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In recent years, many interpretable methods based on class activation maps (CAMs) have served as an important judging basis for the predictions of convolutional neural networks (CNNs). However, these methods still suffer from the problems of gradient noise, weight distortion, and perturbation deviation. In this work, we present self-attention class activation map (SA-CAM) and shed light on how it uses the self-attention mechanism to refine the existing CAM methods. In addition to generating basic activation feature maps, SA-CAM adds an attention skip connection as a regularization item for each feature map which further refines the focus area of an underlying CNN model. By introducing an attention branch and constructing a new attention operator, SA-CAM greatly alleviates the limitations of the CAM methods. The experimental results on the ImageNet dataset show that SA-CAM can not only generate highly accurate and intuitive interpretation but also have robust stability in adversarial comparison with the state-of-the-art CAM methods.

Procedural noise functions are fundamental tools in computer graphics used for synthesizing virtual geometry and texture patterns. Ideally, a procedural noise function should be compact, aperiodic, parameterized, and randomly accessible. Traditional lattice noise functions such as Perlin noise, however, exhibit periodicity due to the axial correlation induced while hashing the lattice vertices to the gradients. In this paper, we introduce a parameterized lattice noise called prime gradient noise (PGN) that minimizes discernible periodicity in the noise while enhancing the algorithmic efficiency. PGN utilizes prime gradients, a set of random unit vectors constructed from subsets of prime numbers plotted in polar coordinate system. To map axial indices of lattice vertices to prime gradients, PGN employs Szudzik pairing, a bijection F : ℕ2 → ℕ. Compositions of Szudzik pairing functions are used in higher dimensions. At the core of PGN is the ability to parameterize noise generation though prime sequence offsetting which facilitates the creation of fractal noise with varying levels of heterogeneity ranging from homogeneous to hybrid multifractals. A comparative spectral analysis of the proposed noise with other noises including lattice noises show that PGN significantly reduces axial correlation and hence, periodicity in the noise texture. We demonstrate the utility of the proposed noise function with several examples in procedural modeling, parameterized pattern synthesis, and solid texturing.

International audience; Part I of this paper formulated a multitask optimization problem where agents in the network have individual objectives to meet, or individual parameter vectors to estimate, subject to a smoothness condition over the graph. A diffusion strategy was devised that responds to streaming data and employs stochastic approximations in place of actual gradient vectors, which are generally unavailable. The approach relied on minimizing a global cost consisting of the aggregate sum of individual costs regularized by a term that promotes smoothness. We examined the first-order, the second-order, and the fourth-order stability of the multitask learning algorithm. The results identified conditions on the step-size parameter, regularization strength, and data characteristics in order to ensure stability. This Part II examines steady-state performance of the strategy. The results reveal explicitly the influence of the network topology and the regularization strength on the network performance and provide insights into the design of effective multitask strategies for distributed inference over networks.

In synthetic aperture radar (SAR) images, degradation due to multiplicative speckle noise and detail blurring is one of the common problem. This problem is solved by despeckling method. The main objective of image despeckling is to eliminate the speckle noise and preserve the important details of SAR images such as texture, edges, structures and corners. Usually SAR images are high dimensional images and preserving the edge and corner components is one major issue. Anisotropic diffusion also called Perona-Malik diffusion is used to reduce noise without disturbing the significant parts of the image. An homomorphic scheme is proposed using anisotropic diffusion in db2-type wavelet transform. Linear and non-linear filters are used on the approximate part of the image to remove blurring. Method noise thresholding is used to restore the unfiltered part of the despeckled image. The proposed method is applied and tested on correlated speckle noise as well as uncorrelated speckle noise on the real dataset of SAR images. The performance of the proposed method is evaluated by its visual quality and by using other metrics such as PSNR, SSIM, UIQI and RMSE. The performance and computational time are calculated and compared with standard filters and methods. The critical analysis of the result shows that proposed method gives the brilliant outcome in terms of structure, edge preservation and noise suppression. The proposed method has the ability to be used in practical applications. Keywords: Image despeckling, Wavelet transform, Anisotropic diffusion, Method noise

The shrinkage widely linear complex-valued least mean square (SWL-CLMS) algorithm with a variable step-size (VSS) overcomes the tradeoff between fast convergence and low steady-state misalignment, but meanwhile suffers from instability for highly correlated input signals because of the gradient noise amplification problem. To obtain a VSS that is also applicable to the case of highly correlated input signals, in this paper, we propose the VSS widely linear complex-valued normalized least mean square (VSS-WL-CNLMS) algorithm, where the VSS is derived by minimizing the mean-square deviation (MSD). Owing to the normalization, the VSS-WL-CNLMS algorithm is convergent in the mean square sense. By using the Rayleigh distribution, we calculate the mean step-size, which is then combined with the approximate uncorrelating transform to analyze the transient and steady-state mean square error (MSE) behaviors. Simulations for system identification scenario show that the proposed VSS-WL-CNLMS algorithm outperforms some well-known techniques and verify the accuracy of the theoretical analysis.

Driven by the need to solve increasingly complex optimization problems in signal processing and machine learning, there has been increasing interest in understanding the behavior of gradient-descent algorithms in non-convex environments. Most available works on distributed non-convex optimization problems focus on the deterministic setting where exact gradients are available at each agent. In this work and its Part II, we consider stochastic cost functions, where exact gradients are replaced by stochastic approximations and the resulting gradient noise persistently seeps into the dynamics of the algorithm. We establish that the diffusion learning strategy continues to yield meaningful estimates non-convex scenarios in the sense that the iterates by the individual agents will cluster in a small region around the network centroid. We use this insight to motivate a short-term model for network evolution over a finite-horizon. In Part II of this work, we leverage this model to establish descent of the diffusion strategy through saddle points in $O(1/\mu)$ steps, where $\mu$ denotes the step-size, and the return of approximately second-order stationary points in a polynomial number of iterations.

The random cropping data augmentation method is widely used to train convolutional neural network (CNN)-based target detectors to detect targets in optical images (e.g., COCO datasets). It can expand the scale of the dataset dozens of times while consuming only a small amount of calculations when training the neural network detector. In addition, random cropping can also greatly enhance the spatial robustness of the model, because it can make the same target appear in different positions of the sample image. Nowadays, random cropping and random flipping have become the standard configuration for those tasks with limited training data, which makes it natural to introduce them into the training of CNN-based synthetic aperture radar (SAR) image ship detectors. However, in this paper, we show that the introduction of traditional random cropping methods directly in the training of the CNN-based SAR image ship detector may generate a lot of noise in the gradient during back propagation, which hurts the detection performance. In order to eliminate the noise in the training gradient, a simple and effective training method based on feature map mask is proposed. Experiments prove that the proposed method can effectively eliminate the gradient noise introduced by random cropping and significantly improve the detection performance under a variety of evaluation indicators without increasing inference cost.

In general, it is known that an adaptive filter adjusts its parameters iteratively such as size of the working window, decision threshold values used in two stage detection-estimation based switching filters, number of iterations etc. It is also known that nonlinear filters such as median filters and its several variants are popularly known for their ability in dealing with the unknown circumstances. In this paper an efficient and simple adaptive nonlinear filtering scheme is presented to eliminate the impulse noise from the digital images with an impulsive noise detection and reduction scheme based on adaptive nonlinear filter techniques. The proposed scheme employs image statistics based dynamically varying working window and an adaptive threshold for noise detection with a Noise Exclusive Median (NEM) based restoration. The intensity value of the Noise Exclusive Median (NEM) is derived from the processed pixels in local neighborhood of a dynamically adaptive window. In the proposed scheme use of an adaptive threshold value derived from the noisy image statistics returns more precise results for the noisy pixel detection. The proposed scheme is simple and can be implemented as either a single pass or a multi-pass with a maximum of three iterations with a simple stopping criterion. The goodness of the proposed scheme is evaluated with respect to the qualitative and quantitative measures obtained by MATLAB simulations with standard images added with impulsive noise of varying densities. From the comparative analysis it is evident that the proposed scheme out performs the state-of-art schemes, preferably in cases of high-density impulse noise. KEYWORDS Nonlinear filter, median based filter, Noise exclusive median (NEM), adaptive window, local neighborhood, impulse noise, Peak-Signal-to-Noise Ratio (PSNR) For More Details: https://wireilla.com/papers/ijbb/V4N4/4414ijbb01.pdf

For successful deployment of deep neural networks (DNNs) on resource-constrained devices, retraining-based quantization has been widely adopted to reduce the number of DRAM accesses. By properly setting training parameters, such as batch size and learning rate, bit widths of both weights and activations can be uniformly quantized down to 4 bit while maintaining full precision accuracy. In this article, we present a retraining-based mixed-precision quantization approach and its customized DNN accelerator to achieve high energy efficiency. In the proposed quantization, in the middle of retraining, an additional bit (extra quantization level) is assigned to the weights that have shown frequent switching between two contiguous quantization levels since it means that both quantization levels cannot help to reduce quantization loss. We also mitigate the gradient noise that occurs in the retraining process by taking a lower learning rate near the quantization threshold. For the proposed novel mixed-precision quantized network (MPQ-network), we have implemented a customized accelerator using a 65-nm CMOS process. In the accelerator, the proposed processing elements (PEs) can be dynamically reconfigured to process variable bit widths from 2 to 4 bit for both weights and activations. The numerical results show that the proposed quantization can achieve $1.37 {\times }$ better compression ratio for VGG-9 using CIFAR-10 data set compared with a uniform 4-bit (both weights and activations) model without loss of classification accuracy. The proposed accelerator also shows $1.29\times $ of energy savings for VGG-9 using the CIFAR-10 data set over the state-of-the-art accelerator.

State-of-the-art deep learning models have achieved superlative performance across multiple computer vision applications such as object recognition, face recognition, and digits/character classification. Most of these models highly rely on the gradient information flows through the network for learning. By utilizing this gradient information, a simple gradient sign method based attack is developed to fool the deep learning models. However, the primary concern with this attack is the perceptibility of noise for large degradation in classification accuracy. This research address the question of whether an imperceptible gradient noise can be generated to fool the deep neural networks? For this, the role of sign function in the gradient attack is analyzed. The analysis shows that without-sign function, i.e. gradient magnitude, not only leads to a successful attack mechanism but the noise is also imperceptible to the human observer. Extensive quantitative experiments performed using two convolutional neural networks validate the above observation. For instance, AlexNet architecture yields 63.54% accuracy on the CIFAR-10 database which reduces to 0.0% and 26.39% when sign (i.e., perceptible) and without-sign (i.e., imperceptible) of the gradient is utilized, respectively.Further, the role of the direction of the gradient for image manipulation is studied. When an image is manipulated in the positive direction of the gradient, an adversarial image is generated. On the other hand, if the opposite direction of the gradient is utilized for image manipulation, it is observed that the classification error rate of the CNN model is reduced. On AlexNet, the error rate of 36.46% reduces to 4.29% when images of CIFAR-10 are manipulated in the negative direction of the gradient. To explore other enthusiastic results on multiple object databases, including CIFAR-100, fashion-MNIST, and SVHN, please refer to the full paper.

Privacy of machine learning becomes increasingly crucial, abundant emerging technologies have been spawned to solve privacy problem and federated learning (FL) is one of them. FL can replace data transmission through transmission gradient to prevent the leakage of data privacy. Recent researches indicated that privacy can be revealed through gradients and a little auxiliary information. To further verify the safety of gradient transmission mechanism, we propose a novel method called Privacy-leaks From Gradients (PLFG) to infer sensitive information through gradients only. To our knowledge, the weak assumption of this level is currently unique. PLFG uses the gradients obtained from victims in each iteration to build a special model, then updates initial noise through the model to fit victims’ privacy data. Experimental results demonstrate that even if only gradients are leveraged, users’ privacy can be disclosed, and current popular defense (gradient noise addition and gradient compression) cannot defend effectively. Furthermore, we discuss the limitations and feasible improvements of PLFG. We hope our attack can provide different ideas for future defense attempts to protect sensitive privacy.

We prove the existence of nonnegative martingale solutions to a class of stochastic degenerate-parabolic fourth-order PDEs arising in surface-tension driven thin-film flow influenced by thermal noise. The construction applies to a range of mobilites including the cubic one which occurs under the assumption of a no-slip condition at the liquid-solid interface. Since their introduction more than 15 years ago, by Davidovitch, Moro, and Stone and by Gr\"un, Mecke, and Rauscher, the existence of solutions to stochastic thin-film equations for cubic mobilities has been an open problem, even in the case of sufficiently regular noise. Our proof of global-in-time solutions relies on a careful combination of entropy and energy estimates in conjunction with a tailor-made approximation procedure to control the formation of shocks caused by the nonlinear stochastic scalar conservation law structure of the noise., Comment: 50 pages, accepted version

We prove the existence and uniqueness of entropy solutions for nonlinear diffusion equations with nonlinear conservative gradient noise. As particular applications our results include stochastic porous media equations, as well as the one-dimensional stochastic mean curvature flow in graph form., small changes according to the published version

The diffusion strategy for distributed learning from streaming data employs local stochastic gradient updates along with exchange of iterates over neighborhoods. In this work we establish that agents cluster around a network centroid in the mean-fourth sense and proceeded to study the dynamics of this point. We establish expected descent in non-convex environments in the large-gradient regime and introduce a short-term model to examine the dynamics over finite-time horizons. Using this model, we establish that the diffusion strategy is able to escape from strict saddle-points in $O(1/\mu)$ iterations, where $\mu$ denotes the step-size; it is also able to return approximately second-order stationary points in a polynomial number of iterations. Relative to prior works on the polynomial escape from saddle-points, most of which focus on centralized perturbed or stochastic gradient descent, our approach requires less restrictive conditions on the gradient noise process.

To realize the promise of ubiquitous embedded deep network inference, it is essential to seek limits of energy and area efficiency. Low-precision networks offer promise as energy and area scale down quadratically with precision. We demonstrate 8- and 4-bit networks that meet or exceed the accuracy of their full-precision versions on the ImageNet classification benchmark. We hypothesize that gradient noise due to quantization during training increases with reduced precision, and seek ways to overcome this. The number of iterations required by SGD to achieve a given training error is related to the square of (a) the distance of the initial solution from the final and (b) the maximum variance of the gradient estimates. Accordingly, we reduce solution distance by starting with pretrained fp32 baseline networks, and combat noise introduced by quantizing weights and activations during training by training longer and reducing learning rates. Sensitivity analysis indicates that these techniques, coupled with activation function range calibration, are sufficient to discover low-precision networks close to fp32 precision baseline networks. Our results provide evidence that 4-bits suffice for classification.

This work presents and studies a distributed algorithm for solving optimization problems over networks where agents have individual costs to minimize subject to subspace constraints that require the minimizers across the network to lie in a low-dimensional subspace. The algorithm consists of two steps: i) a self-learning step where each agent minimizes its own cost using a stochastic gradient update; ii) and a social-learning step where each agent combines the updated estimates from its neighbors using the entries of a combination matrix that converges in the limit to the projection onto the low-dimensional subspace. We obtain analytical formulas that reveal how the step-size, data statistical properties, gradient noise, and subspace constraints influence the network mean-square-error performance. The results also show that in the small step-size regime, the iterates generated by the distributed algorithm achieve the centralized steady-state MSE performance. We provide simulations to illustrate the theoretical findings.

In this paper, multi-dimensional extension and additional properties of already proposed extraction methods of buried one-dimensional signals in noise are developed. It is shown that heavy denoising uses no a-priori information, works without averaging or smoothing in the time or frequency domain with computation times much lower than those needed by ensemble averaging operations. Extraction is achieved independently of the nature of noise and locations of its spectral extent. Heavy denoising performances, comparative results with wavelets and other denoising algorithms, are illustrated via buried two-dimensional signals and images in noise. Proposed restoration of buried images in mixed sources of noise is able to preserve image information carried by fine structure, edges and texture. This ability opens novel perspectives for image restoration.

Active Noise Control (ANC) methods have been successfully applied to the cancellation of stationary noise. Classical ANC systems use adaptive filtering techniques to produce a waveform that is opposite, or counter-phase, to the signal noise we would like to cancel. However, when the noise is of short duration, adaptive filtering cannot be used since convergence is not achieved. In this paper, a novel active control technique for non-stationary noise is presented. The method uses wave field synthesis (WFS) for the construction of the canceling waveform. The system is tailored for an outdoor environment. The noise acoustic field is acquired by microphones and processed by a WFS engine to pilot a linear array of secondary sources. Experimental results, obtained from both simulations and true tests, demonstrate that the proposed method is able to diminish the overall noise perceived in the area covered by the system.

In this paper, a new variational Bayesian (VB) learning algorithm is proposed to remove sparse impulsive noise from speech signals. The clean signal is modeled using an autoregressive (AR) model on frame basis. The contaminated signal is modeled as the sum of the AR model of the clean speech signal, a sparse noise term and a dense Gaussian noise term. The sparse noise and the dense Gaussian noise terms model the large additive values caused by the impulsive noise and the small additive values or Gaussian noise, respectively. A hierarchical Bayesian model is constructed for the contaminated signal and a VB framework is used to estimate the parameters of the model. The AR model parameter estimation, the speech signal recovery and the sparse impulsive noise removal are carried out simultaneously. The proposed algorithm starts from random initial values and it does not require training and a threshold as compared to other methods. Experiments are performed using a standard speech database and impulsive noise generated from a probabilistic impulsive noise model and real impulsive noise. The comparison of obtained results with other methods demonstrates the performance of the proposed method.

In actual fault diagnosis, useful information is often submerged in heavy noise, and the feature information is difficult to extract. Traditional methods, such like stochastic resonance (SR), which using noise to enhance weak signals instead of suppressing noise, failed in chaotic background. Neural network, which use reference sequence to estimate and reconstruct the background noise, failed in white Gaussian noise. To solve these problems, a novel weak signal detection method aimed at the problem of detecting impact signal buried under heavy chaotic and Gaussian background noise is proposed. First, the proposed method obtains the virtual reference sequence by constructing the Hankel data matrix. Then an M-order optimal FIR filter is designed, which can minimize the output power of background noise and pass the weak periodic signal undistorted. Finally, detection and reconstruction of the weak periodic signal are achieved from the output SBNR (signal to background noise ratio). The simulation shows, compared with the stochastic resonance (SR) method, the proposed method can detect the weak periodic signal in chaotic noise background while stochastic resonance (SR) method cannot. Compared with the neural network method, (a) the proposed method does not need a reference sequence while neural network method needs one; (b) the proposed method can detect the weak periodic signal in white Gaussian noise background while the neural network method fails, in chaotic noise background, the proposed method can detect the weak periodic signal under a lower SBNR (about 8–17 dB lower) than the neural network method; (c) the proposed method can reconstruct the weak periodic signal precisely.

In this paper, we propose a novel method for estimating clean speech from a single channel transient noise corrupted speech. In the proposed method we assume that speech spectrogram is both sparse and has temporal continuity property, and transient noise spectrogram is both sparse and has spectral continuity property. Based on these assumptions, we define a novel regularization model with sparsity and continuity imposing regularization terms for transient noise reduction. Then we solve the proposed model via alternating direction method of multipliers (ADMM) and derive an efficient iterative algorithm. Based on the assumption that transient noise spectrogram is low rank, we construct a binary mask that specifies locations of the transients and apply it in the proposed algorithm to achieve better separation results. Our method straightforwardly estimates speech and is free of noise power spectral density (PSD) estimation and does not need any pre-trained models of speech or noise. Experiments with various types of transient noises demonstrate effectiveness of the proposed method.

The widely studied subspace and linear filtering methods for noise reduction require the noise correlation matrix to be invertible. In certain application scenarios, however, this matrix is either rank deficient or very ill conditioned, so this requirement cannot be fulfilled. In this paper, we investigate possible solutions to this important problem based on subspace techniques for single-channel time-domain noise reduction. The eigenvalue decomposition is applied to both the speech and noise correlation matrices to separate the null and nonnull subspaces. Then, a set of optimal and suboptimal filters are derived from the nullspace of the noise signal. Through simulations, we observe that the proposed filters are able to significantly reduce noise without introducing much distortion to the desired signal. In comparison with the conventional Wiener approach, the developed filters perform significantly better in improving both the signal-to-noise ratio (SNR) and the perceptual evaluation of speech quality (PESQ) score when the noise correlation matrix is rank deficient.

Linear coherent noise attenuation is a troublesome problem in a variety of seismic exploration areas. Traditional methods often use the differences in frequency, wavenumber, or amplitude to separate the useful signal and coherent noise. However, the application of traditional methods is limited or even invalid when the aforementioned differences between useful signal and coherent noise are too small to be distinguished. For this reason, we have managed to develop a new algorithm from the differences in the shape of seismic waves, and thus, introduce mathematical morphological filtering (MMF) into coherent noise attenuation. The morphological operation is calculated in the trace direction of a rotating coordinate system. This rotating coordinate system is along the direction of the trajectory of coherent noise to make the energy of the coherent noise distributed along the horizontal direction. The MMF approach is more effective than mean and median filters in rejecting abnormal values and causes fewer artifacts compared with [Formula: see text]-[Formula: see text] filtering. Our technique requires that coherent noise can be picked successfully. Application of our technique on synthetic and field seismic data demonstrates its successful performance.

A leading edge noise prediction methodology that uses an advanced digital filter method to generate synthetic turbulence is presented for efficient two- and three-dimensional simulations. The digital filter method combines the advantages of the Random Particle-Mesh method, for the mathematical background, and synthetic eddy methods, for the numerical implementation. This allows the generation of non-periodic turbulence without explicitly filtering white noise signals, and gives a significant reduction in the number of constraint parameters and random numbers involved in comparison with previous methods. A new eddy profile is defined through a superposition of Gaussian eddies that matches a target isotropic energy spectrum. The method is used in a linearised Euler equation solver to predict turbulence-aerofoil interaction noise from a number of configurations, including variations in aerofoil thickness, angle of attack and Mach number. A comparison with stochastic turbulence based on Fourier modes indicates that noise predictions are independent of the choice of synthetic turbulence method, provided that streamwise and transverse turbulent velocity components are included. Nevertheless, the advanced digital filter method is advantageous due to its reduced computational cost. This paper also extends the advanced digital filter method to realise a two-dimensional turbulent flow with the key statistics of three-dimensional turbulence, which is suitable to perform low-cost leading edge noise predictions that can be compared with experiments. Tests show that this approach is capable of reproducing experimental noise measurements to within an accuracy of 3 dB, and predicts similar noise levels to fully three-dimensional simulations.

Random noise elimination acts as an important role in the seismic signal processing. Generally, noise in seismic data can be divided into two categories of coherent and incoherent or random noise. Suppression of wide-band noise which is characterized by random oscillation in seismic data over time is one of the challenging issues in the seismic data processing. This paper describes a new noise suppression algorithm for seismic data denoising. The seismic data, trace-by-trace are transformed into sparse subspace using the synchrosqueezed wavelet transform, then the obtained sparse time-frequency representation is decomposed into semilow-rank and sparse components using the Optshrink algorithm. Finally, the denoised seismic trace can be recovered by back-transforming the semilow-rank component to the time domain using inverse synchrosqueezed wavelet transform. The proposed method is assessed using a single synthetic seismic trace and a synthetic seismic section with two crossover linear and curve events with two discontinuities that are buried in the random noise. We have also evaluated the method using a prestack real seismic data set from an oil field in the southwest of Iran. A comparison is performed between the proposed method and the semisoft GoDec algorithm, classical f-x singular spectrum analysis, and prediction Wiener filter. The results visually and quantitatively confirmed the superiority of the proposed method in contrast to the other well-established noise reduction methods.

Estimating image noise levels is a critical task for many image processing applications, where the detection of homogeneous regions always plays a key role. Most conventional methods empirically divide the images into rectangular blocks and then select the most homogeneous ones. However, this approach may result in erroneous homogeneity detection, especially in the case of highly textured images. To address this challenge, a spatially cohesive superpixel model is proposed in this paper, which can decompose a noisy image into patches that adhere to local structures and hence tend to exhibit increased homogeneity. A new similarity measure is also defined, to make the superpixel model more robust to noise. Combined with histogram-based homogeneous superpixel selection and filter-based noise level calculations, our method can accurately estimate the noise level of images with various noise intensities and different image complexities. Moreover, the method is extended to the signal-dependent noise case, which is usually the case of hyperspectral images. Experiments demonstrate that the proposed method outperforms the state-of-the-art methods.

We propose a new procedure for white noise testing of a functional time series. Our approach is based on an explicit representation of the L2-distance between the spectral density operator and its best (L2-)approximation by a spectral density operator corresponding to a white noise process. The estimation of this distance can be easily accomplished by sums of periodogram kernels, and it is shown that an appropriately standardized version of the estimator is asymptotically normal distributed under the null hypothesis (of functional white noise) and under the alternative. As a consequence, we obtain a very simple test (using the quantiles of the normal distribution) for the hypothesis of a white noise functional process. In particular, the test does not require either the estimation of a long-run variance (including a fourth order cumulant) or resampling procedures to calculate critical values. Moreover, in contrast to all other methods proposed in the literature, our approach also allows testing for ‘relevant’ deviations from white noise and constructing confidence intervals for a measure that measures the discrepancy of the underlying process from a functional white noise process.

In this paper, we focus on restoring blurred images with additive noise and multiplicative noise. Based on the statistical property of the Gamma noise, we use a quadratic penalty function technique in order to obtain a component-wise convex model. We employ the alternating minimization method to solve the proposed model and study the convergence of this method. Numerical experiments demonstrate that the proposed model has superior performance in terms of the relative error and the peak signal-to-noise ratio than a state-of-the-art model for restoring blurred images with additive noise and multiplicative noise.

Seismic data are highly corrupted by noise or unwanted energies arising from different kinds of sources. In general, seismic noise can be divided into two categories, namely, coherent noise and random noise, and is treated with essentially different methods. Traditional methods often utilize the differences in frequency, wavenumber, or amplitude to separate signal and noise. However, the application of traditional methods is limited if the above-mentioned differences are too small to distinguish. For this reason, we have proposed a novel morphology-based technique to simultaneously attenuate random noise and coherent noise, i.e., to extract the useful signal. In this technique, we first flatten the signal by normal move out correction or other alternative approaches. For the extraction of the flatten reflections, we propose dual-directional mathematical morphological filtering, which can detect morphological information of the seismic waveforms from two orthogonal directions and then separate signal and other unwanted energy utilizing their difference in morphological scales. Application of the proposed technique on synthetic and field data examples demonstrates a successful performance.

This paper studies the hyperspectral image (HSI) denoising problem under the assumption that the signal is low in rank. In this paper, a mixture of Gaussian noise and sparse noise is considered. The sparse noise includes stripes, impulse noise, and dead pixels. The denoising task is formulated as a low-rank tensor recovery (LRTR) problem from Gaussian noise and sparse noise. Traditional low-rank tensor decomposition methods are generally NP-hard to compute. Besides, these tensor decomposition based methods are sensitive to sparse noise. In contrast, the proposed LRTR method can preserve the global structure of HSIs and simultaneously remove Gaussian noise and sparse noise.The proposed method is based on a new tensor singular value decomposition and tensor nuclear norm. The NP-hard tensor recovery task is well accomplished by polynomial time algorithms. The convergence of the algorithm and the parameter settings are also described in detail. Preliminary numerical experiments have demonstrated that the proposed method is effective for low-rank tensor recovery from Gaussian noise and sparse noise. Experimental results also show that the proposed LRTR method outperforms other denoising algorithms on real corrupted hyperspectral data.

In this paper, an effective directional interpolation- and inpainting-based impulse noise removal algorithm is proposed. Firstly, each noisy pixel is classified to either the low-density noise or the middle/high density noise. Secondly, a directional interpolation-based noise removal procedure is proposed to denoise the low-density noise. Thirdly, an inpainting-based noise removal procedure is proposed to denoise the middle/high-density noise. Based on ten typical test images, each image with noise level ranging from 30 to 90%, the experimental results demonstrate that in terms of peak-signal-to-noise-ratio (PSNR), structural similarity index (SSIM), and visual effect, the proposed algorithm has the best quality performance when compared with six state-of-the-art noise removal algorithms.

Estimating variances in noise is of key importance in many image processing applications, such as filtering, enhancement, quality assessment, and detecting forgery. For the existing detection methods that are based on inconsistencies in noise, the conventional approach is to estimate the noise variance of each region first and then identify the regions with extremely higher or lower variance as splicing regions. However, due to the impossibility of completely separating image noise and inherent texture, inevitably, each estimate is overestimated, especially for regions that have more complex textures. In this paper, we consider the issue that the estimation of the noise of each region frequently is inaccurate due to the complexity of the texture of the region. Based on this consideration and motivated by the scoring strategy-based, object-proposal technique, an approach that incorporates the inhomogeneity scoring strategy is proposed to provide a more convincing result to expose image-splicing manipulations. Specifically, first, the image is segmented into small patches, and the noise variance of each patch is computed by using the kurtosis concentration-based pixel-level noise estimation method. Then, the inhomogeneity score is computed using the spectral residual-based saliency measurement method. After using a linear equation fitting based on the estimated sample of variance and the inhomogeneity score of each patch, the suspicious region can be identified by seeking the conjunct patches that are out of the linear constraint. The experimental results demonstrated the efficacy and robustness of the proposed method.

An accurate quantitative noise estimate is required in many image/video processing applications like denoising, computer vision, pattern recognition and tracking. But blind and accurate estimation of noise in an unknown image is a challenging task and hence is an open area of research. We propose the first elegant and novel blind noise estimation method based on random image tile selection and statistical sampling theory for estimating standard deviation of zero mean Gaussian and speckle noise in digital images. Randomly selected samples, i.e., pixels with $$3\times 3$$ neighborhood, are checked for availability of edges in the tile. If there is an edge in the tile at more than one neighboring pixel, the tile is excluded. Only non-edge tiles are used for estimation of noise in the tile and subsequently in the image using the concepts of statistical sampling theory. Finally, we propose a supervised curve fitting approach using the proposed noise estimation model for more accurate estimation of standard deviation of the two types of noise. The proposed technique is computationally efficient as it is a selective random sample-based spatial domain technique. Benchmarking with other contemporary techniques published so far shows that the proposed technique clearly outperforms the others by at least 5% improved noise estimates, over a very wide range of noise.

We present a novel Wiener smoothing filter procedure for pilot-symbol-assisted estimation of oscillator phase noise. The procedure consists of forward and backward first-order infinite impulse response filtering the pilot symbols and combining the filter outputs to generate an estimate of the phase noise. We analyze the mean-square-error performance of this pilot-symbol-assisted forward–backward Wiener smoothing filter (FBWSF) procedure and show its optimality under the assumption that the phase noise is modeled as a first-order autoregressive moving average process. We then apply the FBWSF as a code-aided phase noise compensation technique in an iterative receiver framework. The iterative receiver presented here first estimates phase noise roughly by using the pilot-symbol-assisted FBWSF; then, it refines the estimates with the code-aided version of FBWSF. The resulting receiver achieves excellent error performance at a feasible level of computational complexity.

Objective: In this paper, we present and test a new method for the identification and removal of nonstationary utility line noise from biomedical signals. Methods : The method, band limited atomic sampling with spectral tuning (BLASST), is an iterative approach that is designed to 1) fit nonstationarities in line noise by searching for best-fit Gabor atoms at predetermined time points, 2) self-modulate its fit by leveraging information from frequencies surrounding the target frequency, and 3) terminate based on a convergence criterion obtained from the same surrounding frequencies. To evaluate the performance of the proposed algorithm, we generate several simulated and real instances of nonstationary line noise and test BLASST along with alternative filtering approaches. Results: We find that BLASST is capable of fitting line noise well and/or preserving local signal features relative to tested alternative filtering techniques. Conclusion : BLASST may present a useful alternative to bandpass, notch, or other filtering methods when experimentally relevant features have significant power in a spectrum that is contaminated by utility line noise, or when the line noise in question is highly nonstationary. Significance : This is of particular significance in electroencephalography experiments, where line noise may be present in the frequency bands of neurological interest and measurements are typically of low enough strength that induced line noise can dominate the recorded signals. In conjunction with this paper, the authors have released a MATLAB toolbox that performs BLASST on real, vector-valued signals (available at https://github.com/VisLab/blasst ).

In seismic exploration, random noise suppression is one of the key problems in seismic data processing. For random noise attenuation, the most important thing is the understanding of seismic random noise generation and propagation. Seismic random noise is considered as temporal and spatial random processes, and it can be analyzed only qualitatively for now, due to its high variability. In this paper, we classify seismic random noise sources by their generation factors and simulate the random noise of the desert in West China. According to Green’s function, it can be assumed that seismic random noise sources are point-like sources that are distributed around geophones. A seismic random noise record is taken as the superimposed wave field exited by all the independent sources in a homogeneous isotropy half-infinite surface. Based on the wind vibration theory and preliminary study about ambient vibrations, the noise source functions are determined. We obtain the waveforms of different kinds of noise by solving the inhomogeneous wave equations and analyze the characteristics qualitatively and quantitatively. The seismic synthetic record with a 1.6-s time and 250-m distances is obtained, and the characteristics are compared between the simulated and the real noise record in time domain and space domain, respectively. The comparative results show the same characteristics of the simulated noise and the real noise, which demonstrates the feasibility of the proposed method. According to the noise modeling, it is known that the near-field cultural noise is the main component of the random noise in the desert, on the basis of which complex diffusion filtering is selected. The filtered results by complex diffusion filtering is compared with the results of time–frequency peak filtering, which is a popular filtering method of seismic random noise suppression in recent years. The comparative results show that complex diffusion filtering is more suitable for the noise of the desert in the Tarim Basin. This result proves that seismic random noise modeling can provide the guidance for noise attenuation. It lays a foundation for researching the propagation characteristics and better attenuation of seismic random noise in the future.

In this brief, we report exact analytical and numerical evidence of the occurrence of the stochastic resonance (SR) phenomenon in simple electrical circuits driven by a quadratic Gaussian colored noise and by a Gaussian white noise. As an example, we have used an RL configuration. However, it is clear that the phenomenon occurs in any other configuration governed by the same type of evolution equation. The main result is that the phenomenon occurs with a quadratic colored noise. When noise enters only linearly we have verified that the SR occurs both with colored noise and white noise. The robustness of our results were verified by calculating the variance as a function of time in each case. We believe that the results obtained could be observed in a laboratory experiment using some kind of digital resistance. The white noise limit with quadratic noise was excluded.

Spatial smoothing techniques have been widely used to estimate the directions-of-arrival (DOAs) of coherent signals. However, in general these techniques are derived under the condition of uniform white noise and, therefore, their performance may be significantly deteriorated when nonuniform noise occurs. This motivates us to develop new methods for DOA estimation of coherent signals in nonuniform noise in this paper. In our methods, the noise covariance matrix is first directly or iteratively calculated from the array covariance matrix. Then, the noise component in the array covariance matrix is eliminated to achieve a noise-free array covariance matrix. By mitigating the effect of noise nonuniformity, conventional spatial smoothing techniques developed for uniform white noise can thus be employed to reconstruct a full-rank signal covariance matrix, which enables us to apply the subspace-based DOA estimation methods effectively. Simulation results demonstrate the effectiveness of the proposed methods.

In this paper, the stochastic resonance (SR) phenomenon induced by a multiplicative periodic signal in a forest growth system which is excited by additive Gaussian noise, multiplicative non-Gaussian noise and noise correlation time is investigated. According to the fast descent method, the unified colored noise approximation and the SR theory, the analytical expression of the signal-to-noise ratio (SNR) is derived in the adiabatic limit. Via numerical calculations, each effect of the addictive noise intensity, the multiplicative noise intensity and the departure parameter from the Gaussian noise upon the signal-to-noise ratio (SNR) is discussed. It is shown that the addictive noise intensity always plays a significant role in stimulating the SR phenomenon. Conversely, the multiplicative noise intensity generally plays a remarkable role in restraining the effect of SR in most cases except for the case of M = 0.01 . Moreover, the noise correlation time can also excite the SR effect. On the other hand, the departure parameter from the Gaussian noise and the forest growth rate can produce entirely different effects on the SNR under the different conditions of the system parameters.

Recorded seismic signals are often corrupted by noise. We have developed an automatic noise-attenuation method for single-channel seismic data, based upon high-resolution time-frequency analysis. Synchrosqueezing is a time-frequency reassignment method aimed at sharpening a time-frequency picture. Noise can be distinguished from the signal and attenuated more easily in this reassigned domain. The threshold level is estimated using a general cross-validation approach that does not rely on any prior knowledge about the noise level. The efficiency of the thresholding has been improved by adding a preprocessing step based on kurtosis measurement and a postprocessing step based on adaptive hard thresholding. The proposed algorithm can either attenuate the noise (either white or colored) and keep the signal or remove the signal and keep the noise. Hence, it can be used in either normal denoising applications or preprocessing in ambient noise studies. We tested the performance of the proposed method on synthetic, microseismic, and earthquake seismograms.

Recovering the image corrupted by additive white Gaussian noise (AWGN) and impulse noise is a challenging problem due to its difficulties in an accurate modeling of the distributions of the mixture noise. Many efforts have been made to first detect the locations of the impulse noise and then recover the clean image with image in painting techniques from an incomplete image corrupted by AWGN. However, it is quite challenging to accurately detect the locations of the impulse noise when the mixture noise is strong. In this paper, we propose an effective mixture noise removal method based on Laplacian scale mixture (LSM) modeling and nonlocal low-rank regularization. The impulse noise is modeled with LSM distributions, and both the hidden scale parameters and the impulse noise are jointly estimated to adaptively characterize the real noise. To exploit the nonlocal self-similarity and low-rank nature of natural image, a nonlocal low-rank regularization is adopted to regularize the denoising process. Experimental results on synthetic noisy images show that the proposed method outperforms existing mixture noise removal methods.