Signal-to-noise Ratio Variation Research Articles

Normalized GNSS interference pattern technique for altimetry.

It is well known that reflected signals from Global Navigation Satellite Systems (GNSS) can be used for altimetry applications, such as monitoring of water levels and determining snow height. Due to the interference of these reflected signals and the motion of satellites in space, the signal-to-noise ratio (SNR) measured at the receiver slowly oscillates. The oscillation rate is proportional to the change in the propagation path difference between the direct and reflected signals, which depends on the satellite elevation angle. Assuming a known receiver position, it is possible to compute the distance between the antenna and the surface of reflection from the measured oscillation rate. This technique is usually known as the interference pattern technique (IPT). In this paper, we propose to normalize the measurements in order to derive an alternative model of the SNR variations. From this model, we define a maximum likelihood estimate of the antenna height that reduces the estimation time to a fraction of one period of the SNR variation. We also derive the Cramér–Rao lower bound for the IPT and use it to assess the sensitivity of different parameters to the estimation of the antenna height. Finally, we propose an experimental framework, and we use it to assess our approach with real GPS L1 C/A signals.

MO‐G‐18C‐09: Thermal Characterization and Initial Imaging Results From the Diffusive Quantitative Imaging Phantom (DQIP)

Purpose:The goals of this project were a) to characterize thermal relaxation of the phantom and b) to demonstrate correlations between temperature, signal‐to‐noise ratio (SNR) and diffusion tensor imaging (DTI) metrics. A site‐based clinical DTI protocol was used in this study. The hypothesis is that thermal stability of the phantom will be adequate such that temperature monitoring during a scan may be neglected.Methods:The Diffusive Quantitative Imaging Phantom (DQIP) is a prototype phantom consisting of fifteen cylindrical compartments containing capillary arrays, encased in a larger compartment. Thermal stability of the phantom was established using a cork container and a Peltier incubator. After the phantom was cooled or heated, thermal relaxation was measured as the phantom was allowed to return to room temperature, with and without cork. A clinical‐grade DTI protocol was used to collect scan and temperaturedependent data from the phantom over ten days. SNR and thermal dependences of fractional anisotropy (FA) and apparent diffusion coefficient (ADC) were characterized by scanning a heated or cooled phantom over several hours.Results:The phantom temperature was stable within ±0.08°C/hour per degree difference from the scan room using the cork enclosure, compared to ±0.3°C/hour per degree difference without the cork enclosure. During scanning, temperature variation was ∼ 0.1°C/hour. The dependences of (FA, ADC) on (SNR, temperature) were characterized for the heating and cooling experiments. However, for the range of temperature (1.2°C) and SNR (max: ±77%) variations in a particular compartment over all daily measurements, no significant improvement in total variation was achieved after regressing out temperature and SNR, although one compartment showed significant decline after regression.Conclusion:Thermal stability of the DQIP phantom and incubator system is sufficient for neglecting temperature variations during scanning. For a standard clinical protocol, SNR dependence of FA and ADC are not sufficient to warrant correction.Schott Glass North America and The Phantom Laboratory have donated materials and personnel time to this project.

Quiet time short‐period and day‐to‐day variations in E × B drift studied using 150 km radar echoes from Gadanki

AbstractIn this paper we present short‐period and day‐to‐day variations in E × B drift during low solar and magnetically quiet conditions, based on radar observations of daytime 150 km echoes from Gadanki, India. Short‐period (<100 min) variations in E × B drift show amplitude as large as 7 m s−1 and display large day‐to‐day variation. Spectral analysis reveals that drift velocity fluctuations consist of several components of short periods in the range of 4–100 min. Among these periods, the most frequently occurring periods are 6–60 min. Observations also show that amplitudes of these periods increase with increasing period. Interestingly, signal‐to‐noise ratio (SNR) variations also show periods of 3–19 min, which have also been observed in velocity variations. In addition, amplitudes of the periodic variations in SNR tend to increase with increasing period, which is also similar to those observed in drift velocity fluctuations. No correlation between SNR and velocity variations, however, has been found. Noticeable day‐to‐day variations in drift velocity are found in all seasons, and the variation is as large as ±25 m s−1. Day‐to‐day variations also show wave‐like features with period of 2–4 days. Observed E × B drift variations of 7 m s−1 at short time scale and 25 m s−1 on a day‐to‐day basis indicate zonal electric field variations of 0.25 mV/m and 0.9 mV/m, respectively. We surmise that quiet time E × B drift variations with periods <100 min and 2–4 days are likely to be the manifestations of gravity wave and planetary wave wind‐induced electric fields, respectively, consistent with those reported earlier.

Sea level time series and ocean tide analysis from multipath signals at five GPS sites in different parts of the world

We present sea level observations derived from the analysis of signal-to-noise ratio (SNR) data recorded by five coastal GPS stations. These stations are located in different regions around the world, both in the northern and in the southern hemisphere, in different multipath environments, from rural coastal areas to busy harbors, and experience different tidal ranges.The recorded SNR data show periodic variations that originate from multipath, i.e. the interference of direct and reflected signals. The general assumption is that for satellite arcs facing the open sea, the rapid SNR variations are due to reflections off the sea surface. The SNR data recorded from these azimuth intervals were analyzed by spectral analysis with two methods: a standard analysis method assuming a static sea level during a satellite arc and an extended analysis method assuming a time dependent sea level during a satellite arc.The GPS-derived sea level results are compared to sea level records from co-located traditional tide gauges, both in the time and in the frequency domain. The sea level time series are highly correlated with correlation coefficients to the order of 0.89–0.99. The root-mean-square (RMS) difference is 6.2cm for the station with the lowest tidal range of 165cm and 43cm for the station with the highest tidal range of 772cm. The relative accuracy, defined as the ratio of RMS and tidal range, is between 2.4% and 10.0% for all stations.Comparing the standard analysis method and the extended analysis method, the results based on the extended analysis method agree better with the independent tide gauge records for the stations with a high tidal range. For the station with the highest tidal range (772cm), the RMS is reduced by 47% when using the extended analysis method. Furthermore, the results also indicate that the standard analysis method, assuming a static sea level, can be used for stations with a tidal range of up to about 270cm, without performing significantly worse than the extended analysis method.Tidal amplitudes and phases are derived by harmonic analysis of the sea level records. Again, a high level of agreement is observed between the tide gauge and the GPS-derived results. Comparing the GPS-derived results, the results based on the extended analysis method show a higher degree of agreement with the traditional tide gauge results for stations with larger tidal ranges. Spectral analysis of the residuals after the harmonic analysis reveals remaining signal power at multiples of the draconitic day. This indicates that the observed SNR data are to some level disturbed by additional multipath signals, in particular for GPS stations that are located in harbors.

Zero Delay Joint Source Channel Coding for Multivariate Gaussian Sources over Orthogonal Gaussian Channels

Communication of a multivariate Gaussian source transmitted over orthogonal additive white Gaussian noise channels using delay-free joint source channel codes (JSCC) is studied in this paper. Two scenarios are considered: (1) all components of the multivariate Gaussian are transmitted by one encoder as a vector or several ideally collaborating nodes in a network; (2) the multivariate Gaussian is transmitted through distributed nodes in a sensor network. In both scenarios, the goal is to recover all components of the multivariate Gaussian at the receiver. The paper investigates a subset of JSCC consisting of direct source-to-channel mappings that operate on a symbol-by-symbol basis to ensure zero coding delay. A theoretical analysis that helps explain and quantify distortion behavior for such JSCC is given. Relevant performance bounds for the network are also derived with no constraints on complexity and delay. Optimal linear schemes for both scenarios are presented. Results for Scenario 1 show that linear mappings perform well, except when correlation is high. In Scenario 2, linear mappings provide no gain from correlation when the channel signal-to-noise ratio (SNR) gets large. The gap to the performance upper bound is large for both scenarios, regardless of SNR, when the correlation is high. The main contribution of this paper is the investigation of nonlinear mappings for both scenarios. It is shown that nonlinear mappings can provide substantial gain compared to optimal linear schemes when correlation is high. Contrary to linear mappings for Scenario 2, carefully chosen nonlinear mappings provide a gain for all SNR, as long as the correlation is close to one. Both linear and nonlinear mappings are robust against variations in SNR.

Signal-to-noise ratio of the spatially modulated imaging spectrometer based on modified Sagnac interferometer

The basic principle of the spatially modulated imaging spectrometer, based on modified Sagnac interferometer, is outlined. According to radiometry, electromagnetism and Fourier transform spectroscopy, the radiation flux received by each pixel of the detector is calculated, and then the exact expression of the signal-to-noise ratio (SNR), at a distance x away from the zero-order fringe, is given. To analyze and discuss the effects of various parameters on SNR, the computer simulation is carried out, and some important conclusions are obtained. Using the root mean square method, the SNR variations of the whole optical system, changing with Sagnac interferometer acute angles β1 and β2, are simulated, and the condition β1=β2 can make the system SNR higher and more stable. This work can provide theoretical basis and practical guidance for improving the spatially modulated imaging spectrometer’s SNR together with its engineering realization.

Influence of the antiscatter grid on dose and image quality in pediatric interventional cardiology X‐ray systems

To present a methodology and experimental results to assess the influence, in terms of dose and image quality, of the antiscatter grid (AG) in a pediatric cardiology X-ray system. Entrance surface air kerma and image quality, using a test object and different added thicknesses of polymethyl methacrylate (PMMA), for three different acquisition protocols, were measured with and without the AG, for fluoroscopy and cine modes. The image quality parameters, signal-to-noise ratio (SNR), high-contrast spatial resolution (HCSR) and two figures of merit (FOM) were evaluated. The average bucky factor values measured during this experiment were 1.99, 2.49, 2.85, and 3.30, respectively for 4, 8, 12, and 16 cm of PMMA. SNR variations do not appear to be relevant when removing the AG. However, the use of AG improves HCSR significantly. Imaging the test object with 4 cm of PMMA seems appropriate without the AG, but for 8 cm (equivalent to chest thicknesses of 12 cm) and greater thicknesses, a good image quality would require the use of AG. The AG should not be used for neonates and very young children with chest thicknesses equal to or less than 6 cm and weight less that 6 kg.

T1 and extracellular volume mapping in the heart: estimation of error maps and the influence of noise on precision.

BackgroundQuantitative measurements in the myocardium may be used to detect both focal and diffuse disease processes that result in an elevation of T1 and/or extracellular volume (ECV) fraction. Detection of abnormal myocardial tissue by these methods is affected by both the accuracy and precision. The sensitivity for detecting abnormal elevation of T1 and ECV is limited by the precision of T1 estimates which is a function of the number and timing of measurements along the T1-inversion recovery curve, the signal-to-noise ratio (SNR), the tissue T1, and the method of fitting.MethodsThe standard deviation (SD) of T1 and ECV estimates are formulated and SD maps are calculated on a pixel-wise basis using the Modified Look-Locker Inversion recovery (MOLLI) method. SD estimates are validated by numerical simulation using Monte-Carlo analysis and with phantoms using repeated trials. SD estimates are provided for pre- and post-contrast optimized protocols for a range of T1s and SNRs. In-vivo examples are provide for normal, myocarditis, and HCM in human subjects. The formulation of SD maps was extended to R1 and ECV.ResultsThe measured myocardial SNR ranged from 23 to 43 across the heart using the specific T1-mapping protocol in this study. In this range of SNRs, the estimated SD for T1 was approximately 20-45 ms for pre-contrast myocardial T1 around 1000 ms, and was approximately 10-20 ms for post contrast T1 around 400 ms. The proposed estimate of SD was an unbiased estimate of the standard deviation of T1 validated by numerical simulation and had > 99% correlation with phantom measurements. The measured SD maps exhibited variation across the heart due to drop off in surface coil sensitivity as expected for the variation in SNR. Focal elevation in T1 and ECV was shown to have statistical significance on a pixel-wise basis for in-vivo examples.ConclusionsPixel-wise estimates of T1 mapping errors have been formulated and validated, and the formulation has been extended to ECV. The ability to quantify the measurement error has potential to determine the statistical significance of subtle abnormalities that arise due to diffuse disease processes involving fibrosis and/or edema and is useful both as a confidence metric for overall quality, and in optimization and comparison of imaging protocols.

Multichannel Two-Stage Beamforming with Unconstrained Beamformer and Distortion Reduction

This paper proposes a novel multichannel speech enhancement technique for reverberant rooms that is effective when noise sources are spatially stationary, such as a projector fan noise, an air-conditioner noise, and unwanted speech sources at the back of microphones. Speech enhancement performance of the conventional multichannel Wiener filter (MWF) degrades when the Signal-to-Noise Ratio (SNR) of the current microphone input signal changes from the noise-only period. Furthermore, the MWF structure is computationally inefficient, because the MWF updates the whole spatial beamformer periodically to track switching of the speakers (e.g. turn-taking). In contrast to the MWF, the proposed method reduces noise independently of the SNR. The proposed method has a novel two-stage structure, which reduces noise and distortion of the desired source signal in a cascade manner by using two different beamformers. The first beamformer focuses on noise reduction without any constraint on the desired source, which is insensitive to SNR variation. However, the output signal after the first beamformer is distorted. The second beamformer focuses on distortion reduction of the desired source signal. Theoretically, complete elimination of distortion is assured. Additionally, the proposed method has a computationally efficient structure optimized for spatially stationary noise reduction problems. The first beamformer is updated only when the speech enhancement system is initialized. Only the second beamformer is updated periodically to track switching of the active speaker. The experimental results indicate that the proposed method can reduce spatially stationary noise source signals effectively with less distortion of the desired source signal even in a reverberant conference room.

An Adaptive Algorithm for the Determination of the Onset and Offset of Muscle Contraction by EMG Signal Processing

Estimation of on-off timing of human skeletal muscles during movement is an ongoing issue in surface electromyography (sEMG) signal processing for relevant clinical applications. Widely used single threshold methods still rely on the experience of the operator to manually establish a threshold level. In this paper, a novel approach to address this issue is presented. Based on the generalized likelihood ratio test, the maximum likelihood (ML) method is improved with an adaptive threshold technique based on the signal-to-noise ratio (SNR) estimate in the initial time before accurate sEMG analyses. The dependence of optimal threshold on SNR is determined by minimizing the onset/offset estimate error on a large set of simulated signals with well-known signal parameters. Accuracy and precision of the algorithm were assessed by using a set of simulated signals and real sEMG signals recorded from two healthy subjects during elbow flexion-extension movements with and without workload. Comparison with traditional algorithms shows that with a moderate increase in the computational effort the ML algorithm performs well even for low levels of EMG activity, while the proposed adaptive method is most robust with respect to variations in SNRs. Also, we discuss the results of analyzing the sEMG recordings from the selected proximal muscles of the upper limb in two hemiparetic subjects. The detection algorithm is automatic and user-independent, managing the detection of both onset and offset activation, and is applicable in presence of noise allowing use by skilled and unskilled operators alike.

Selective excitation of two‐dimensional arbitrarily shaped voxels with parallel excitation in spectroscopy

Parallel excitation is being studied intensively for applications in MR imaging and in particular for selecting arbitrary shapes as regions of interest. In this work, parallel excitation was applied to arbitrarily shaped voxel selection in spectroscopy and investigated for different excitation k-space trajectories (radial, rectilinear, and spiral) and acceleration factors. Each trajectory was segmented into multiple excitations to increase the overall bandwidth during target selection. Acceleration by parallel excitation was used to decrease the number of segments. Evaluation of spatial and spectral localization of the target of interest was performed in simulation and phantom experiments, and was compared with the point resolved spectroscopy (PRESS) experiment with standard voxels. The selective excitation experiments demonstrated excellent spatial localization and a broad frequency response, although PRESS was superior in direct comparisons with respect to signal-to-noise ratio (SNR) and outer volume suppression. Extensive SNR variation was observed dependent on trajectory (8%-90%), with the preferred radial case producing approximately 40%-60% SNR of the PRESS case. Accelerated trajectories at R = 4 provided comparable artifact signal and target excitation accuracy compared with their nonaccelerated counterparts; however, further acceleration (R = 8) resulted in increased artifact (33% increase at R = 8).

Reducing the effects of noise on atmospheric imaging radars using multilag correlation

[1] Atmospheric imaging radars offer the capability to scrutinize structures within the illuminated volume at high temporal and spatial resolutions. The retrieval of the mean signal power using an imaging radar is obtained by subtracting the noise power from the covariance function at lag zero. The results obtained at low signal-to-noise ratio (SNR) are problematic when the noise power is unsuccessfully estimated, and are difficult to interpret when adaptive weights are used because of the temporally varying noise power. In this paper, a processing technique that improves the retrieval of the mean signal power by exploiting the temporal correlation difference between the desired signal and system noise is presented. Simulations of its performance are presented for the special case of a Gaussian received spectrum for variations in SNR, normalized spectrum width, and number of time series samples. The technique is also applied to real data collected with the Turbulent Eddy Profiler, a vertically pointing phased array radar developed at the University of Massachusetts, between 1435 and 1457 UTC 15 June 2003. Even though the performance of this technique in terms of its variance and bias depends on the SNR, spectrum width, and number of time series samples, results from both simulations and real data are promising as an enhanced mean signal power in the low SNR regions is obtained.

MRI‐phased array evaluation using a human body model

AbstractWe develop methodology to evaluate MRI‐phased array receivers using an anatomically and electromagnetically accurate human body model. The human body model accurately represents the different permittivity and conductivity values of various tissue types in the human body, at the frequency of interest. The phased array receiver is a posterior array with 16 coils, typically placed on the patient table for imaging. We obtain the electric and magnetic fields associated with each coil using the finite‐difference time‐domain method and estimate a simplified metric to evaluate the receiver array contribution to the signal‐to‐noise ratio (SNR) distribution. The results highlight SNR variation in the left–right direction, an artifact seen in imaging, but not apparent in quasi‐static simulations with uniform phantoms. We use the results to compare two design variations of 16‐coil phased arrays. In addition, we use the results to compare imaging methods that have potential to reduce the computational complexity of high channel count arrays by reducing the number of data streams used in image reconstruction. © 2010 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 37B: 20–28, 2010

The range of signal‐to‐noise ratios needed to equalize identification of different consonants.

Individual consonants vary in intelligibility when speech is presented in constant‐intensity speech‐spectrum noise. This variation in consonant intelligibility is explained at various levels, ranging from bottom‐up energetic masking of different‐intensity auditory cues needed to identify different consonants, to the top‐down use of context information. This study focuses on bottom‐up auditory cues by measuring the differences in signal‐to‐noise ratio (SNR) needed to equate consonant identification in consonant‐vowel‐consonant (CVC) syllables. The goal is to develop a CVC test with high sensitivity to changes in consonant perception because each consonant is presented at SNRs above the perceptual floor and below the perceptual ceiling. In order to present the initial and final consonants of each CVC at independently controlled SNRs, the intensity of the noise was changed during 100 ms centered in the vowel. In 16 young normal‐hearing listeners, the SNR range required to equate identification across the 20 leading and trailing consonants was greater than 40 dB. In spite of these large SNR variations occurring during the test (and sometimes even within a single CVC) the expected pattern of consonant confusions was obtained, suggesting that the mid‐vowel adjustment of noise intensity did not interfere with normal consonant‐perception processes.

Cardiac cine MRI: Comparison of 1.5 T, non-enhanced 3.0 T and blood pool enhanced 3.0 T imaging

Introduction Cardiac cine imaging using balanced steady state free precession sequences (bSSFP) suffers from artefacts at 3.0 T. We compared bSSFP cardiac cine imaging at 1.5 T with gradient echo imaging at 3.0 T with and without a blood pool contrast agent. Materials and methods Eleven patients referred for cardiac cine imaging underwent imaging at 1.5 T and 3.0 T. At 3.0 T images were acquired before and after administration of 0.03 mmol/kg gadofosveset. Blood pool signal-to-noise ratio (SNR), temporal variations in SNR, ejection fraction and myocardial mass were compared. Subjective image quality was scored on a four-point scale. Results Blood pool SNR increased with more than 75% at 3.0 T compared to 1.5 T ( p < 0.001); after contrast administration at 3.0 T SNR increased with 139% ( p < 0.001). However, variations in blood pool SNR at 3.0 T were nearly three times as high versus those at 1.5 T in the absence of contrast medium ( p < 0.001); after contrast administration this was reduced to approximately a factor 1.4 ( p = 0.21). Saturation artefacts led to significant overestimation of ejection fraction in the absence of contrast administration (1.5 T: 44.7 ± 3.1 vs. 3.0 T: 50.7 ± 4.2 [ p = 0.04] vs. 3.0 T post contrast: 43.4 ± 2.9 [ p = 0.55]). Subjective image quality was highest for 1.5 T (2.8 ± 0.3), and lowest for non-enhanced 3.0 T (1.7 ± 0.6; p = 0.006). Conclusions GRE cardiac cine imaging at 3.0 T after injection of the blood pool agent gadofosveset leads to improved objective and subjective cardiac cine image quality at 3.0 T and to the same conclusions regarding cardiac ejection fraction compared to bSSFP imaging at 1.5 T.

Symbolic Statistical Analysis of SNR Variation for Delta&amp;#x2013;Sigma Modulators

Traditional methods for statistical analysis of delta-sigma modulators are based on Monte Carlo analysis to iteratively change the design parameters and evaluate the histogram of signal-to-noise ratio (SNR). But Monte Carlo analysis is time-consuming, especially when a number of candidate designs need to be considered. In this brief, a systematic symbolic formulation of statistical SNR variation is made so that variations of capacitors are directly translated to SNR variation. In addition, the symbolic formulation is derived from a generic modulator topology, so that the derived symbolic formulation is applicable to any topology that is covered by the generic topology. Experiments have shown the symbolic formulation can provide fast and reasonably accurate estimation of statistical SNR variation, especially for high-order modulators.

Stochastic resonance of amplitude modulation wave in single-mode laser driven by color noises

By adding modulation wave to the equation of the laser intensity in the gain-noise model of the single-mode laser, we use the linear approximation method to calculate the power spectrum and signal-to-noise ratio(SNR) of the laser intensity, which is driven by two color noises correlated in the form of exponential function. The result shows that the correlated time and the correlated strength between the noises have great effect on the stochastic resonance(SR), and the variations of SNR with the frequency of the carrier signal ω and the modulator signal Ω are quite different from the curve of variation of white noise.

Dose–image quality optimisation in digital chest radiography

A range of techniques has been developed in conventional radiography for the chest, because of technical difficulties in imaging the wide variation of tissue densities. These techniques can differ significantly in tube potential selection, for scatter reduction and in application of manual or automatic exposure control. In this study a geometric chest phantom designed to simulate a chest image, has been used to study image quality on an indirect digital radiography (DR) system. Relative values for the signal-to-noise ratio (SNR), have been derived from analysis of contrast detail objects within the lung, heart and subdiaphragm regions of the phantom. Results showing the variation in SNR and detail perception with tube potential are presented for three radiographic techniques: using a grid, an air gap and no scatter reduction. SNR measurements provided a useful objective measure for assessment of image quality for optimising DR systems.

Optical heterodyne detection of random electromagnetic beams

Abstract In this paper we present a general analysis for the optical heterodyne detection of random electromagnetic beams. To describe the ensemble of quasimonochromatic beams which are partially polarized and partially coherent, we use a recently developed matrix treatment. We derive an expression for the signal-to-noise ratio (SNR) in terms of the beam coherence polarization matrices of the beams on the detector surface. Numerical examples are given for the SNR variation in the case of partially polarized Gaussian Schell model beams and the optimum detection is discussed in terms of beam parameters of the local oscillator.

Optical heterodyne detection of random electromagnetic beams

In this paper we present a general analysis for the optical heterodyne detection of random electromagnetic beams. To describe the ensemble of quasimonochromatic beams which are partially polarized and partially coherent, we use a recently developed matrix treatment. We derive an expression for the signal-to-noise ratio (SNR) in terms of the beam coherence polarization matrices of the beams on the detector surface. Numerical examples are given for the SNR variation in the case of partially polarized Gaussian Schell model beams and the optimum detection is discussed in terms of beam parameters of the local oscillator.