Using Pearson’s System of Curves to Approximate the Distributions of the Difference between Two Correlated Estimates of Signal-to-Noise Ratios: The Cases of Bivariate Normal and Bivariate Lognormal Distributions

Background: The signal-to-noise ratio (SNR) is recognized as an index of measurements reproducibility. We derive the maximum likelihood estimators of SNR and discuss confidence interval construction on the difference between two correlated SNRs when the readings are from bivariate normal and bivariate lognormal distribution. We use the Pearsons system of curves to approximate the difference between the two estimates and use the bootstrap methods to validate the approximate distributions of the statistic of interest. Methods: The paper uses the delta method to find the first four central moments, and hence the skewness and kurtosis which are important in the determination of the parameters of the Pearsons distribution. Results: The approach is illustrated in two examples;one from veterinary microbiology and food safety data and the other on data from clinical medicine. We derived the four central moments of the target statistics, together with the bootstrap method to evaluate the parameters of Pearsons distribution. The fitted Pearsons curves of Types I and II were recommended based on the available data. The R-codes are also provided to be readily used by the readers.

Acquisition Practice of High Signal-to-Noise Ratio in YTB Block of Sichuan Basin

YTB block in Sichuan basin is a favorable area to exploit oil and gas in shallow tight rock. 3D seismic project of this zone has two characteristics. Firstly, it has high requirements for the tolerance rate of the construction process and the acquisition of high signal-to-noise ratio seismic data;Second, there are widely obstacles and noises that lead to difficult acquisition construction organization. In acquisition practice, high signal-to-noise ratio seismic data was obtained by reasonable design of construction scheme, optimization of excitation parameters, improvement of receiving conditions and optimization of obstacle crossing observation system. .

Effective DOA Estimation Under Low Signal-to-Noise Ratio Based on Multi-Source Information Meta Fusion

Efficiently performing high-resolution direction of arrival(DOA)estimation under low signal-to-noise ratio(SNR)conditions has always been a challenge task in the literatures.Obvi-ously,in order to address this problem,the key is how to mine or reveal as much DOA related in-formation as possible from the degraded array outputs.However,it is certain that there is no per-fect solution for low SNR DOA estimation designed in the way of winner-takes-all.Therefore,this paper proposes to explore in depth the complementary DOA related information that exists in spa-tial spectrums acquired by different basic DOA estimators.Specifically,these basic spatial spec-trums are employed as the input of multi-source information fusion model.And the multi-source in-formation fusion model is composed of three heterogeneous meta learning machines,namely neural networks(NN),support vector machine(SVM),and random forests(RF).The final meta-spec-trum can be obtained by performing a final decision-making method.Experimental results illus-trate that the proposed information fusion based DOA estimation method can really make full use of the complementary information in the spatial spectrums obtained by different basic DOA estim-ators.Even under low SNR conditions,promising DOA estimation performance can be achieved.

An innovative detection method of high frequency BPSK signal with low signal-to-noise ratio

Based on chaotic oscillator system, this paper proposes a novel method on high frequency low signal- to-noise ratio BPSK（ Binary Phase Shift Keying） signal detection. Chaotic oscillator system is a typical non-lin- ear system which is sensitive to periodic signals and immune to noise at the same time. Those properties make it possible to detect low signal-to-noise ratio signals. The BPSK signal is a common signal type which is widely used in modern communication. Starting from the analysis of advantages of chaotic, os~.illator system and signal features of the BPSK signal, we put forward a unique method that can detect low signar-to-noise ratio BPSK sig- nals with high frequency. The simulation results show that the novel method can dclct.t low signal-to-noise ratio BPSK signals with frequency in an order of magnitude of l0s Hz, and the input Signal-to-Noise Ratio threshold can be -20 dB.

Signal-to-noise ratio of lensless ghost interference with thermal incoherent light

Factors influencing the signal-to-noise ratio （SNR） of lensless ghost interference with thermal incoherent light are investigated. Our result shows that the SNR of lensless ghost interference is related to the transverse length of the object, the position of the object in the imaging system and the transverse size of the light source. Furthermore, the effects of these factors on the SNR are discussed in detail by numerical simulations.

Noises and Signal-to-Noise Ratio of Nanosize EIS and ISFET Biosensors

The results of comparative theoretical analyzes of the behavior of internal low-frequency noises, signal-to-noise ratio and sensitivity to DNA molecules for EIS and ISFET based nanosize biosensors are presented. It is shown that EIS biosensor is more sensitive to the presence of DNA molecules in aqueous solution than ISFET sensor. Internal electrical noises level decreases with the increase of concentration of DNA molecules in aqueous solution. In the frequency range 10−3 - 103 Hz noises level for EIS sensor about in three orders is higher than for ISFET sensor. In the other hand, signal-to-noise ratio for capacitive EIS biosensor is much higher than for ISFET sensor.

Influence of signal-to-noise ratio on accuracy of spectral analysis by near infrared spectroscopy

As one of the important indicators of spectrometer,signal-to-noise ratio(SNR)reflects the ability of spectrometer to detect weak signals.To investigate the influence of SNR on the prediction accuracy of spectral analysis,we first introduce the major factors affecting the spectral SNR.Taking green tea as an example,the influence of spectral SNR on the prediction accuracy of the origin identification model is analyzed by experiments.At the same time,the relationship between the spectral SNR and prediction accuracy of spectral analysis model is fitted.Based on this,the common methods for improving the spectral SNR are discussed.The results show that the accuracy of the prediction set model first decreases slowly,then decreases linearly,and finally tends to be flat as the spectral SNR decreases.Through calculation,in order to achieve the prediction accuracy of prediction model reaching 90%and 85%,the spectral SNR is required to be higher than 23.42 dB and 21.16 dB,respectively.The overall results provide certain parameters support for the development of new online analytical spectroscopic instruments,especially for the technical indicators of SNR.

Enhancement of signal-to-noise ratio of ultracold polar NaCs molecular spectra by phase locking detection

We report a method of high-sensitively detecting the weak signal in photoassociation （PA） spectra of ultracold NaCs molecules by phase sensitive-demodulated trap-loss spectra of Na atoms from a photomultiplier tube. We find that the signal-to-noise ratio （SNR） of the PA spectra is strongly dependent on the integration time and the sensitivity of the lock-in amplifier, and our results show reasonable agreement with the theoretical analyses of the SNR with the demodulation parameters. Meanwhile, we investigate the effect of the interaction time of the PA laser with the colliding Na-Cs atom pairs on the SNR of the PA spectra. The atom loss rate is dependent on both the PA-induced atom loss and the loading of the MOT. The high-sensitive detection of the excited ultracold NaCs molecules lays a solid foundation for further study of the formation and application of ultracold NaCs molecules.

Signal-to-noise ratio of Raman signal measured by multichannel detectors

Raman spectroscopy has been widely used to characterize the physical properties of two-dimensional materials(2DMs).The signal-to-noise ratio(SNR or S/N ratio)of Raman signal usually serves as an important indicator to evaluate the instrumental performance rather than Raman intensity itself.Multichannel detectors with outstanding sensitivity,rapid acquisition speed and low noise level have been widely equipped in Raman instruments for the measurement of Raman signal.In this mini-review,we first introduce the recent advances of Raman spectroscopy of 2DMs.Then we take the most commonly used CCD detector and IGA array detector as examples to overview the various noise sources in Raman measurements and analyze their potential influences on SNR of Raman signal in experiments.This overview can contribute to a better understanding on the SNR of Raman signal and the performance of multichannel detector for numerous researchers and instrumental design for industry,as well as offer practical strategies for improving spectral quality in routine measurement.

Calculation method of the signal-to-noise ratio attribute of seismic data based on structural orientation

At present,most signal-to-noise ratio(SNR)estimation methods can only calculate the global and not the local SNR of seismic data.This paper proposes a calculation method of a structure-oriented-based seismic SNR attribute.The purpose is to characterize the temporal and spatial variation of the seismic data SNR.First,the local slope parameters of the seismic events are calculated using a plane wave decomposition filter.Then,the singular value decomposition method is used to calculate the local seismic data SNR,thereby obtaining it in time and space.The proposed method overcomes the insufficiency of a conventional global SNR to characterize any local seismic data features and uses the SNR as an attribute of seismic data to more accurately describe the signal-noise energy distribution characteristics of seismic data in time and space.The results of a theoretical model test and real data processing show that the SNR attribute can be used not only for seismic data quality evaluation but also for analysis and evaluation of denoising methods.

Signal-to-noise ratio comparison of angular signal radiography and phase stepping method

Grating-based x-ray phase contrast imaging has the potential to be applied in future medical applications as it is compatible with both laboratory and synchrotron source. However, information retrieval methods are important because acquisition speed, scanning mode, image quality, and radiation dose depend on them. Phase-stepping （PS） is a widely used method to retrieve information, while angular signal radiography （ASR） is a newly established method. In this manuscript, signal-to-noise ratios （SNRs） of ASR are compared with that of PS. Numerical experiments are performed to validate theoretical results. SNRs comparison shows that for refraction and scattering images ASR has higher SNR than PS method, while for absorption image both methods have same SNR. Therefore, our conclusions would have guideline in future preclinical and clinical applications.

Local Correlated Noise Improvement of Signal-to-Noise Ratio Gain in an Ensemble of Noisy Neuron

We theoretically investigate the collective response of an ensemble of leaky integrate-and-fire neuron units to a noisy periodic signal by including local spatially correlated noise. By using the linear response theory, we obtained the analytic expression of signal-to-noise ratio (SNR). Numerical simulation results show that the rms amplitude of internal noise can be increased up to?an optimal value where the output SNR reaches a maximum value. Due to the existence of the local spatially correlated noise in the units of the ensemble, the SNR gain of the collective ensemble response can exceed unity and can be optimized when the nearest-neighborhood correlation is negative. This nonlinear collective phenomenon of SNR gain amplification in an ensemble of leaky integrate-and-fire neuron units can be related to the array stochastic resonance (SR) phenomenon. Furthermore, we also show that the SNR gain can also be optimized by tuning the number of neuron units, frequency and?amplitude of the weak periodic signal. The present study illustrates the potential to utilize the local spatially correlation noise and the number of ensemble units for optimizing the collective response of the neuron to inputs, as well as a guidance in the design of information processing devices to weak signal detection.

ONE-WAY MULTIVARIATE REPEATED MEASUREMENTS ANALYSIS OF VARIANCE MODEL

The one-way multivariate repeated measurements analysis of variance (1-way MRM ANOVA) model for complete data and the sphericity test are studied.

Effect of signal-to-noise ratio on the automatic clustering of X-ray diffraction patterns from combinatorial libraries

Hierarchical clustering algorithm has been applied to identify the X-ray diffraction(XRD)patterns from a high-throughput characterization of the combinatorial materials chips.As data quality is usually correlated with acquisition time,it is important to study the hierarchical clustering performance as a function of data quality in order to optimize the efficiency of high-throughput experiments.This work investigated the effects of signal-to-noise ratio on the performance of hier-archical clustering using 29 distance metrics for the XRD patterns from Fe−Co−Ni ternary combinatorial materials chip.It is found that the clustering accuracies evaluated by the F1 score only fluctuate slightly with signal-to-noise ratio varying from 15.5 to 22.3(dB)under the experimental condition.This suggests that although it may take 40-50 s to collect a visually high-quality diffraction pattern,the measurement time could be significantly reduced to as low as 4 s without substantial loss in phase identification accuracy by hierarchical clustering.Among the 29 distance metrics,Pearsonχ^(2)shows the highest mean F1 score of 0.77 and lowest standard deviation of 0.008.It shows that the distance matrixes calculated by Pearsonχ^(2)are mainly controlled by the XRD peak shifting characteristics and visualized by the metric multidimensional data scaling.

SUBSPACE-BASED NOISE VARIANCE AND SNR ESTIMATION FOR MIMO OFDM SYSTEMS

This paper proposes a subspace-based noise variance and Signal-to-Noise Ratio (SNR) estimation algorithm for Multi-Input Multi-Output (MIMO) wireless Orthogonal Frequency Division Multiplexing (OFDM) systems. The special training sequences with the property of orthogonality and phase shift orthogonality are used in pilot tones to obtain the estimated channel correlation matrix. Partitioning the observation space into a delay subspace and a noise subspace, we achieve the measurement of noise variance and SNR. Simulation results show that the proposed estimator can obtain accurate and real-time measurements of the noise variance and SNR for various multipath fading channels, demonstrating its strong robustness against different channels.

Mixed Noise Parameter Estimation Based on Variance Stable Transform

The ultimate goal of image denoising from video is to improve the given image,which can reduce noise interference to ensure image quality.Through denoising technology,image quality can have effectively optimized,signal-to-noise ratio can have increased,and the original mage information can have better reflected.As an important preprocessing method,people have made extensive research on image denoising algorithm.Video denoising needs to take into account the various level of noise.Therefore,the estimation of noise parameters is particularly important.This paper presents a noise estimation method based on variance stability transformation,which estimates the parameters of variance stability transformation by minimizing the noise distribution peak,and improves the parameter accuracy of mixed peak estimation by comparing and analyzing the changes of parameters.The experimental results show that the new algorithm of noise estimation has achieved good effects,which are making the field of video denoising more extensive.

Evaluation of Third-Order Method for the Tests of Variance Component in Linear Mixed Models

Mixed models provide a wide range of applications including hierarchical modeling and longitudinal studies. The tests of variance component in mixed models have long been a methodological challenge because of its boundary conditions. It is well documented in literature that the traditional first-order methods: likelihood ratio statistic, Wald statistic and score statistic, provide an excessively conservative approximation to the null distribution. However, the magnitude of the conservativeness has not been thoroughly explored. In this paper, we propose a likelihood-based third-order method to the mixed models for testing the null hypothesis of zero and non-zero variance component. The proposed method dramatically improved the accuracy of the tests. Extensive simulations were carried out to demonstrate the accuracy of the proposed method in comparison with the standard first-order methods. The results show the conservativeness of the first order methods and the accuracy of the proposed method in approximating the p-values and confidence intervals even when the sample size is small.

Estimation of Population Variance Using the Coefficient of Kurtosis and Median of an Auxiliary Variable under Simple Random Sampling

In this study we have proposed a modified ratio type estimator for population variance of the study variable y under simple random sampling without replacement making use of coefficient of kurtosis and median of an auxiliary variable x. The estimator’s properties have been derived up to first order of Taylor’s series expansion. The efficiency conditions derived theoretically under which the proposed estimator performs better than existing estimators. Empirical studies have been done using real populations to demonstrate the performance of the developed estimator in comparison with the existing estimators. The proposed estimator as illustrated by the empirical studies performs better than the existing estimators under some specified conditions i.e. it has the smallest Mean Squared Error and the highest Percentage Relative Efficiency. The developed estimator therefore is suitable to be applied to situations in which the variable of interest has a positive correlation with the auxiliary variable.

An approximate point-based alternative for the estimation of variance under big BAF sampling

Background:A new variance estimator is derived and tested for big BAF(Basal Area Factor)sampling which is a forest inventory system that utilizes Bitterlich sampling(point sampling)with two BAF sizes,a small BAF for tree counts and a larger BAF on which tree measurements are made usually including DBHs and heights needed for volume estimation.Methods:The new estimator is derived using the Delta method from an existing formulation of the big BAF estimator as consisting of three sample means.The new formula is compared to existing big BAF estimators including a popular estimator based on Bruce’s formula.Results:Several computer simulation studies were conducted comparing the new variance estimator to all known variance estimators for big BAF currently in the forest inventory literature.In simulations the new estimator performed well and comparably to existing variance formulas.Conclusions:A possible advantage of the new estimator is that it does not require the assumption of negligible correlation between basal area counts on the small BAF factor and volume-basal area ratios based on the large BAF factor selection trees,an assumption required by all previous big BAF variance estimation formulas.Although this correlation was negligible on the simulation stands used in this study,it is conceivable that the correlation could be significant in some forest types,such as those in which the DBH-height relationship can be affected substantially by density perhaps through competition.We derived a formula that can be used to estimate the covariance between estimates of mean basal area and the ratio of estimates of mean volume and mean basal area.We also mathematically derived expressions for bias in the big BAF estimator that can be used to show the bias approaches zero in large samples on the order of 1n where n is the number of sample points.

Speech Separation Methodology for Hearing Aid

In the design of hearing aids(HA),the real-time speech-enhancement is done.The digital hearing aids should provide high signal-to-noise ratio,gain improvement and should eliminate feedback.In generic hearing aids the perfor-mance towards different frequencies varies and non uniform.Existing noise can-cellation and speech separation methods drops the voice magnitude under the noise environment.The performance of the HA for frequency response is non uni-form.Existing noise suppression methods reduce the required signal strength also.So,the performance of uniform sub band analysis is poor when hearing aid is con-cern.In this paper,a speech separation method using Non-negative Matrix Fac-torization(NMF)algorithm is proposed for wavelet decomposition.The Proposed non-uniformfilter-bank was validated by parameters like band power,Signal-to-noise ratio(SNR),Mean Square Error(MSE),Signal to Noise and Dis-tortion Ratio(SINAD),Spurious-free dynamic range(SFDR),error and time.The speech recordings before and after separation was evaluated for quality using objective speech quality measures International Telecommunication Union-Telecommunication standard ITU-T P.862.