Estimation Of Phase Shift Research Articles

Estimation and Compensation of Phase Shifts in SAR Focusing of Spotlight Data Acquired With Discrete Antenna Steering

Modern spaceborne synthetic aperture radar sensors are able to operate the spotlight mode to achieve very high resolution images at microwave frequencies. This mode is characterized by antenna steering to increase the illumination interval. The steering is carried out by beam switching on bursts during the data acquisition interval. In addition to an unavoidable spectrum modulation in azimuth, phase shifts can occur from burst to burst. In this letter, we describe the problem and a procedure able to estimate the phase shifts based on the image contrast maximization technique for subsequent compensation at the data focusing stage. Results on real data acquired by the COSMO-SkyMed sensor demonstrate the effectiveness of the proposed solution.

Noise Resistant Method for Cardiac Pulse Wave Arrival Time Estimation

Pulse arrival time is the time interval which is needed for pulse wave to travel the distance from the heart to some distal place on the body. Almost all definitions of pulse arrival time estimation are based on high quality photoplethysmogram signals. However, when subject movement is involved movement artifacts dominate in the signal, e.g., records from orthostatic test, and estimation of pulse arrival time becomes complicated. The aim of this study is to present pulse arrival time estimation method which is based on instantaneous phase shift estimation between extracted fundamental frequency components and compare it with a classical method which based on photoplethysmogram signal derivative maximum. The results showed that the proposed method is better for pulse arrival time estimation when signals are noisy. The method yielded pulse arrival time with the highest agreement, accuracy, precision and lowest variability. There is high intraclass correlation when signal to noise ratio are 0 dB and 10 dB (0.5317 and 0.8630). The classical method incorrectly estimates pulse arrival time when are using real signals. However, larger dataset is needed in order to get statistically significant results. Variability of pulse arrival time and arterial blood pressure is higher in the vertical posture. DOI: http://dx.doi.org/10.5755/j01.eee.20.8.8442

Improved Estimation of the Specific Differential Phase Shift Using a Compilation of Kalman Filter Ensembles

A new algorithm for the accurate estimation of the specific differential phase shift on propagation (Kdp) from noisy total differential phase shift (Ψdp) measurements is presented for data acquired with a polarimetric weather radar. The new approach, which is based on the compilation of ensembles of Kalman filter estimates, does not rely on additional data like the reflectivity or the differential reflectivity in order to constrain the solution, and it is based on Ψdp only. The dependence of the solution on Ψdp only allows one to apply the algorithm in various environmental conditions without reducing its performance. Drawbacks that are usually inherent in algorithms of this kind (like the loss of the small-scale structure and the smoothing of high peak values) are partially overcome by a two-step algorithm design, which first determines an ensemble of possible solutions and then selects and averages the ensemble members such that the estimated Kdp profile has a better agreement with the truth. The algorithm is thoroughly evaluated and compared with a commonly used algorithm on stochastically simulated profiles of raindrop size distribution. It is found that the accuracy of the Kdp values estimated with the new algorithm significantly increases. The algorithm is also experimentally evaluated by applying it on X-band radar data that were acquired in northern Brazil during the CHUVA campaign and at a high alpine site in Switzerland during snowfall. Results show that the spatial fine structure and the high values of precipitation are better represented with the new method.

Robust phase-shift estimation method for statistical generalized phase-shifting digital holography.

We propose a robust phase-shift estimation method for statistical generalized phase-shifting digital holography using a slightly off-axis optical configuration. The phase randomness condition in the Fresnel diffraction field of an object can be sufficiently established by the linear phase factor of the oblique incident reference wave. Signed phase-shift values can be estimated with a statistical approach regardless of the statistical properties of the Fresnel diffraction field of the object. We present computer simulations and optical experiments to verify the proposed method.

Current spectrum estimation using Prony's estimator and coherent resampling

Purpose – A highly accurate method of current spectrum estimation of a nonlinear load is presented in this paper. Using the method makes it possible to evaluate the current injection frequency domain model of a nonlinear load from previously recorded time domain voltage and current waveforms. The paper aims to discuss these issues. Design/methodology/approach – The method incorporates the idea of coherent resampling (resampling synchronously with the base frequency of the signal) followed by the discrete Fourier transform (DFT) to obtain the frequency spectrum. When DFT is applied to a synchronously resampled signal, the spectrum is free of negative DFT effects (the spectrum leakage, for example). However, to resample the signal correctly it is necessary to know its base frequency with high accuracy. To estimate the base frequency, the first-order Prony's frequency estimator was used. Findings – It has been shown that the presented method may lead to superior results in comparison with window interpolated Fourier transform and time-domain quasi-synchronous sampling algorithms. Research limitations/implications – The method was designed for steady-state analysis in the frequency domain. The voltage and current waveforms across load terminals should be recorded simultaneously to allow correct voltage/current phase shift estimation. Practical implications – The proposed method can be used in case when the frequency domain model of a nonlinear load is desired and the voltage and current waveforms recorded across load terminals are available. The method leads to correct results even when the voltage/current sampling frequency has not been synchronized with the base frequency of the signal. It can be used for off-line frequency model estimation as well as in real-time DSP systems to restore coherent sampling of the analysed signals. Originality/value – The method proposed in the paper allows to estimate a nonlinear load frequency domain model from current and voltage waveforms with higher accuracy than other competitive methods, while at the same time its simplicity and computational efficiency is retained.

Accuracy of Phase-Based Algorithms for the Estimation of the Specific Differential Phase Shift Using Simulated Polarimetric Weather Radar Data

The specific differential phase shift on propagation K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dp</sub> is widely employed in the study of precipitation, although little is known about the effective accuracy of its estimates. The aim of this letter is to analyze the quality of K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dp</sub> estimates, using realistic simulated fields of drop size distributions. Two classical and one recently proposed estimation algorithms are tested, which are chosen among the algorithms that use the measured and noisy total differential phase shift Ψ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dp</sub> as their main input. A data set of six simulated rain events, from which polarimetric radar variables can be derived, is employed in this letter. The mean normalized absolute error in the estimation of K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dp</sub> at the radar resolution volume scale ranges from 27% to 30% for all the algorithms proposed, and significant negative biases up to -50% emerge at the highest values of K <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">dp</sub> for the most biased algorithm. The new algorithm, which is based on Kalman filtering, is able to keep these localized bias values around -25% and outperforms the classical algorithms in terms of efficiency, correlation, and root-mean-square error.

Utilization of multi-rate signal processing for GNSS-SDR receivers

In this article, we propose a low-complexity solution for the decimation chain in the digital front-end (DFE) of global navigation satellite system (GNSS) receivers. The received signals are typically highly oversampled in the DFE of GNSS receivers to reduce the ranging error and therefore to improve the positioning accuracy in the tracking stage of the GNSS receivers. However, this oversampling imposes unnecessary complexity on the acquisition stage of the GNSS receivers where an approximate estimate of the code phase and Doppler frequency shift is produced. Therefore, reducing the sampling frequency for the acquisition stage reduces the overall receiver complexity without any significant effect on the performance of such receivers. The proposed solution for the decimation chain involves the use of infinite impulse response (IIR) filters as the decimation filter as they can be implemented more efficiently in comparison to finite impulse response (FIR). In addition, a hybrid time-frequency domain filtering scheme is proposed here to alleviate the effects of non-linear phase in the decimation IIR filter as well as the analog front-end receivers. The advantages of this proposed method is explored and stated, both from performance and complexity perspectives, through rigorous comparison with alternative available solutions.

Improving chemical shift encoded water–fat separation using object‐based information of the magnetic field inhomogeneity

The purpose of this work was to improve the robustness of existing chemical shift encoded water-fat separation methods by incorporating object-based information of the B0 field inhomogeneity. The primary challenge in water-fat separation is the estimation of phase shifts that arise from B0 field inhomogeneity, which is composed of the background field and susceptibility-induced field. The susceptibility-induced field can be estimated if the susceptibility distribution is known or can be approximated. In this work, the susceptibility distribution is approximated from the source images using the known susceptibility values of water, fat, and air. The field estimate is then demodulated from the source images before water-fat separation. Chemical shift encoded source images were acquired in anatomical regions that are prone to water-fat swaps. The images were processed using algorithms from the ISMRM Fat-Water Toolbox, with and without the object-based field map information. The estimates were compared to examine the benefit of using the object-based field map information. Multiple cases are shown in which water-fat swaps were avoided by using the object-based information of the B0 field map. Object-based information of the B0 field may improve the robustness of existing chemical shift encoded water-fat separation methods.

Estymacja kąta przesunięcia fazowego przy nagrzewaniu indukcyjnym w.cz.

In the paper chosen digital methods of phase shift determination are presented: one operating in the time domain (based on zero crossing detection), and two operating in frequency domain (Fourier transform and Hilbert transform based). The results of the experimental verification of above mentioned methods in two different measurement systems are presented. The main focus was to verify the possibility of their use for the signals of induction heating equipments recorded with the low sampling frequencies. (Estimation of phase shift at high frequency induction heating).

A highly accurate ultrasonic ranging method based on onset extraction and phase shift detection

The opposite-type ultrasonic ranging application is widely used in spatial 3D coordinates measurement systems. The traditional phase shift (PS) estimation based on multi-frequency ultrasonic pulse is a highly accurate ranging method but has high requirement to the transducers and signal processing algorithm. This paper proposes a novel opposite-type ultrasonic ranging method with single frequency pulse. It can estimate the time of flight (TOF) roughly through extracting the signal’s onset based on self-correlation and correct the TOF accurately through detecting the phase shift between the transmission and reception signals. In order to reduce the noise disturbance to this algorithm, a new de-noising method based on wavelet decomposition is presented, and the de-noising effect is analyzed by MATLAB simulation. Finally, three separate ultrasonic ranging experiments were designed to validate the effects of wavelet de-noising, PS detection and temperature field compensation. The accuracy of distance measurement can achieve 0.5mm for the distance up to 5000mm.

Phase shift estimation from variances of fringe pattern differences

This paper presents a simple algorithm for estimating phase shifts from only three interferograms. In it, the fringe pattern differences are computed first in order to remove the background component, and then the variances and further the standard deviations (SDs) of fringe pattern differences are calculated. The phase shifts are estimated, by using the law of cosines, from a triangle whose lengths of sides are the SDs just calculated. This algorithm offers several advantages over others, e.g., being efficient, easy to implement, accurate, and less sensitive to noise. Numerical simulations and an experiment are performed to demonstrate its validity.

Generalized phase-shifting interferometry by parameter estimation with the least squares method

A simple non-iterative algorithm for generalized phase-shifting interferometry is proposed. This algorithm recovers the wrapped phase from two or more interferograms with unknown phase steps between 0 and π rad. The proposal is based on the least squares method to calculate four parameters: background and modulation light, phase steps and wrapped phase distribution. This algorithm, by a new interferogram normalization procedure, can handle interferograms with variable spatiotemporal visibility overcoming the restriction and drawbacks from usual variable spatial visibility approaches. The algorithm works very well for processing interferograms which include many fringes. This behaviour will be explicated and discussed. The effectiveness and robustness of this algorithm are supported by numerical simulation and by the evaluation of experimental interferograms. The phase-shift estimation quality is verified by two different techniques. By the properties of this algorithm, such as the low computing time and free of user intervention, we believe it could be used in automatic real-time applications.

Simultaneous quantification of myocardial and blood flow velocities based on duplex mode ultrasound imaging

BackgroundUltrasound imaging of the heart is a commonly used clinical tool to assess cardiac function. The basis for this analysis is the quantification of cardiac blood flow and myocardial velocities. These are typically measured using different imaging modes and on different cardiac cycles. However, due to beat-to-beat variations such as irregular heart rhythm and transient events, simultaneous acquisition is preferred. There exists specialized ultrasound systems for this purpose; however, it would be beneficial if this could be achieved using conventional ultrasound systems due to their wide availability. The conventional Duplex mode ultrasound allows simultaneous acquisition, however at a highly reduced spatial and temporal resolution.MethodsThe aim of this work was to present and evaluate the performance of a novel method to recover myocardial tissue velocity using conventional Duplex ultrasound imaging, and to demonstrate its feasibility for the assessment of simultaneous blood flow and myocardial velocity in-vivo. The essence of the method was the estimation of the axial phase shift of robust echogenic structures between subsequent image frames. The performance of the method was evaluated on synthetic tissue mimicking B-mode image sequences at different frame rates (20–60 Hz) and tissue velocities (peak velocities 5-15cm/s), using cardiac deformation and displacement characteristics. The performance was also compared to a standard 2-D speckle tracking technique.ResultsThe method had an overall high performance at frame rates above 25 Hz, with less than 15% error of the peak diastolic velocity, and less than 10 ms peak timing error. The method showed superior performance compared to the 2-D tracking technique at frame rates below 50 Hz. The in-vivo quantification of simultaneous blood flow and myocardial tissue velocities verified the echocardiographic patterns and features of healthy subjects and the specific patient group.ConclusionsA novel myocardial velocity quantification method was presented and high performance at frame rates above 25 Hz was shown. In-vivo quantification of simultaneous myocardial and blood flow velocities was feasible using the proposed method and conventional Duplex mode imaging. We propose that the methodology is suitable for retrospective as well as prospective studies on the mechanics and hemodynamics of the heart.

Quantum Metrological Limits via a Variational Approach

The minimum achievable statistical uncertainty in the estimation of physical parameters is determined by the quantum Fisher information. Its computation for noisy systems is still a challenging problem. Using a variational approach, we present an equation for obtaining the quantum Fisher information, which has an explicit dependence on the mathematical description of the noise. This method is applied to obtain a useful analytical bound to the quantum precision in the estimation of phase-shifts under phase diffusion, which shows that the estimation uncertainty cannot be smaller than a noise-dependent constant.

Useful Multiparticle Entanglement and Sub-Shot-Noise Sensitivity in Experimental Phase Estimation

We experimentally demonstrate a general criterion to identify entangled states useful for the estimation of an unknown phase shift with a sensitivity higher than the shot-noise limit. We show how to exploit this entanglement on the examples of a maximum likelihood as well as of a Bayesian phase estimation protocol. Using an entangled four-photon state we achieve a phase sensitivity clearly beyond the shot-noise limit. Our detailed comparison of methods and quantum states for entanglement enhanced metrology reveals the connection between multiparticle entanglement and sub-shot-noise uncertainty, both in a frequentist and in a Bayesian phase estimation setting.

Estimation of phase shifts linked only to the coating for a dielectric mirror

The wavefront is an important characteristic for a dielectric mirror. Its measurement is usually performed with interferometers. We introduce a new method to evaluate only the coating wavefront distortion due to nonuniform thickness errors by using a reflectometer. This method uses some reflectance or transmittance maps at a wavenumber σ(m) for which the reflectance or transmittance factor variation is high. These variations are translated into some central wavenumber σ(c) variations, which enables the determination of a phase map from experimental treatment.

OPTIMIZED QUBIT PHASE ESTIMATION IN NOISY QUANTUM CHANNELS

We address the estimation of phase-shifts for qubit systems in the presence of noise. Different sources of noise are considered including bit flip, bit-phase flip and phase flip. We derive the ultimate quantum limits to precision of estimation by evaluating the analytical expressions of the quantum Fisher information and assess performances of feasible measurements by evaluating the Fisher information for realistic spin-like measurements. We also propose an experimental scheme to test our results.

Two-Dimensional Flow Imaging in the Carotid Bifurcation Using a Combined Speckle Tracking and Phase-Shift Estimator: A Study Based on Ultrasound Simulations and in vivo Analysis

A two-dimensional (2-D) blood velocity estimator is presented combining speckle tracking (ST) and phase-shift estimation (PE) to measure lateral (vx) and axial (vz) velocities respectively. Estimator properties were assessed in a carotid bifurcation using ultrasound simulations based on computational fluid dynamics, allowing validation toward a ground truth. Simulation results were supported with in vivo data of a healthy carotid. ST and PE estimates were combined as: (1) vx from 2D-ST and vz from PE, (2) vx from 2D-ST and vz from PE with aliasing correction based on ST and (3) vz from PE and only lateral ST for vx. Regression analysis showed a 35% to 77% decrease in standard deviation for vz for PE compared with ST. Aliasing correction based on ST improved results but also introduced spurious artifacts. A marginal decrease in performance was observed when only tracking laterally. Further work will focus on in vivo trials in patients with carotid plaques. (E-mail: abigail.swillens@ugent.be)

Lateral superresolution using a posteriori phase shift estimation for a moving object: experimental results

Structured illumination imaging uses multiple images of an object having different phase shifts in the sinusoidally patterned illumination to obtain lateral superresolution in stationary specimens in microscopy. In our recent work we have discussed a method to estimate these phase shifts a posteriori, allowing us to apply this technique to non-stationary objects such as in vivo tissue. Here we show experimental verification of our earlier simulations for phase shift estimation a posteriori. We estimated phase shifts in fluorescence microscopy images for an object having unknown, random translational motion and used them to obtain an artifact-free reconstruction having the expected superresolution.

Combined mixed approach algorithm for in‐line phase‐contrast x‐ray imaging

In the past decade, phase-contrast imaging (PCI) has been applied to study different kinds of tissues and human body parts, with an increased improvement of the image quality with respect to simple absorption radiography. A technique closely related to PCI is phase-retrieval imaging (PRI). Indeed, PCI is an imaging modality thought to enhance the total contrast of the images through the phase shift introduced by the object (human body part); PRI is a mathematical technique to extract the quantitative phase-shift map from PCI. A new phase-retrieval algorithm for the in-line phase-contrast x-ray imaging is here proposed. The proposed algorithm is based on a mixed transfer-function and transport-of-intensity approach (MA) and it requires, at most, an initial approximate estimate of the average phase shift introduced by the object as prior knowledge. The accuracy in the initial estimate determines the convergence speed of the algorithm. The proposed algorithm retrieves both the object phase and its complex conjugate in a combined MA (CMA). Although slightly less computationally effective with respect to other mixed-approach algorithms, as two phases have to be retrieved, the results obtained by the CMA on simulated data have shown that the obtained reconstructed phase maps are characterized by particularly low normalized mean square errors. The authors have also tested the CMA on noisy experimental phase-contrast data obtained by a suitable weakly absorbing sample consisting of a grid of submillimetric nylon fibers as well as on a strongly absorbing object made of a 0.03 mm thick lead x-ray resolution star pattern. The CMA has shown a good efficiency in recovering phase information, also in presence of noisy data, characterized by peak-to-peak signal-to-noise ratios down to a few dBs, showing the possibility to enhance with phase radiography the signal-to-noise ratio for features in the submillimetric scale with respect to the attenuation-based imaging. It has been shown that phase-retrieved radiographies can be used both to have quantitative phase information about soft tissues, complementary to the attenuation information, and to enhance the visibility of details inside soft tissues, with higher efficiency with respect to phase radiography.