Seismic random noise suppression using an adaptive nonlocal means algorithm

Nonlocal means filtering is a noise attenuation method based on redundancies in image information. It is also a nonlocal denoising method that uses the self-similarity of an image, assuming that the valid structures of the image have a certain degree of repeatability that the random noise lacks. In this paper, we use nonlocal means filtering in seismic random noise suppression. To overcome the problems caused by expensive computational costs and improper filter parameters, this paper proposes a block-wise implementation of the nonlocal means method with adaptive filter parameter estimation. Tests with synthetic data and real 2D post-stack seismic data demonstrate that the proposed algorithm better preserves valid seismic information and has a higher accuracy when compared with traditional seismic denoising methods （e.g., f-x deconvolution）, which is important for subsequent seismic processing and interpretation.

Seismic dip estimation based on the twodimensional Hilbert transform and its application in random noise attenuation

In seismic data processing, random noise seriously affects the seismic data quality and subsequently the interpretation. This study aims to increase the signal-to-noise ratio by suppressing random noise and improve the accuracy of seismic data interpretation without losing useful information. Hence, we propose a structure-oriented polynomial fitting filter. At the core of structure-oriented filtering is the characterization of the structural trend and the realization of nonstationary filtering. First, we analyze the relation of the frequency response between two-dimensional（2D） derivatives and the 2D Hilbert transform. Then, we derive the noniterative seismic local dip operator using the 2D Hilbert transform to obtain the structural trend. Second, we select polynomial fitting as the nonstationary filtering method and expand the application range of the nonstationary polynomial fitting. Finally, we apply variableamplitude polynomial fitting along the direction of the dip to improve the adaptive structureoriented filtering. Model and field seismic data show that the proposed method suppresses the seismic noise while protecting structural information.

Random noise attenuation by f–x spatial projection-based complex empirical mode decomposition predictive filtering

The frequency–space（f–x） empirical mode decomposition（EMD） denoising method has two limitations when applied to nonstationary seismic data. First, subtracting the first intrinsic mode function（IMF） results in signal damage and limited denoising. Second, decomposing the real and imaginary parts of complex data may lead to inconsistent decomposition numbers. Thus, we propose a new method named f–x spatial projection-based complex empirical mode decomposition（CEMD） prediction filtering. The proposed approach directly decomposes complex seismic data into a series of complex IMFs（CIMFs） using the spatial projection-based CEMD algorithm and then applies f–x predictive filtering to the stationary CIMFs to improve the signal-to-noise ratio. Synthetic and real data examples were used to demonstrate the performance of the new method in random noise attenuation and seismic signal preservation.

An iterative curvelet thresholding algorithm for seismic random noise attenuation

In this paper,we explore the use of iterative curvelet thresholding for seismic random noise attenuation.A new method for combining the curvelet transform with iterative thresholding to suppress random noise is demonstrated and the issue is described as a linear inverse optimal problem using the L1 norm.Random noise suppression in seismic data is transformed into an L1 norm optimization problem based on the curvelet sparsity transform. Compared to the conventional methods such as median filter algorithm,FX deconvolution, and wavelet thresholding,the results of synthetic and field data processing show that the iterative curvelet thresholding proposed in this paper can sufficiently improve signal to noise radio（SNR） and give higher signal fidelity at the same time.Furthermore,to make better use of the curvelet transform such as multiple scales and multiple directions,we control the curvelet direction of the result after iterative curvelet thresholding to further improve the SNR.

Improved random noise attenuation using f-x empirical mode decomposition and local similarity

Conventional f-x empirical mode decomposition（EMD） is an effective random noise attenuation method for use with seismic profiles mainly containing horizontal events.However,when a seismic event is not horizontal,the use of f-x EMD is harmful to most useful signals.Based on the framework of f-x EMD,this study proposes an improved denoising approach that retrieves lost useful signals by detecting effective signal points in a noise section using local similarity and then designing a weighting operator for retrieving signals.Compared with conventional f-x EMD,f-x predictive filtering,and f-x empirical mode decomposition predictive filtering,the new approach can preserve more useful signals and obtain a relatively cleaner denoised image.Synthetic and field data examples are shown as test performances of the proposed approach,thereby verifying the effectiveness of this method.

Random noise suppression for seismic data using a non-local Bayes algorithm

For random noise suppression of seismic data, we present a non-local Bayes （NL- Bayes） filtering algorithm. The NL-Bayes algorithm uses the Gaussian model instead of the weighted average of all similar patches in the NL-means algorithm to reduce the fuzzy of structural details, thereby improving the denoising performance. In the denoising process of seismic data, the size and the number of patches in the Gaussian model are adaptively calculated according to the standard deviation of noise. The NL-Bayes algorithm requires two iterations to complete seismic data denoising, but the second iteration makes use of denoised seismic data from the first iteration to calculate the better mean and covariance of the patch Gaussian model for improving the similarity of patches and achieving the purpose of denoising. Tests with synthetic and real data sets demonstrate that the NL-Bayes algorithm can effectively improve the SNR and preserve the fidelity of seismic data.

Inversion-based data-driven time-space domain random noise attenuation method

Conventional time-space domain and frequency-space domain prediction filtering methods assume that seismic data consists of two parts, signal and random noise. That is, the so-called additive noise model. However, when estimating random noise, it is assumed that random noise can be predicted from the seismic data by convolving with a prediction error filter. That is, the source-noise model. Model inconsistencies, before and after denoising, compromise the noise attenuation and signal-preservation performances of prediction filtering methods. Therefore, this study presents an inversion-based time-space domain random noise attenuation method to overcome the model inconsistencies. In this method, a prediction error filter （PEF）, is first estimated from seismic data; the filter characterizes the predictability of the seismic data and adaptively describes the seismic data＇s space structure. After calculating PEF, it can be applied as a regularized constraint in the inversion process for seismic signal from noisy data. Unlike conventional random noise attenuation methods, the proposed method solves a seismic data inversion problem using regularization constraint; this overcomes the model inconsistency of the prediction filtering method. The proposed method was tested on both synthetic and real seismic data, and results from the prediction filtering method and the proposed method are compared. The testing demonstrated that the proposed method suppresses noise effectively and provides better signal-preservation performance.

Modeling random telegraph signal noise in CMOS image sensor under low light based on binomial distribution

The random telegraph signal noise in the pixel source follower MOSFET is the principle component of the noise in the CMOS image sensor under low light. In this paper, the physical and statistical model of the random telegraph signal noise in the pixel source follower based on the binomial distribution is set up. The number of electrons captured or released by the oxide traps in the unit time is described as the random variables which obey the binomial distribution. As a result,the output states and the corresponding probabilities of the first and the second samples of the correlated double sampling circuit are acquired. The standard deviation of the output states after the correlated double sampling circuit can be obtained accordingly. In the simulation section, one hundred thousand samples of the source follower MOSFET have been simulated,and the simulation results show that the proposed model has the similar statistical characteristics with the existing models under the effect of the channel length and the density of the oxide trap. Moreover, the noise histogram of the proposed model has been evaluated at different environmental temperatures.

Random noise stimulation in the treatment of patients with neurological disorders

Random noise stimulation technique involves applying any form of energy(for instance,light,mechanical,electrical,sound)with unpredictable intensities through time to the brain or sensory receptors to enhance sensory,motor,or cognitive functions.Random noise stimulation initially employed mechanical noise in auditory and cutaneous stimuli,but electrical energies applied to the brain or the skin are becoming more frequent,with a series of clinical applications.Indeed,recent evidence shows that transcranial random noise stimulation can increase corticospinal excitability,improve cognitive/motor performance,and produce beneficial aftereffects at the behavioral and psychological levels.Here,we present a narrative review about the potential uses of random noise stimulation to treat neurological disorders,including attention deficit hyperactivity disorder,schizophrenia,amblyopia,myopia,tinnitus,multiple sclerosis,post-stroke,vestibular-postural disorders,and sensitivity loss.Many of the reviewed studies reveal that the optimal way to deliver random noise stimulation-based therapies is with the concomitant use of neurological and neuropsychological assessments to validate the beneficial aftereffects.In addition,we highlight the requirement of more randomized controlled trials and more physiological studies of random noise stimulation to discover another optimal way to perform the random noise stimulation interventions.

Random telegraph noise on the threshold voltage of multi-level flash memory

We investigate the impact of random telegraph noise（RTN） on the threshold voltage of multi-level NOR flash memory.It is found that the threshold voltage variation（？Vth） and the distribution due to RTN increase with the programmed level（Vth） of flash cells. The gate voltage dependence of RTN amplitude and the variability of RTN time constants suggest that the large RTN amplitude and distribution at the high program level is attributed to the charge trapping in the tunneling oxide layer induced by the high programming voltages. A three-dimensional TCAD simulation based on a percolation path model further reveals the contribution of those trapped charges to the threshold voltage variation and distribution in flash memory.

Dynamics of entropic uncertainty for three types of three-level atomic systems under the random telegraph noise

We study the dynamics of the entropic uncertainty for three types of three-level atomic systems coupled to an environment modeled by random matrices. The results show that the entropic uncertainty in the Ξ-type atomic system is lower than that in the V-type atomic system which is exactly the same as that in the Λ-type atomic system. In addition, the effect of relative coupling strength on entropic uncertainty is opposite in Markov region and non-Markov region, and the influence of a common environment and independent environments in Markov region and non-Markov region is also opposite. One can reduce the entropic uncertainty by decreasing relative coupling strength or placing the system in two separate environments in the Markov case. In the non-Markov case, the entropic uncertainty can be reduced by increasing the relative coupling strength or by placing the system in a common environment.

Efficient Global Threshold Vector Outlyingness Ratio Filter for the Removal of Random Valued Impulse Noise

This research paper proposes a filter to remove Random Valued Impulse Noise (RVIN) based on Global Threshold Vector Outlyingness Ratio (GTVOR) that is applicable for real time image processing. This filter works with the algorithm that breaks the images into various decomposition levels using Discrete Wavelet Transform (DWT) and searches for the noisy pixels using the outlyingness of the pixel. This algorithm has the capability of differentiating high frequency pixels and the “noisy pixel” using the threshold as well as window adjustments. The damage and the loss of information are prevented by means of interior mining. This global threshold based algorithm uses different thresholds for different quadrants of DWT and thus helps in recovery of noisy image even if it is 90% affected. Experimental results exhibit that this method outperforms other existing methods for accurate noise detection and removal, at the same time chain of connectivity is not lost.

Seismic data denoising based on mixed time-frequency methods

Deconvolution denoising in the f-x domain has some defects when facing situations like complicated geology structure, coherent noise of steep dip angles, and uneven spatial sampling. To solve these problems, a new filtering method is proposed, which uses the generalized S transform which has good time-frequency concentration criterion to transform seismic data from the time-space to time-frequency-space domain （t-f-x）. Then in the t-f-x domain apply Empirical Mode Decomposition （EMD） on each frequency slice and clear the Intrinsic Mode Functions （IMFs） that noise dominates to suppress coherent and random noise. The model study shows that the high frequency component in the first IMF represents mainly noise, so clearing the first IMF can suppress noise. The EMD filtering method in the t-f-x domain after generalized S transform is equivalent to self-adaptive f-k filtering that depends on position, frequency, and truncation characteristics of high wave numbers. This filtering method takes local data time-frequency characteristic into consideration and is easy to perform. Compared with AR predictive filtering, the component that this method filters is highly localized and contains relatively fewer low wave numbers and the filter result does not show over-smoothing effects. Real data processing proves that the EMD filtering method in the t-f-x domain after generalized S transform can effectively suppress random and coherent noise of steep dips.

Estimation of Parameters of Boundary Value Problems for Linear Ordinary Differential Equations with Uncertain Data

In this paper we construct optimal, in certain sense, estimates of values of linear functionals on solutions to two-point boundary value problems (BVPs) for systems of linear first-order ordinary differential equations from observations which are linear transformations of the same solutions perturbed by additive random noises. It is assumed here that right-hand sides of equations and boundary data as well as statistical characteristics of random noises in observations are not known and belong to certain given sets in corresponding functional spaces. This leads to the necessity of introducing minimax statement of an estimation problem when optimal estimates are defined as linear, with respect to observations, estimates for which the maximum of mean square error of estimation taken over the above-mentioned sets attains minimal value. Such estimates are called minimax mean square or guaranteed estimates. We establish that the minimax mean square estimates are expressed via solutions of some systems of differential equations of special type and determine estimation errors.

oncausal spatial prediction filtering based on an ARMA model

Conventional f-x prediction filtering methods are based on an autoregressive model. The error section is first computed as a source noise but is removed as additive noise to obtain the signal, which results in an assumption inconsistency before and after filtering. In this paper, an autoregressive, moving-average model is employed to avoid the model inconsistency. Based on the ARMA model, a noncasual prediction filter is computed and a self-deconvolved projection filter is used for estimating additive noise in order to suppress random noise. The 1-D ARMA model is also extended to the 2-D spatial domain, which is the basis for noncasual spatial prediction filtering for random noise attenuation on 3-D seismic data. Synthetic and field data processing indicate this method can suppress random noise more effectively and preserve the signal simultaneously and does much better than other conventional prediction filtering methods.

Denoising of seismic data via multi-scale ridgelet transform

Noise has traditionally been suppressed or eliminated in seismic data sets by the use of Fourier filters and, to a lesser degree, nonlinear statistical filters. Although these methods are quite useful under specific conditions, they may produce undesirable effects for the low signal to noise ratio data. In this paper, a new method, multi-scale ridgelet transform, is used in the light of the theory of ridgelet transform. We employ wavelet transform to do sub-band decomposition for the signals and then use non-linear thresholding in ridgelet domain for every block. In other words, it is based on the idea of partition, at sufficiently fine scale, a curving singularity looks straight, and so ridgelet transform can work well in such cases. Applications on both synthetic data and actual seismic data from Sichuan basin, South China, show that the new method eliminates the noise portion of the signal more efficiently and retains a greater amount of geologic data than other methods, the quality and consecutiveness of seismic event are improved obviously as well as the quality of section is improved.

Entropy Correlations and Entanglement of a Superconducting Charge Qubit in a Resonant Cavity in the Presence of Noise

We study the dynamics of the entropy correlations and entanglement in a system of interaction of a superconducting charge qubit with a single-mode resonant cavity subject to noise considered as two-state random phase telegraph noise. We show that although the noise has an apparent suppressing effect on the evolution of the entropies of the qubit and the field and also on the entanglement in the system, the entropy exchange between the qubit and the field is independent of it during the time evolution of the system.

A voltage-controlled chaotic oscillator based on carbon nanotube field-effect transistor for low-power embedded systems

This paper presents a compact and low-power-based discrete-time chaotic oscillator based on a carbon nanotube field-effect transistor implemented using Wong and Deng＇s well-known model. The chaotic circuit is composed of a nonlinear circuit that creates an adjustable chaos map, two sample and hold cells for capture and delay functions, and a voltage shifter that works as a buffer and adjusts the output voltage for feedback. The operation of the chaotic circuit is verified with the SPICE software package, which uses a supply voltage of 0.9 V at a frequency of 20 kHz. The time series, frequency spectra, transitions in phase space, sensitivity with the initial condition diagrams, and bifurcation phenomena are presented. The main advantage of this circuit is that its chaotic signal can be generated while dissipating approximately 7.8 μW of power, making it suitable for embedded systems where many chaos-signal generators are required on a single chip.

ixed Cadzow filtering method in fractional Fourier domain

Conventional frequency domain method used in random noise attenuation singular value decomposition （SVD） filtering processing causes bending event damage. To mitigate this problem, we present a mixed Cadzow filtering method based on fractional Fourier transform to suppress random noise in 3D seismic data. First, the seismic data is transformed to the time-frequency plane via the fractional Fourier transform. Second, based on the Eigenimage filtering method and Cadzow filtering method, the mixed high-dimensional Hankel matrix is built; then, SVD is performed. Finally, random noise is eliminated effectively by reducing the rank of the matrix. The theoretical model and real applications of the mixed filtering method in a region of Sichuan show that our method can not only suppress noise effectively but also preserve the frequency and phase of effective signals quite well and significantly improve the signal-to-noise ratio of 3D post-stack seismic data.

A Noise-Resistant Superpixel Segmentation Algorithm for Hyperspectral Images

The superpixel segmentation has been widely applied in many computer vision and image process applications.In recent years,amount of superpixel segmentation algorithms have been proposed.However,most of the current algorithms are designed for natural images with little noise corrupted.In order to apply the superpixel algorithms to hyperspectral images which are always seriously polluted by noise,we propose a noiseresistant superpixel segmentation(NRSS)algorithm in this paper.In the proposed NRSS,the spectral signatures are first transformed into frequency domain to enhance the noise robustness;then the two widely spectral similarity measures-spectral angle mapper(SAM)and spectral information divergence(SID)are combined to enhance the discriminability of the spectral similarity;finally,the superpixels are generated with the proposed frequency-based spectral similarity.Both qualitative and quantitative experimental results demonstrate the effectiveness of the proposed superpixel segmentation algorithm when dealing with hyperspectral images with various noise levels.Moreover,the proposed NRSS is compared with the most widely used superpixel segmentation algorithm-simple linear iterative clustering(SLIC),where the comparison results prove the superiority of the proposed superpixel segmentation algorithm.