Estimation Of Phase Shift Research Articles

Phase-based block matching applied to motion estimation with unconventional beamforming strategies

A phase-based block matching method adapted to motion estimation with unconventional beamforming strategies is presented. The unconventional beamforming technique used allows us to obtain 2-D RF images with axial and lateral modulations. Based on these images, we propose a method that uses phase images instead of amplitude images. This way of proceeding allows us to provide an analytical solution to the local displacement estimation so that no minimization of a classical cost function is used for the local estimation. For this reason, the local estimator is directly applied to signals, without the need to process a complex cross-correlation function, as is done with most of the phase shift estimators. In this paper, the method is applied to elastography. Results with simulated data show that a downsampling of axial and lateral modulated signals leads to very little change in the accuracy and in the spatial resolution of the proposed method. For example, for decimation factors of 2 in the axial direction and of 4 in the lateral direction, the mean axial absolute error is 3 mum. The same estimation with original images provides a mean axial error of 0.7 microm. The accuracy of the lateral motion is unchanged in this case. The accuracy of our method with downsampled signals is an important issue in the purpose of a real-time implementation. With experimental data, for the same level of estimation error, classical block matching using the maximum of cross correlation as a local estimator requires images that are 36 times larger (in number of pixels) and consequently a computational time roughly 10 times longer. Our phase block matching is also shown to provide 10 percent less error than a motion estimation method based on seeking the zero of the complex correlation function phase. Finally, it is shown that given the separability of the local estimator that we propose, our method can be applied on both n-D signals and classical RF ultrasound images. The phase block matching method presented was implemented in real time on an ultrasound research scanner.

Bayesian estimation in homodyne interferometry

We address phase-shift estimation by means of squeezed vacuum probe and homodyne detection. We analyse Bayesian estimator, which is known to asymptotically saturate the classical Cramér–Rao bound to the variance, and discuss convergence looking at the a posteriori distribution as the number of measurements increases. We also suggest two feasible adaptive methods, acting on the squeezing parameter and/or the homodyne local oscillator phase, which allow us to optimize homodyne detection and approach the ultimate bound to precision imposed by the quantum Cramér–Rao theorem. The performances of our two-step methods are investigated by means of Monte Carlo simulated experiments with a small number of homodyne data, thus giving a quantitative meaning to the notion of asymptotic optimality.

Contrast Biases the Autocorrelation Phase Shift Estimation in Doppler Tissue Imaging

Quantitative assessment of regional myocardial function at rest and during stress with Doppler tissue imaging (DTI) plays an important role in daily routine echocardiography. However, reliable visual analysis is largely dependent on image quality and adequate border delineation, which still remains a challenge in a significant number of patients. In this respect, an ultrasound contrast agent (UCA) is often used to improve visualization in patients with suboptimal image quality. The knowledge of how DTI measurements will be affected by UCA present in the tissue is therefore of significant importance for an accurate interpretation of local myocardial motion. The aim of this paper was to investigate how signal contribution from UCA and nonlinear wave propagation influence the performance of the autocorrelation phase shift estimator used for DTI applications. Our results are based on model experiments with a clinical 2-D grayscale scanner and computational simulations of the DTI velocity estimator for synthetically-derived pulses, simulated bubble echoes and experimentally-sampled RF data of transmitted pulses and backscattered contrast echoes. The results show that destruction of UCA present in the tissue will give rise to an apparent bidirectional velocity bias of individual velocity estimates, but that spatial averaging of individual velocity measurements within a region-of-interest will result in a negative bias (away from the transducer) of the estimated mean or mean peak velocity. The UCA destruction will also have a significant impact on the measured integrated mean velocity over time, i.e., displacement. To achieve improved visualization with UCA during DTI-examinations, we either recommend that it is performed at low acoustic powers, mechanical index ≤0.3, thereby minimizing the effects from bubble rupture, or that each Doppler pulse package is preceded by a destruction burst similar to “Flash imaging” to clear the target area of contrast microbubbles. (E-mail: marcus.ressner@imt.liu.se)

Analytic Estimation of Subsample Spatial Shift Using the Phases of Multidimensional Analytic Signals

In this correspondence, a method of analytic subsample spatial shift estimation based on an a priori n-D signal model is proposed. The estimation uses the linear phases of n analytic signals defined with the multidimensional Hilbert transform. This estimation proposes: i) an analytic solution to the n-D shift estimation and ii) an estimation without processing complex cross-correlation function or cross-spectra between signals contrary to most phase shift estimators. The method provides better performance in estimating subsample shifts than two classical estimators, one using the maximum of cross-correlation function and the other seeking the zero of the complex correlation function phase. Two delay estimators using the in-phase and quadrature-phase components of signals are also compared to our estimator. Like most estimators using the complex signal phases, the estimator proposed herein presents the advantage of unaltered accuracy when low sampled signals are used. Moreover, we show that this method can be applied to motion tracking with ultrasound images. Thus, included in a block-based motion estimation method and tested with ultrasound data, this estimator provides an analytical solution to the translation estimation problem.

Estimation of a nonparametric regression spectrum for multivariate time series

Estimation of a nonparametric regression spectrum based on the periodogram is considered. Neither trend estimation nor smoothing of the periodogram is required. Alternatively, for cases where spectral estimation of phase shifts fails and the shift does not depend on frequency, a time domain estimator of the lag-shift is defined. Asymptotic properties of the frequency and time domain estimators are derived. Simulations and a data example illustrate the methods.

A cavity-QED scheme for Heisenberg-limited interferometry

We propose a Ramsey interferometry experiment using an entangled state of N atoms to approach the Heisenberg limit for the estimation of an atomic phase shift if the atom number parity is perfectly determined. In a more realistic situation, due to statistical fluctuations of the atom source and the finite detection efficiency, the parity is unknown. We then achieve about half the Heisenberg limit. The scheme involves an ensemble of circular Rydberg atoms which dispersively interact successively with two initially empty microwave cavities. The scheme does not require very high-Q cavities. An experimental realization with about ten entangled Rydberg atoms is achievable with a state of art apparatus.

Blind phase shift estimation in phase-shifting interferometry

A blind phase shift estimation algorithm that allows simultaneous calculation of phases and phase shifts from three or more interferograms is presented. In phase-shifting interferometry, the phase shift errors introduce specific correlations between the calculated background intensity distribution and the fringe component. These correlations can be measured with a cross-power spectrum. By minimization of an objective function based on this cross-power spectrum, the actual phase shifts are estimated and used for phase recovery. The validity of this algorithm is verified by both the numerical simulation and the experiment results.

A non-iterative method for phase-shift estimation and wave-front reconstruction in phase-shifting digital holography

This paper derives an analytical formula for extracting the amount of phase-shift in phase-shifting digital holography when the object wave intensity can be measured, which is obtained by simply solving the object wave reconstruction equation. Since it eliminates the requirements of approximation and iteration in existing techniques, a much faster processing speed can be obtained. It also has higher estimation accuracy than those iterative methods with a large iterative step size.

Influence of reentry turbulent plasma fluctuation on EM wave propagation

Electromagnetic wave propagation in turbulent plasma media during reentry is being investigated. Emphasis is placed on the effects of electron density fluctuations on electromagnetic wave propagation. The objective of this paper is to specify the source of noise in electromagnetic signal reception due to turbulence in the flow about a high velocity flight vehicle. A review of existing ground and flight test data is conducted, including electron density fluctuation measurements. Analytical algorithms deduced from first principles are being developed and validated with experimental measurements. A Navier–Stokes model, three-dimensional parabolized Navier–Stokes, and a coupled boundary-layer and inviscid flow codes are used to estimate the mean and variance of the electron density on the frustum and at the vehicle’s base region. Analytical and numerical solutions solving Maxwell’s equations and a commercial off the shelf code are used to estimate the phenomena of electromagnetic wave propagation in inhomogeneous plasma media. Results include the estimation of signal attenuation and phase shift induced by the mean electron density and by electron density fluctuations in the flowfield. Comparisons are made between the predictions and available data.

Rapid tracking of small displacements with ultrasound

Time-delay estimators, such as normalized cross correlation and phase-shift estimation, form the computational basis for elastography, blood flow measurements, and acoustic radiation force impulse (ARFI) imaging. This paper examines the performance of these algorithms for small displacements (less than half the ultrasound pulse wavelength). The effects of noise, bandwidth, stationary echoes, kernel size, downsampling, interpolation, and quadrature demodulation on the accuracy of the time delay estimates are measured in terms of bias and jitter. Particular attention is given to the accuracy and resolution of the displacement measurements and to the computational efficiency of the algorithms. In most cases, Loupas' two-dimensional (2-D) autocorrelator performs as well as the gold standard, normalized cross correlation. However, Loupas' algorithm's calculation time is significantly faster, and it is particularly suited to operate on the signal data format most commonly used in ultrasound scanners. These results are used to implement a real-time ARFI imaging system using a commercial ultrasound scanner and a computer cluster. Images processed with the algorithms are examined in an ex vivo liver ablation study.

Adaptive quantum estimation of phase shifts

We discuss an adaptive interferometric approach to quantum estimation of phase shifts. In a first step we find optimized two-mode input states for a generalized Mach-Zehnder interferometer. These two states show a small phase variance at the so-called Heisenberg limit. It turns out that they can be generated by entangling a coherent state and a squeezed vacuum at a beam splitter. Moreover, the interferometric setup allows us to describe an adaptive estimation scheme for arbitrary phase shifts if we assume a fixed mean photon number as a quantum resource.

A Comparative Study of Two Discrete-Time Phase Delay Estimators

Two simple discrete-time methods for unbiased estimation of the phase-shift between two real sinusoidal signals in white noise are proposed. The first estimator removes the bias of the recently proposed quadrature delay estimator (QDE) by utilizing all in-phase and quadrature-phase components of the received signals. The phase estimate of the second method is given by the phase difference of the discrete-time Fourier transforms (DTFTs) of two complex sinusoids derived from the real signals. In particular, we have derived the mean square phase-shift error of the DTFT-based estimator as well as the minimum achievable variance for phase-shift estimation, which are identical. Computer simulations show that the two proposed estimators are superior to the biased QDE and can attain optimum performance, although the second estimator has a larger signal-to-noise ratio operation range.

Classification of BPSK and QPSK Signals Using an Antenna Array

We propose in this paper the use of a uniform linear array to improve the classification accuracy of two phase-shift keying (PSK) signals at different multiplicities, in particular, binary PSK (BPSK) and quadrature PSK (QPSK) signals. The proposed modulation classifier is based on the likelihood ratio test, where an additive white Gaussian noise with direct line-of-sight transmission is assumed. The likelihood functions of the two PSK signals depend on an unknown phase shift due to the signal arrival angle and the spatial separation of the antenna elements. A computationally efficient two-step processing is proposed to estimate the phase shifts to be used in the likelihood ratio test. The proposed phase shift estimation method reduces the computation significantly compared to the maximum likelihood solution, which requires numerical exhaustive search, and has an estimation accuracy reaching the Cram\'er-Rao lower bound at moderate signal-to-noise ratios. The proposed classifier improves the performance considerably compared to a single element receiver. Furthermore, the proposed classifier demodulates the transmitted symbol sequence in conjunction with the classification process, and no separate demodulation for the data symbol is needed after classification. Simulation results for BPSK and QPSK classification are provided.

Optimal estimation of multiple phases

We study the issue of simultaneous estimation of several phase shifts induced by commuting operators on a quantum state. We derive the optimal positive operator-valued measure corresponding to the multiple-phase estimation. In particular, we discuss the explicit case of the optimal detection of double phase for a system of identical qutrits and generalise these results to optimal multiple phase detection for d-dimensional quantum states.

CIRCADIAN PHASE AND PERIOD RESPONSES TO LIGHT STIMULI IN TWO NOCTURNAL RODENTS

We report period response curves (τRC) for two nocturnal Murid species from India, Mus booduga and Mus platythrix. We further discuss the method of phase shift estimation in the presence of τ-changes, because such changes pose a serious methodological problem in the estimation of phase shifts. Although the τRC indicates that most of the phase shifts are associated with small changes in τ, the period changes across all the phases showed a significant positive correlation with the phase shifts. We conclude that τRCs are a reality even in nocturnal mammals, although their amplitude is less than what is usually found in diurnal mammals, and requires a larger data set to be distinguished from noise.

Light-Induced resetting of the circadian pacemaker: quantitative analysis of transient versus steady-state phase shifts.

The suprachiasmatic nuclei of the hypothalamus contain the major circadian pacemaker in mammals, driving circadian rhythms in behavioral and physiological functions. This circadian pacemaker's responsiveness to light allows synchronization to the light-dark cycle. Phase shifting by light often involves several transient cycles in which the behavioral activity rhythm gradually shifts to its steady-state position. In this article, the authors investigate in Syrian hamsters whether a phase-advancing light pulse results in immediate shifts of the PRC at the next circadian cycle. In a first series of experiments, the authors aimed a light pulse at CT 19 to induce a phase advance. It appeared that the steady-state phase advances were highly correlated with activity onset in the first and second transient cycle. This enabled them to make a reliable estimate of the steady-state phase shift induced by a phase-advancing light pulse on the basis of activity onset in the first transient cycle. In the next series of experiments, they presented a light pulse at CT 19, which was followed by a second light pulse aimed at the delay zone of the PRC on the next circadian cycle. The immediate and steady-state phase delays induced by the second light pulse were compared with data from a third experiment in which animals received a phase-delaying light pulse only. The authors observed that the waveform of the phase-delay part of the PRC (CT 12-16) obtained in Experiment 2 was virtually identical to the phase-delay part of the PRC for a single light pulse (obtained in Experiment 3). This finding allowed for a quantitative assessment of the data. The analysis indicates that the delay part of the PRC-between CT 12 and CT 16-is rapidly reset following a light pulse at CT 19. These findings complement earlier findings in the hamster showing that after a light pulse at CT 19, the phase-advancing part of the PRC is immediately shifted. Together, the data indicate that the basis for phase advancing involves rapid resetting of both advance and delay components of the PRC.

Parameter estimation in quantum optics

We address several estimation problems in quantum optics by means of the maximum-likelihood principle. We consider Gaussian state estimation and the determination of the coupling parameters of quadratic Hamiltonians. Moreover, we analyze different schemes of phase-shift estimation. Finally, the absolute estimation of the quantum efficiency of both linear and avalanche photodetectors is studied. In all the considered applications, the Gaussian bound on statistical errors is attained with a few thousand data.

Simulation of photon acceleration in a plasma wake

The frequency shifting of an ultrashort (femtosecond) low intensity laser pulse in the presence of a plasma wave is investigated using particle simulations. One-dimensional simulations confirm the existence of photon trajectories similar to the trajectories of trapped or untrapped charged particles in a plasma wave. In the case when a plasma wake is produced by a relativistically intense laser pulse with a duration of the order of one plasma period, some full oscillations of the photon frequency take place only for the untrapped photons moving backward in the plasma wave frame before the intense laser pulse depletion due to the energy transfer to the plasma wake occurs. An analytical estimate of the probe pulse phase and frequency shift in two-dimensional (2-D) axially symmetrical plasma wake is performed. Axially symmetrical particle simulations in 2-D, with experimentally attainable parameters, display a frequency shift of the probe pulse of a few percent. In these analytical estimates and 2-D simulations special attention has been given to the modeling of the probe pulse optical collecting line that is typically used in plasma diagnostics.

Prediction of wave pressures on smooth impermeable seawalls

Simple prediction methods are proposed to estimate the wave induced pressures on smooth impermeable seawalls. Based on the physics of the wave structure interaction, the sloped seawall is divided into a total of five zones (zones 1, 2 and 3 during run-up (corresponding pressures are called as positive pressures) and zones 4 and 5 during run-down (corresponding pressures are called negative pressures)) (Fig. 1 ). Zone 1 (0<z<d−Hi/2), where the wave pressure is governed by the partial reflection and phase shift; Zone 2 (d−Hi/2<z<d), where the effect of wave breaking and turbulence is significant; Zone 3 (d<z<Run-up height), where the pressure is induced by the run-up water; Zone 4 (Run-down<z<d), where the wave pressure is caused by the run-down effect and Zone 5 (0<z<d-Run down), where the negative wave pressures are due to partial reflection and phase shift effects. Here d is the water depth at the toe of the seawall, Hi is the incident wave height and z is the vertical elevation with toe of the seawall as origin and z is positive upward. For wave pressure prediction in zones 1 and 5, the empirical formula proposed by Ahrens et al. (1993)to estimate the wave reflection and Sutherland and Donoghue's recommendations (1998) for the estimation of phase shift of the waves caused by the sloped structures are used. Multiple regression analysis is carried out on the measured pressure data and empirical formulas are proposed for zones 2, 3 and 4. The recommendations of Van der Meer and Breteler (1990)and Schüttrumpf et al. (1994) for the prediction of wave run-down are used for pressure prediction at zone 4. Comparison of the proposed prediction formulas with the experimental results reveal that the prediction methods are good enough for practical purposes. The present study also shows a strong relation between wave reflection, wave run-up, wave run-down and phase shift of waves on wave pressures on the seawalls.

Quantum phase resolution and phase distribution

We discuss generation and measurement strategies for maximum-likelihood estimation of small phase shifts. We demonstrate that optimal encoding of small phase shifts and optimal measurements of small phase shifts require different states. We also show that states with identical phase resolution may have rather different Pegg-Barnett phase distributions. Hence, the connection between phase distribution and quantum phase resolution is rather weak.