Noise Probability Research Articles

Optimizing Coherence Suppression in a Laser Broadened by Phase Modulation With Noise

Phase noise can be modulated onto the output of a laser with an electro-optic phase modulator (EOM) to create a highly incoherent broadened source with low intensity noise. This technique leaves a small but finite fraction of the coherent carrier power that can be highly detrimental in applications requiring incoherent light. This article shows that the carrier suppression in a laser broadened by this technique can be calculated for an arbitrary noise probability density function. The carrier suppression can be varied experimentally by adjusting the noise voltage standard deviation Gv <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">σ</sub> and saturation voltage V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sat</sub> of the amplifier that amplifies the noise source that drives the EOM. Simulations show that suppressions better than -30 dB are attainable for reasonable tolerances in Gv <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">σ</sub> , for example an EOM with a V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">π</sub> of 4.7 V, a V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sat</sub> of 6.3 V, and Gv <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">σ</sub> /V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">π</sub> = 0.73 ± 0.03. Even greater tolerances can be achieved with a higher V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sat</sub> (21 V), lower V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">π</sub> (3.5 V), and Gv <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">σ</sub> /V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">π</sub> ≈ 3.2 ± 2.3. This model aids in selecting these parameters such that the carrier suppression is resilient to fluctuations in these voltages due to temperature variations and aging of the components. The model predictions are validated by testing a fiber optic gyroscope interrogated with a broadened laser for various Gv <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">σ</sub> and V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sat</sub> and inferring the carrier suppression from its measured noise. A -44-dB carrier suppression was observed for a nonlinear amplifier with Gv <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">σ</sub> = 3.43 V, V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">sat</sub> = 6.3 V, and an EOM with V <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">π</sub> = 4.7 V, in agreement with predictions.

DOA estimation under Bernoulli-Gaussian impulsive noise

Direction of arrival algorithms have ability to distinguish between directions of individual sources under additive white Gaussian noise. However, presence of the impulsive noise can corrupt the angles estimation. In this paper, the performance of MUSIC and ESPRIT, as estimation algorithms, is investigated in impulsive noise with white Gaussian noise environment. The impulsive noise is modelled using Bernoulli-Gaussian model and the effect of varying its statistical parameters on the estimation ability is tested. Three sources with different angles are simulated and a uniform linear array is utilized to capture the impinging signals. The performance analysis includes impulsive noise probability of occurrence and amplitude intensity which both control the impulsive power. The mean square error of the estimated angles is adopted as a metric to measure the performance. The simulation results provide a map of all the expected possible impulsive noise cases which influence the MUSIC and ESPRIT direction of arrival algorithms. The expected cases show that the performance degradation happening in ESPRIT is more than that of MUSIC. At 0 dB SNR, the impulsive noise increases the mean square error by almost 15 dB and 20 dB for MUSIC and ESPRIT, respectively.

Research on Noise Reduction and Enhancement Algorithm of Girth Weld Image

In order to eliminate the salt pepper and Gaussian mixed noise in X-ray weld image, the extreme value characteristics of salt and pepper noise are used to separate the mixed noise, and the non local mean filtering algorithm is used to denoise it. Because the smoothness of the exponential weighted kernel function is too large, it is easy to cause the image details fuzzy, so the cosine coefficient based on the function is adopted. An improved non local mean image denoising algorithm is designed by using weighted Gaussian kernel function. The experimental results show that the new algorithm reduces the noise and retains the details of the original image, and the peak signal-to-noise ratio is increased by 1.5 dB. An adaptive salt and pepper noise elimination algorithm is proposed, which can automatically adjust the filtering window to identify the noise probability. Firstly, the median filter is applied to the image, and the filtering results are compared with the pre filtering results to get the noise points. Then the weighted average of the middle three groups of data under each filtering window is used to estimate the image noise probability. Before filtering, the obvious noise points are removed by threshold method, and then the central pixel is estimated by the reciprocal square of the distance from the center pixel of the window. Finally, according to Takagi Sugeno (T-S) fuzzy rules, the output estimates of different models are fused by using noise probability. Experimental results show that the algorithm has the ability of automatic noise estimation and adaptive window adjustment. After filtering, the standard mean square deviation can be reduced by more than 20%, and the speed can be increased more than twice. In the enhancement part, a nonlinear image enhancement method is proposed, which can adjust the parameters adaptively and enhance the weld area automatically instead of the background area. The enhancement effect achieves the best personal visual effect. Compared with the traditional method, the enhancement effect is better and more in line with the needs of industrial field.

Mid-infrared photon counting and resolving via efficient frequency upconversion

Optical detectors with single-photon sensitivity and large dynamic range would facilitate a variety of applications. Specifically, the capability of extending operation wavelengths into the mid-infrared region is highly attractive. Here we implement a mid-infrared frequency upconversion detector for counting and resolving photons at 3 μm. Thanks to the spectrotemporal engineering of the involved optical fields, the mid-infrared photons could be spectrally translated into the visible band with a conversion efficiency of 80%. In combination with a silicon avalanche photodiode, we obtained unprecedented performance with a high overall detection efficiency of 37% and a low noise equivalent power of 1.8 × 10 − 17 W / Hz 1 / 2 . Furthermore, photon-number-resolving detection at mid-infrared wavelengths was demonstrated, for the first time to our knowledge, with a multipixel photon counter. The implemented upconversion detector exhibited a maximal resolving photon number up to 9 with a noise probability per pulse of 0.14% at the peak detection efficiency. The achieved photon counting and resolving performance might open up new possibilities in trace molecule spectroscopy, sensitive biochemical sensing, and free-space communications, among others.

Analysis of phase estimation for star QAM coherent optical packet switched system

The development of data centers, 5th generation wireless network remote network education and cloud computing is increasingly demanding optical packet switched (OPS) optical interconnect networks. The blind phase estimation algorithm is one of the important phase estimation algorithms in the star QAM OPS network. However, the blind phase estimation algorithm can cause system performance degradation rapidly in the case of low signal to noise ratio (SNR). To our best knowledges, the principle and processing mechanism of the problem have not been analyzed and studied in detail. In this paper, the blind phase estimation is analyzed for the first time based on SNR and phase noise probability model at low optical signal to noise ratio. Based on the analysis, the common single differential and doubly differential coding schemes are explained for blind phase estimation. Then, the performance of the blind phase estimation + single differential and blind phase estimation + doubly differential algorithms for star QAM OPS system be compared in detail, including time-varying phase processing capability, transmission performance and tolerance to laser linewidth. The experiments be performed to verify the performance of the blind phase estimation + single differential and blind phase estimation + doubly differential algorithms.

One-Bit Sine-Fit

This article introduces a novel procedure for the estimation of the frequency, amplitude, and phase of a sinusoidal signal after one-bit quantization. The estimator requires knowledge of the quantizer threshold but does not require information about the noise probability density function (PDF), possibly affecting measurement results. The threshold must be different from zero for estimating the amplitude but not necessarily for estimating the frequency or the phase. The algorithm requires an irrational value of the ratio between the sinusoidal frequency and the sampling rate. The procedure allows also the estimation of the noise variance and the cumulative distribution function (CDF). Theoretical properties are analyzed, and experimental results are provided to validate the estimation procedure.

Qubit dynamics with classical noise

We study the evolution of a qubit evolving according to the Schrödinger equation with a Hamiltonian containing noise terms, modeled by random diagonal and off-diagonal matrix elements. We show that the noise-averaged qubit density matrix converges to a final state, in the limit of large times t. The convergence speed is polynomial in 1/t, with a power depending on the regularity of the noise probability density and its low frequency behaviour. We evaluate the final state explicitly. We show that in the two regimes of weak and of strong off-diagonal noise, the process implements the dephasing channel in the energy- (localized) and the delocalized basis, respectively.

Exponential upper bounds for the runtime of randomized search heuristics

We argue that proven exponential upper bounds on runtimes, an established area in classic algorithms, are interesting also in heuristic search and we prove several such results. We show that any of the algorithms randomized local search, Metropolis algorithm, simulated annealing, and (1+1) evolutionary algorithm can optimize any pseudo-Boolean weakly monotonic function under a large set of noise assumptions in a runtime that is at most exponential in the problem dimension n. This drastically extends a previous such result, limited to the (1+1) EA, the LeadingOnes function, and one-bit or bit-wise prior noise with noise probability at most 1/2, and at the same time simplifies its proof. With the same general argument, among others, we also derive a sub-exponential upper bound for the runtime of the (1,λ) evolutionary algorithm on the OneMax problem when the offspring population size λ is logarithmic, but below the efficiency threshold. To show that our approach can also deal with non-trivial parent population sizes, we prove an exponential upper bound for the runtime of the mutation-based version of the simple genetic algorithm on the OneMax benchmark, matching a known exponential lower bound.

Automated quantitative subsurface evaluation of fiber reinforced polymers

Quantitative non destructive subsurface analysis with increased reliability for defect detection makes it useful for a variety of industrial applications to assess the integrity and subsequent strength of materials either during or post manufacturing. Traditional non stationary thermal wave based subsurface analysis approaches are skill intensive and time consuming for analysis with human intervention. This paper proposes an automated classification and regression tree based quantitative post processing modality along with thermal wave model to characterize the subsurface anomalies using quadratic frequency modulated thermal wave imaging. It also validates the proposed mathematical modeling using experimentation carried over carbon fiber reinforced and glass fiber reinforced plastic specimens used in aerospace industry. Subsurface details have been visualized in terms of their depths using the proposed modality being evaluated from the proposed mathematical model. In addition, its detection capability and reliability over other contemporary approaches have been assessed using signal to noise ratio and probability of detection respectively.

Kepler Data Analysis: Non-Gaussian Noise and Fourier Gaussian Process Analysis of Stellar Variability

Abstract We develop a statistical analysis model of Kepler stellar flux data in the presence of planet transits, non-Gaussian noise, and stellar variability. We first develop a model for the Kepler noise probability distribution in the presence of outliers, which make the noise probability distribution non-Gaussian. We develop a signal likelihood analysis based on this probability distribution, in which we model the signal as a sum of the star variability and planetary transits. We argue that these components need to be modeled together if optimal signal is to be extracted from the data. For the stellar variability model we develop an optimal Gaussian process analysis using a Fourier-based Wiener filter approach, where the power spectrum is non-parametric and learned from the data. We develop high dimensional optimization of the objective function, where we jointly optimize all the model parameters, including thousands of star variability modes, and planet transit parameters. We apply the method to Kepler-90 data and show that it gives a better match to the stellar variability than the existing methods, and robustly handles noise outliers. As a consequence, the planet radii have a higher value than what the existing methods give, including splines and celerite.

Weighted Local Times of a Sub-fractional Brownian Motion as Hida Distributions

The sub-fractional Brownian motion is a Gaussian extension of the Brownian motion. It has the properties of self-similarity, continuity of the sample paths, and short-range dependence, among others. The increments of sub-fractional Brownian motion is neither independent nor stationary. In this paper we study the sub-fractional Brownian motion using a white noise analysis approach. We recall the represention of sub-fractional Brownian motion on the white noise probability space and show that Donsker's delta functional of a sub-fractional Brownian motion is a Hida distribution. As a main result, we prove the existence of the weighted local times of a $d$-dimensional sub-fractional Brownian motion as Hida distributions.

Fuzzy Decision Tree Based Characterization of Subsurface Anomalies

Recent intervention of machine learning based methodologies into infrared thermography proves to provide better defect detection and characterization. This paper provides a Fuzzy decision tree based quantitative post processing modality along with a theoretical model for thermal waves to characterize the subsurface anomalies using quadratic frequency modulated thermal wave imaging. A carbon fiber reinforced polymers (CFRP) and mild steel (MS) specimens having flat bottom holes with different depths and sizes are processed through experimental evaluation. A direct depth estimation is provided by the proposed modality being evaluated from the proposed mathematical model. In addition, its detection capability and reliability over other contemporary approaches is compared using signal to noise ratio, defect sizing and probability of defect detection.

Quantum dephasing induced by non-Markovian random telegraph noise

We theoretically study the dynamical dephasing of a quantum two level system interacting with an environment which exhibits non-Markovian random telegraph fluctuations. The time evolution of the conditional probability of the environmental noise is governed by a generalized master equation depending on the environmental memory effect. The expression of the dephasing factor is derived exactly which is closely associated with the memory kernel in the generalized master equation for the conditional probability of the environmental noise. In terms of three important types memory kernels, we discuss the quantum dephasing dynamics of the system and the non-Markovian character exhibiting in the dynamical dephasing induced by non-Markovian random telegraph noise. We show that the dynamical dephasing of the quantum system does not always exhibit non-Markovian character which results from that the non-Markovian character in the dephasing dynamics depends both on the environmental non-Markovian character and the interaction between the system and environment. In addition, the dynamical dephasing of the quantum system can be modulated by the external modulation frequency of the environment. This result is significant to quantum information processing and helpful for further understanding non-Markovian dynamics of open quantum systems.

Trapping Depth and Transition Probability of Four-Level Random Telegraph Noise in a Gate-All-Around Poly-Si Nanowire Transistor

In this article, we investigate the four-level random telegraph noise (RTN) characteristics of a gate-all-around (GAA) nanowire (NW) transistor. The RTN-testing devices were fabricated with the sidewall spacer etching technique. The effective channel length and width are approximately 150 and 30 nm, respectively. By decoupling the four-level RTN, we are able to extract the time constants associated with the two traps. Circle-shaped approximations are used to mimic the triangular NW for evaluating the depths of the traps. The extracted depths of the two traps are very close to each other, which is consistent with the time-evolution measured results. We've also explored the probabilities of transitions between two specific current levels in the RTN characteristics, as well as the relative trapping/de-trapping frequencies.

Segmentation and Diagnosis of Papillary Thyroid Carcinomas Based on Generalized Clustering Algorithm in Ultrasound Elastography.

Papillary thyroid carcinomas (PTC) are the most common type of thyroid malignant tumors. Existing methods for clustering high-noise ultrasound images tend to degrade the clustering performance. In order to realize accurate segmentation of thyroid nodule in noisy environment, this paper proposes an improved segmentation algorithm based on adaptive fast generalized clustering. Firstly, the parameter balance factor is adaptively determined according to the noise probability of non-local pixels so as to reflect the spatial structure information in the image more accurately. Then, the balance factor is used to effectively combine the linear weighted filtered image in the AFGC algorithm so as to create the adaptive filtered image. Since the filtering degree depends on the probability whether the pixel is noise in the image, the dynamic noise suppression performance of the proposed method can be greatly improved. A large number of qualitative and quantitative experimental results show that the proposed generalized clustering algorithm can obtain more accurate results when clustering images with high noise. It is suitable for intelligent diagnosis of papillary thyroid convolution in clinical examination.

Development of automated angle-scanning, high-speed surface plasmon resonance imaging and SPRi visualization for the study of dropwise condensation

This paper describes the fabrication and testing of a novel angle-scanning surface plasmon resonance imaging (SPRi) instrument. The combination of two stationary mirrors and two angle-controlled mirrors provides high accuracy (up to 10−3°) and high-speed angular probing. This instrument minimizes the angle-dependent image artifact that arises due to beam walk, which is the biggest challenge for the use of SPRi with angular modulation (AM). In the work described in this paper, two linear stages were employed to minimize the image artifact by adjusting the location of the angle-controlled mirrors and the camera. The SPRi instrument was used to visualize coalescence during dropwise condensation. The results show that the effect of the environment’s temperature on reflectance was less than 1% when the incident angle was carefully chosen for SPRi with intensity modulation (IM). This means that condensation visualization can be carried out at ambient temperatures, without the need for a Peltier stage or a thermally controlled condensing surface. The concept of pixel neighboring was employed to assess the probability of noise and the standard error of thin film measurement. Experimental analyses during dropwise condensation show (1) the presence of a thin film with thickness of one monolayer, and (2) surface coverage of 0.71 m2/m2 by the thin film in the area between the droplets. In addition, analyses showed the existence of a dry area at the part of the substrate exposed by coalescence to ambient air. The results of this work undermine the validity of the film rupture theory as the dropwise condensation mechanism.Graphic abstract

Algorithm for Estimating Type and Probability of Impulse Noise in Color Images

Abstract—Color digital images are often contaminated by impulse noise during transmitting and recording of information. Efficient methods for elimination of impulse noise are needed to improve image quality. An algorithm for estimating of the type and probability of impulse noise in color images using morphological operations is proposed. Results of computer experiments are presented to demonstrate the performance of the proposed algorithm for estimating of the type and probability of impulse noise for several interference models.

Benefits of noise in M-estimators: Optimal noise level and probability density

For the robust estimation of a location parameter, we consider a parallel array of maximum likelihood type estimators (M-estimators). We investigate the possibility of added noise as a design variable of the M-estimators, and characterize a nonzero optimal amount of added noise maximizing the efficiency for estimation. The added noise shows its benefits to the asymptotic efficiency of the M-estimator when the noise level and the noise probability density are optimally tuned. The optimal noise level can be theoretically derived by maximizing the asymptotic efficiency as the probability density of added noise is given. Based on the Parzen-window density estimation technique, we approximate the infinite-dimensional non-convex optimization of the optimal probability density of added noise as a simpler optimization problem with respect to a finite-dimensional vector under certain constraints. This approximate solution for the optimal probability density of added noise shows its feasibility for various M-estimators with an arbitrary array size, which is also validated by simulation results.

Weighted Local Times of a Sub-fractional Brownian Motion as Hida Distributions

The sub-fractional Brownian motion is a Gaussian extension of the Brownian motion. It has the properties of self-similarity, continuity of the sample paths, and short-range dependence, among others. The increments of sub-fractional Brownian motion is neither independent nor stationary. In this paper we study the sub-fractional Brownian motion using a white noise analysis approach. We recall the represention of sub-fractional Brownian motion on the white noise probability space and show that Donsker's delta functional of a sub-fractional Brownian motion is a Hida distribution. As a main result, we prove the existence of the weighted local times of a $d$-dimensional sub-fractional Brownian motion as Hida distributions.

Single-photon-level light storage in cold atoms using the Autler-Townes splitting protocol

Broadband spin-photon interfaces for long-lived storage of photonic quantum states are key elements for quantum information technologies. Yet, reliable operation of such memories in the quantum regime is challenging due to photonic noise arising from technical and/or fundamental limitations in the storage-and-recall processes controlled by strong electromagnetic fields. Here, we experimentally implement a single-photon-level spin-wave memory in a laser-cooled Rubidium gas, based on the recently proposed Autler-Townes splitting (ATS) protocol. We demonstrate storage of 20-ns-long laser pulses, each containing an average of 0.1 photons, for 200 ns with an efficiency of $12.5\%$ and signal-to-noise ratio above 30. Notably, the robustness of ATS spin-wave memory against motional dephasing allows for an all-spatial filtering of the control-field noise, yielding an ultra-low unconditional noise probability of $3.3\times10^{-4}$, without the complexity of spectral filtering. These results highlight that broadband ATS memory in ultracold atoms is a preeminent option for storing quantum light.