Incoherent Averaging Research Articles

Universality of quantum time dilation

Time dilation is a difference in measured time between two clocks that either move with different velocities or experience different gravitational potentials. Both of these effects stem from the theory of relativity and are usually associated with classically defined trajectories, characterized by position, momentum, and acceleration. However, when spatial degrees of freedom are treated in a quantum way and a clock is allowed to be in a coherent superposition of either two momenta or two heights, additional quantum corrections to classical time dilation appear, called kinematic and gravitational quantum time dilations, respectively. We show that similarly to its classical counterpart, kinematic quantum time dilation is universal for any clock mechanism, while gravitational quantum time dilation is not. We also show that although both of these effects reduce to incoherent averaging of different classical time dilation contributions, there exists an additional quantum time dilation effect that has no classical analog and can be extracted from higher-order corrections to the system’s Hamiltonian.

Estimation of Medium Depolarization Index with Noise Immunity in Catheter-Based PS-OCT toward Vascular Plaques Detection.

Medium depolarization imaging by catheter-based polarization-sensitive optical coherence tomography (PS-OCT) can provide valuable insight into significant features of lipid, macrophages, and cholesterol crystals in atherosclerotic vulnerable plaques. In this paper, we demonstrate a method to achieve an accurate estimation of the medium depolarization index (EMDI) with noise immunity in catheter-based PS-OCT. EMDI is calculated by an iterative approximation based on Lu-Chipman matrix decomposition and Frobenius norm judgment of incoherent averaging of Mueller matrices. Monte Carlo simulation results verify that the medium depolarization measurement by EMDI is 3.3 times more accurate compared with those of the depolarization index (DI) and degree of polarization uniformity (DOPU). In experiments, we design a microsphere suspension with various concentrations and measure EMDI under different additive noise. Consistently, the measurement accuracy by EMDI is increased 2.85 times compared to those by DI and DOPU. For vascular plaques detection, we use protein and cholesterol gel as plaque phantoms. Based on PS-OCT images of plaque phantom in vitro and in ex vivo porcine coronary artery, the recognition rate of plaque by EMDI is 2.99 to 4.65 times higher than those by DI and DOPU evaluated by spatial response of the Laplacian operator (SRLO).

Efficient framework of solving time-gated reflection matrix for imaging through turbid medium.

Imaging through turbid medium is a long pursuit in many research fields, such as biomedicine, astronomy and automatic vehicle, in which the reflection matrix-based method is a promising solution. However, the epi-detection geometry suffers from round-trip distortion and it is challenging to isolate the input and output aberrations in non-ideal cases due to system imperfections and measurement noises. Here, we present an efficient framework based on single scattering accumulation together with phase unwrapping that can accurately separate input and output aberrations from the noise-affected reflection matrix. We propose to only correct the output aberration while suppressing the input aberration by incoherent averaging. The proposed method is faster in convergence and more robust against noise, avoiding precise and tedious system adjustments. In both simulations and experiments, we demonstrate the diffraction-limited resolution capability under optical thickness beyond 10 scattering mean free paths, showing the potential of applications in neuroscience and dermatology.

GNSS-R Observations of Marine Plastic Litter in a Water Flume: An Experimental Study

Currently, eight million metric tons of plastic end up in the oceans every year, and microplastics in different forms are present in almost all water systems in the world: streams, rivers, lakes, or oceans, and even in our blood. Detection of marine litter is an urgent task. Some works have recently reported the potential of GNSS-Reflectometry to detect marine plastic litter from space. This study presents the results of a controlled field experiment conducted under the auspices of ESA at the “Atlantic Basin” at the Deltares research institute (Delft, The Netherlands). Several types of wave conditions were created: sinusoidal and with JONSWAP spectrum, with different significant wave heights, and with different types of plastics and marine litter collected from the Dutch coast. Experimental results show the difficulty in detecting marine plastic litter based on a change of the reflected power. However, a statistical analysis of the GNSS-R estimated reflectivities (amplitude and phase) computed with very short integration times (coherent integration time Tcoh = 1 ms, and no incoherent averaging: Nincoh = 1) show that it may be possible to detect large accumulations of some types of marine litter that dampen the water waves, such as nets, bottles in a net, food wraps, and bags.

Analysis and reduction of noise-induced depolarization in catheter based polarization sensitive optical coherence tomography.

In catheter based polarization sensitive optical coherence tomography (PS-OCT), a optical fiber with a rapid rotation in the catheter can cause low signal-to-noise ratio (SNR), polarization state instability, phase change of PS-OCT signals and then heavy noise-induced depolarization, which has a strong impact on the phase retardation measurement of the sample. In this paper, we analyze the noise-induced depolarization and find that the effect of depolarization can be reduced by polar decomposition after incoherent averaging in the Mueller matrix averaging (MMA) method. Namely, MMA can reduce impact of noise on phase retardation mapping. We present a Monte Carlo method based on PS-OCT to numerically describe noise-induced depolarization effect and contrast phase retardation imaging results by MMA and Jones matrix averaging (JMA) methods. The peak signal to noise ratio (PSNR) of simulated images processed by MMA is higher than about 8.9 dB than that processed by JMA. We also implement experiments of multiple biological tissues using the catheter based PS-OCT system. From the simulation and experimental results, we find the polarization contrasts processed by the MMA are better than those by JMA, especially at areas with high depolarization, because the MMA can reduce effect of noise-induced depolarization on the phase retardation measurement.

Comparison of similar Mueller and Jones matrix method in catheter based polarization sensitive optical coherence tomography

Catheter based polarization sensitive optical coherence tomography (PS-OCT) can provide composition information of coronary atherosclerotic plaque beyond the intensity based OCT, but it encounters a notable challenge that is how to reduce polarization properties variations owing to a rapidly rotating optical fiber in the catheter. Similar Jones matrix (SJM) and similar Mueller matrix (SMM) based polarization determination methods can provide a stable phase retardation imaging in a catheter based PS-OCT. In this paper, we systematically contrast SJM and SMM methods. Firstly, we theoretically illustrate the discrepancy between the eigenvalue decomposition in SJM and the polar decomposition in SMM. We find the SMM can reduce phase retardation error caused by non-coaxial diattenuation using polar decomposition. Secondly, we present a real incoherent averaging method in SMM. We find that incoherent averaging in SMM avoids a time-consuming global phase collection and more effectively reduce noise compared with complex coherent averaging in SJM. By polarization imaging for multiple biological tissues using a catheter based PS-OCT, we experimentally manifest that the areas with high diattenuation are highly correlated to the difference between images processed by SJM and SMM. At the same time, the SMM with incoherent averaging has a better performance than the SJM with coherent averaging especially at areas with low signal to noise ratio (SNR).

Metabolite cycled liver 1 H MRS on a 7 T parallel transmit system.

IntroductionSingle‐voxel 1H MRS in body applications often suffers from respiratory and other motion induced phase and frequency shifts, which lead to incoherent averaging and hence to suboptimal results.MethodsHere we show the application of metabolite cycling (MC) for liver STEAM‐localized 1H MRS on a 7 T parallel transmit system, using eight transmit‐receive fractionated dipole antennas with 16 additional, integrated receive loops. MC‐STEAM measurements were made in six healthy, lean subjects and compared with STEAM measurements using VAPOR water suppression. Measurements were performed during free breathing and during synchronized breathing, for which the subjects did breathe in between the MRS acquisitions. Both intra‐session repeatability and inter‐session reproducibility of liver lipid quantification with MC‐STEAM and VAPOR‐STEAM were determined.ResultsThe preserved water signal in MC‐STEAM allowed for robust phase and frequency correction of individual acquisitions before averaging, which resulted in in vivo liver spectra that were of equal quality when measurements were made with free breathing or synchronized breathing. Intra‐session repeatability and inter‐session reproducibility of liver lipid quantification were better for MC‐STEAM than for VAPOR‐STEAM. This may also be explained by the more robust phase and frequency correction of the individual MC‐STEAM acquisitions as compared with the VAPOR‐STEAM acquisitions, for which the low‐signal‐to‐noise ratio lipid signals had to be used for the corrections.ConclusionNon‐water‐suppressed MC‐STEAM on a 7 T system with parallel transmit is a promising approach for 1H MRS applications in the body that are affected by motion, such as in the liver, and yields better repeatability and reproducibility compared with water‐suppressed measurements.

Motion correction in magnetic resonance spectroscopy.

In vivo proton magnetic resonance spectroscopy and spectroscopic imaging (MRS/MRSI) are valuable tools to study normal and abnormal human brain physiology. However, they are sensitive to motion, due to strong crusher gradients, long acquisition times, reliance on high magnetic field homogeneity, and particular acquisition methods such as spectral editing. The effects of motion include incorrect spatial localization, phase fluctuations, incoherent averaging, line broadening, and ultimately quantitation errors. Several retrospective methods have been proposed to correct motion-related artifacts. Recent advances in hardware also allow prospective (real-time) correction of the effects of motion, including adjusting voxel location, center frequency, and magnetic field homogeneity. This article reviews prospective and retrospective methods available in the literature and their implications for clinical MRS/MRSI. In combination, these methods can attenuate or eliminate most motion-related artifacts and facilitate the acquisition of high-quality data in the clinical research setting.

Computational aberration correction in spatiotemporal optical coherence (STOC) imaging.

Spatiotemporal optical coherence (STOC) imaging is a new technique for suppressing coherent cross talk noise in Fourier-domain full-field optical coherence tomography (FD-FF-OCT). In STOC imaging, the time-varying inhomogeneous phase masks modulate the incident light to alter the interferometric signal. Resulting interference images are then processed as in standard FD-FF-OCT and averaged incoherently or coherently to produce cross-talk-free volumetric optical coherence tomography (OCT) images of the sample. Here, we show that coherent averaging is suitable when phase modulation is performed for both interferometer arms simultaneously. We explain the advantages of coherent over incoherent averaging. Specifically, we show that modulated signal, after coherent averaging, preserves lateral phase stability, enabling computational phase correction to compensate for geometrical aberrations. Ultimately, we employ it to correct for aberrations present in the image of the photoreceptor layer of the human retina that reveals otherwise invisible photoreceptor mosaics.

Mueller matrix ellipsometry of waveplates for control of their properties and alignment

In this paper, the authors characterize high-order quartz waveplates in the wide spectral range (from 193 to 1700 nm) using a commercial Mueller matrix ellipsometer RC2-DI-Woollam. They demonstrate that Mueller matrix ellipsometry is a powerful tool to obtain the waveplate retardation in a wide spectral range together with azimuthal angles of optical axes with good accuracy. Moreover, they deal with depolarization caused by a finite monochromator bandwidth, which is included in the model using incoherent averaging of Mueller matrices. The application of Lu–Chipman Mueller matrix decomposition to extract depolarization from data is also demonstrated. Finally, Lu–Chipman decomposition is used to demonstrate the presence of the optical activity in quartz, which one may misinterpret with incorrect alignment of the waveplate azimuth angle.

Coherently averaged power spectral estimate for signal detection

A common approach to detect sinusoidal signals buried in noise is based on spectral analysis, such as the periodogram. The fluctuations of the spectral components associated with the noise can be alleviated via incoherent averaging of the power spectral estimates of each segment, which is the basis of Welch’s method. However, Welch’s method only utilizes the incoherent information between segments of signals. In this paper, we propose a method of coherent averaging between segments, which enhances ratio of time-invariant sinusoidal signals relative to the level of the noise background. The gain of coherent averaged power spectral estimate has been derived in terms of time duration of the signal. The proposed method provides a flexible, computationally efficient implementation of signal detection, which can be formulated to allow for various integration times to be realised in different frequency bands. Simulation and experimental results show that the proposed method outperforms the Welch’s method and the periodogram method.

Retrieval of Ocean Wind Speed Using Airborne Reflected GNSS Signals

This paper develops the models that can be used in different flight scenarios to retrieve the wind speed using the width of the normalized delay waveform (NDW). First, the factors that influence the NDW width, including the wind speed, wind direction, flight height, and elevation angle, are analyzed. The contribution of each independent variable to the regression is explored. The results show that the wind speed, flight height, and elevation angle contribute more significantly than the wind direction so the wind direction can be ignored in the model. The multiple regression, in which the function terms of NWD width, flight height, and elevation angle above are taken as independent variables and wind speed is taken as the dependent variable, is proposed to develop the model of retrieving wind speed. Through the simulation, a root-mean-square error (RMSE) over 3 m/s can be obtained. In order to improve the retrieval performance, a Back-Propagation (BP) network is trained as an alternative to the analytical models above. Better performance is achieved with an RMSE less than 2.5 m/s under the same conditions with the analytical model. The errors of retrieved wind speed are analyzed. The conclusions are that: 1) both analytical model and BP network have inherent regression biases, especially for high wind speed from 15 to 20m/s so that at wind speeds higher than 16 m/s, the tendency for retrieval accuracy to rapidly become worse appears and 2) the number of incoherent averaging should be over 1000 to reduce the impact of thermal and speckle noise. At the end of the paper, airborne data are processed to retrieve wind speed utilizing proposed models and the matching method to compare in-situ wind speed from the National Centers for Environmental Prediction (NCEP) Climate Forecast System (CFS). By comparing the retrieval results, the proposed methods could obtain the accuracy with the same level of matching method.

Ionospheric Attenuation of Polarized Foregrounds in 21 cm Epoch of Reionization Measurements: A Demonstration for the HERA Experiment

Foregrounds with polarization states that are not smooth functions of frequency present a challenge to HI Epoch of Reionization (EoR) power spectrum measurements if they are not cleanly separated from the desired Stokes I signal. The intrinsic polarization impurity of an antenna's electromagnetic response limits the degree to which components of the polarization state on the sky can be separated from one another, leading to the possibility that this frequency structure could be confused for HI emission. We investigate the potential of Faraday rotation by the Earth's ionosphere to provide a mechanism for both mitigation of, and systematic tests for, this contamination. Specifically, we consider the delay power spectrum estimator, which relies on the expectation that foregrounds will be separated from the cosmological signal by a clearly demarcated boundary in Fourier space, and is being used by the Hydrogen Epoch of Reionization Array (HERA) experiment. Through simulations of visibility measurements which include the ionospheric Faraday rotation calculated from real historical ionospheric plasma density data, we find that the incoherent averaging of the polarization state over repeated observations of the sky may attenuate polarization leakage in the power spectrum by a factor of 10 or more. Additionally, this effect provides a way to test for the presence of polarized foreground contamination in the EoR power spectrum estimate.

Robust retrospective frequency and phase correction for single-voxel MR spectroscopy.

Subject motion and static field (B0 ) drift are known to reduce the quality of single voxel MR spectroscopy data due to incoherent averaging. Retrospective correction has previously been shown to improve data quality by adjusting the phase and frequency offset of each average to match a reference spectrum. In this work, a new method (RATS) is developed to be tolerant to large frequency shifts (>7Hz) and baseline instability resulting from inconsistent water suppression. In contrast to previous approaches, the variable-projection method and baseline fitting is incorporated into the correction procedure to improve robustness to fluctuating baseline signals and optimization instability. RATS is compared to an alternative method, based on time-domain spectral registration (TDSR), using simulated data to model frequency, phase, and baseline instability. In addition, a J-difference edited glutathione in-vivo dataset is processed using both approaches and compared. RATS offers improved accuracy and stability for large frequency shifts and unstable baselines. Reduced subtraction artifacts are demonstrated for glutathione edited MRS when using RATS, compared with uncorrected or TDSR corrected spectra. The RATS algorithm has been shown to provide accurate retrospective correction of SVS MRS data in the presence of large frequency shifts and baseline instability. The method is rapid, generic and therefore readily incorporated into MRS processing pipelines to improve lineshape, SNR, and aid quality assessment.

Revisiting the GNSS-R Waveform Statistics and Its Impact on Altimetric Retrievals

This paper analyzes the ocean altimetry precision of global navigation satellite systems’ reflectometry (GNSS-R) by characterizing the noise statistics of the measured waveform. For this purpose, we first investigate the dependence of the altimetry precision on the statistics of the observed waveform and then derive an analytical model of the waveform statistics after incoherent averaging. The main data set used for altimetry analysis and model validation is the GPS L5 signals obtained from an airborne experiment. Two different delay estimators, based on the leading-edge derivative (DER) and the waveform fitting (FIT) over the leading edge, have been implemented. Later, the relationship between the statistics of the observed waveform and the altimetry precision is derived and validated for both the estimators with the airborne data. Then, the analytical model of the statistics of the incoherently averaged waveform is built from the correlation properties of the complex waveform, and also validated with both airborne and the TechDemoSat-1 spaceborne data. After that, the proposed waveform statistics and altimetry precision models are applied to spaceborne cases with different orbit altitudes. The altimetry performance of different onboard processing methods, i.e., conventional GNSS-R and interferometric GNSS-R, and delay estimators, i.e., DER and FIT, are preliminarily assessed. Finally, the dependence of altimetry precision on different parameters is analyzed and a simplified model of altimetry precision is proposed for the spaceborne case.

Evaluation of the precision of different Delay-Doppler Processor (DDP) algorithms using CryoSat-2 data over open ocean

This article explores the modification and inclusion of different algorithms within an in-house Delay-Doppler Processor (DDP) chain in order to understand their potentiality and the related impact in terms of geophysical retrievals’ precision, when operating the synthetic aperture radar (SAR) mode of CryoSat-2 mission over open ocean. To do so, a flexible and tunable processing chain has been developed by isardSAT, being able to accommodate the different algorithms/options. Two different levels of analysis have been carried out. On one hand, the CryoSat-2 nominal SAR processing baseline is compared against the one considered in the state-of-the-art Sentinel-3 ocean topographic mission, and then, against a modified version of CS-2, where the samples set to zero by the processor on the stack are not included in the incoherent averaging. On the other, the integration of an advanced processing at stack level and based on the amplitude compensation and dilation compensation (ACDC) is evaluated within the CryoSat-2 DDP. A comparative study of the different DDP configurations is presented exploiting SAR full bit rate (FBR) data from CryoSat-2 over two regions in the central Pacific Ocean and the Agulhas box. Ad-hoc SAR ocean re-trackers are exploited to derive the geophysical parameters (sea surface height-SSH and significant wave height-SWH), such that the performance of the different baselines can be quantified in terms of precision, i.e., estimation noise.

Image processing for cryogenic transmission electron microscopy of symmetry-mismatched complexes.

Cryogenic transmission electron microscopy (cryo-TEM) is a high-resolution biological imaging method, whereby biological samples, such as purified proteins, macromolecular complexes, viral particles, organelles and cells, are embedded in vitreous ice preserving their native structures. Due to sensitivity of biological materials to the electron beam of the microscope, only relatively low electron doses can be applied during imaging. As a result, the signal arising from the structure of interest is overpowered by noise in the images. To increase the signal-to-noise ratio, different image processing-based strategies that aim at coherent averaging of signal have been devised. In such strategies, images are generally assumed to arise from multiple identical copies of the structure. Prior to averaging, the images must be grouped according to the view of the structure they represent and images representing the same view must be simultaneously aligned relatively to each other. For computational reconstruction of the 3D structure, images must contain different views of the original structure. Structures with multiple symmetry-related substructures are advantageous in averaging approaches because each image provides multiple views of the substructures. However, the symmetry assumption may be valid for only parts of the structure, leading to incoherent averaging of the other parts. Several image processing approaches have been adapted to tackle symmetry-mismatched substructures with increasing success. Such structures are ubiquitous in nature and further computational method development is needed to understanding their biological functions.

Sea Ice Detection Based on Differential Delay-Doppler Maps from UK TechDemoSat-1.

Global Navigation Satellite System (GNSS) signals can be exploited to remotely sense atmosphere and land and ocean surface to retrieve a range of geophysical parameters. This paper proposes two new methods, termed as power-summation of differential Delay-Doppler Maps (PS-D) and pixel-number of differential Delay-Doppler Maps (PN-D), to distinguish between sea ice and sea water using differential Delay-Doppler Maps (dDDMs). PS-D and PN-D make use of power-summation and pixel-number of dDDMs, respectively, to measure the degree of difference between two DDMs so as to determine the transition state (water-water, water-ice, ice-ice and ice-water) and hence ice and water are detected. Moreover, an adaptive incoherent averaging of DDMs is employed to improve the computational efficiency. A large number of DDMs recorded by UK TechDemoSat-1 (TDS-1) over the Arctic region are used to test the proposed sea ice detection methods. Through evaluating against ground-truth measurements from the Ocean Sea Ice SAF, the proposed PS-D and PN-D methods achieve a probability of detection of 99.72% and 99.69% respectively, while the probability of false detection is 0.28% and 0.31% respectively.

Envisat RA-2 Individual Echoes: A Unique Dataset for a Better Understanding of Inland Water Altimetry Potentialities

The exploitation of synthetic aperture properties in nadir-looking radars is opening new scenarios in the framework of satellite radar altimetry. Both recent and upcoming missions including Cryosat-2, Sentinel-3, Sentinel-6 and SWOT take benefit from the coherent processing of radar data, aimed at improving range measurements in particular contexts, such as ice, open ocean, coastal zone, and even inland waters. This work investigates the possibilities offered by current and future satellite radar altimetry missions for the study of inland water bodies, probing into the peculiarities of the expected radar returns and their potential usage. In this regard, signals collected by the RA-2 instrument (Radar Altimeter 2) onboard the Envisat mission offer an unprecedented possibility, even with a relatively low pulse repetition frequency, to analyze the peculiarities of actual signals for detecting and ranging small water surfaces. In particular, the RA-2 instrument offers a global archive of Individual Echoes (IEs), collected at the native sampling rate of 1795 Hz, in addition to the 18 Hz data obtained by incoherent averaging, which are typically delivered to the users as standard products. RA-2 shares with future radar platforms such as Sentinel-6 a continuous and interleaved working modality, as was recommended by the scientific community in designing next missions’ requirements. This is a further reason to consider the usage of RA-2 IEs as particularly attractive. Whilst only available for a small percentage of the earth’s surface, sufficient IE data exist to study the height retrieval capability of these echoes, in particular for what concerns small water bodies, where we show that enough coherence is exhibited for focusing relatively narrow surfaces and range them correctly. A peculiar aspect of this work lies in the assumption that most of the returned echoes (in RA-2 IEs) are specular. A theoretical framework is developed according to this assumption, which is validated by investigating real RA-2 data and observing their related specular features. In particular, we discuss how specular echoes are expected to be very common in inland altimetry, and are most often associated with small to medium size lakes and rivers. This paper illustrates the expected electromagnetic behavior of specular water targets by exploiting the classical radar cross-section (RCS) theory for specular surfaces. Results from the model are compared with real IE data in three selected case studies, regarding two rivers of variable width and one flood plain, in order to check different hydrological regimes. The model very closely matches the data in all cases, making the results of this validation activity very promising. In particular, we demonstrate the feasibility of using satellite radar altimetry in rivers much smaller than what was considered possible until now.

A Model-free CAF Fringe Search Algorithm with Wavelet Boosting for VLBI Observation

Very-Long-Baseline interferometry (VLBI) is a powerful tool in radio astronomy, geodesy, and deep space exploration. Priori predicted delay models are needed to make interferometry fringes, but in some cases they would be difficult to get. This paper proposes an effective algorithm named CAF-W algorithm to search fringes from the raw data in a large search range without priori predicted delay models. The cross-ambiguity function (CAF) is used to make a time-frequency correlation in the delay–delay rate plane. The wavelet boosting algorithm is used to eliminate interference and enhance the CAF peak, whose position would give the delay and delay rate estimations. Incoherent averaging and sliding search window techniques are used to overcome the wide search range and the poor signal-to-noise ratio in VLBI observations. The CAF-W algorithm could be performed with fast algorithms so the computation burden is affordable. This algorithm has successfully achieved VLBI fringes from the raw data without priori predicted delay models in VLBI observations.