equation, then the weighted kalman filter is used to unwrap phase, this can increase the accuracy of the results. Finally, experiments are carried out in the InSAR data application under the condition of steep terrain, and with the conventional kalman filtering phase unwrapping algorithm are compared, the effectiveness of the proposed method is verified.

Cognitive Radio (CR) networks has been presented in the last decade as a solution to the problem of increasing congestion in frequency spectrum, through opportunistic spectrum access techniques. One of the main components of Cognitive Radio receivers is the Automatic Modulation Classification (AMC), in which the CR can blindly identify the modulation scheme of a detected signal. AMC has several applications, including military, spectrum surveillance and management, and commercial applications. In this paper we propose an AMC based on two different Neural Networks (NN) classifiers: Feed-Forward with Resilient Back-Propagation NN and Probabilistic NN. NN classifiers take their inputs as a feature vector from a Features extraction phase. Features selected for classification are the statistical features of the received signal's instantaneous amplitude, frequency and phase. Simulations show that both NN classifiers can achieve over 80% correct classification up to Signal-to-Noise Ratio (SNR) of 5 dB, and the probability of correct classification increases up to 99% at a SNR of 15 dB.

Phase-Locking value (PLV) is used to measure phase synchrony of narrowband signals, therefore, it is able to provide a measure of dynamic functional connectivity (DFC) of brain interactions. Currently used PLV methods compute the convolution of the signal at the target frequency with a complex Gabor wavelet centered at that frequency. The phase of this convolution is extracted for all time-bins over trials for a pair of neural signals. These time-bins set a limit on the temporal resolution for PLV, hence, for DFC. Therefore, these methods cannot provide a true DFC in a strict sense. PLV is defined as the absolute value of the characteristic function of the difference of instantaneous phases (IP) of two analytic signals evaluated at s = 1. It is a function of the time. For the narrowband signal in the stationary Gaussian white noise, we investigated statistics of (i) its phase, (ii) the maximum likelihood estimate of its phase, and (iii) the phase-lock loop (PLL) measurement of its phase, derived the analytic form of the probability density function (pdf) of the difference of IP, and expressed this pdf in terms of signal-to-noise ratio (SNR) of signals. PLV is finally given by analytic formulas in terms of SNRs of a pair of neural signals under investigation. In this new approach, SNR, hence PLV, is evaluated at any time instant over repeated trials. Thus, the new approach can provide a true DFC via PLV. This paper presents detailed derivations of this approach and results obtained by using simulations for magnetoencephalography (MEG) data.

A robust linear phase unwrapping method is proposed to solve the 2/spl pi/ discontinuities in the phase of the cross power spectrum from the binaural inputs using two omnidirectional microphones. The relative incident angle of the interested sound is then estimated according to the time difference of arrival (TDOA) which is obtained from the unwrapped phase of the cross power spectrum. The frequency components associated with the high power are clustered into groups by the phase and frequency distance, and the dominant group is then used to obtain the initial slope estimation. The phase is unwrapped by checking the difference between the actual and the predicted phase by the estimated slope. The re-estimation is then performed by the unwrapped phase. The algorithm is tested under different incident angles and signal to noise ratio (SNR) using real speech signal and white Gaussian noise. The simulation results show the high accuracy and the robustness. This method is also Implemented to control a robot to adaptively adjust itself to the position facing the sound source directly. The satisfactory result was achieved in an open house demonstration.

In this paper, an efficient Fast Block LMS (FBLMS) algorithm is proposed for removing artifacts preserving the low frequency components and tiny features of the ECG. The proposed implementation is suitable for applications requiring large signal to noise ratios with fast convergence rate. The FBLMS algorithm, being the solution of the steepest descent strategy for minimizing the mean squared error in a complete signal occurrence, is shown to be steady-state unbiased and with a lower variance than the LMS algorithm. Finally, we have applied this algorithm on ECG signals from the MIT-BIH data base and compared its performance with the conventional LMS algorithm. The results show that the performance of the FBLMS algorithm is superior than the LMS algorithm. I. INTRODUCTION The extraction of high-resolution ECG signals from record- ings contaminated with background noise is an important issue to investigate. The goal for ECG signal enhancement is to separate the valid signal components from the undesired artifacts, so as to present an ECG that facilitates easy and accurate interpretation. Many approaches have been reported in the literature to address ECG enhancement using adaptive filters (2)-(3), which permit to detect time varying potentials and to track the dynamic variations of the signals. In (3), Thakor et al. proposed an LMS based adaptive recurrent filter to acquire the impulse response of normal QRS complexes, and then applied it for arrhythmia detection in ambulatory ECG recordings. The reference inputs to the LMS algorithm are deterministic functions and are defined by a periodically extended, truncated set of orthonormal basis functions. In these papers, the LMS algorithm operates on an instantaneous basis such that the weight vector is updated every new sample within the occurrence, based on an instantaneous gradient estimate. There are certain clinical applications of ECG signal processing that require adaptive filters with large number of taps. In such applications the conventional LMS algorithm is computationally expensive to implement. The block processing of data samples can significantly reduce the computational complexity. By applying this strategy, a special implementa- tion of the LMS algorithm is called the block LMS algorithm. In a recent study, however, a steady state convergence analysis for the LMS algorithm with deterministic reference inputs showed that the steady-state weight vector is biased, and thus, the adaptive estimate does not approach the Wiener solution. To handle this drawback another strategy was considered for estimating the coefficients of the linear expansion, ie., the BLMS algorithm (8), in which the coefficient vector is updated only once every occurrence based on a block gradient estimation. The BLMS algorithm has been proposed in the case of random reference inputs and has, when the input is stationary, the same steady state misadjustment and convergence speed as the LMS algorithm. A major advantage of the block, or the transform domain, LMS algorithm is that the input signals are approximately uncorrelated. Moreover, the filter output and the weight update terms can be evaluated faster using FFT-based fast BLMS (FBLMS) algorithm. The advantage of this algorithm is less computational complexity and good filtering capability. These characteristics may plays a vital role in biotelemetry, where extraction of noise free ECG signal for efficient diagnosis and fast computations, high data transfer rate are needed to avoid overlapping of pulses and to resolve ambiguities. To the best of our knowledge, transform domain has not been considered previously within the context of filtering artifacts in ECG signals. In this paper, we present a FBLMS algorithm to remove the artifacts from ECG. Such a realization is intrinsically less complex than its BLMS based counterpart. This algorithm enjoys less compu- tational complexity and good filtering capability. To study the performance of the proposed algorithm to effectively remove the noise from the ECG signal, we carried out simulations on MIT-BIH database for different artifacts. The simulation results shows that the proposed algorithm performs better than the LMS counterpart to eliminate the noise from ECG.

The use of linear time-frequency (TF) representa-tions as instantaneous frequency (IF) estimators arises in various fundamental disciplines, mainly thanks to their simplicity and immunity against interfering cross-terms. In this paper, we derive the optimal window width for IF estimation of noisy multicomponent signals based on a family of linear TF transforms that use Gaussian windowing functions and the Fourier oscillatory kernel. Closed-form formulas concerning the estimation bias and the variance are presented, which, thanks to their generality, describe the statistical performance of IF estimators based on transforms with fixed, time-adaptive, frequency-adaptive, or time-frequency adaptive windows. The optimal window is dependent on the unknown first derivative of the IF; therefore, we employ a low-complexity procedure to infer the derivative and optimize the width accordingly. Two adaptive and fully automated TF representations (TFRs) are developed; the first employs a time-adaptive window that minimizes the sum of the mean-squared errors (MSEs) of the IF estimates at each time instant, while in the second TFR, the window is adaptive over time and frequency, minimizing the estimation MSE at each location in the TF domain. Examples using synthetic and real-world signals demonstrate that the proposed algorithms may outperform many popular state-of-the-art techniques, including those that are signal-adaptive, in terms of IF estimation.