Gaussian Impulse Research Articles

A novel image denoising approach based on a non-convex constrained PDE: application to ultrasound images

In this paper, we are interested in the mathematical and simulation study of a new non-convex constrained PDE to remove the mixture of Gaussian–impulse noise densities. The model incorporates a non-convex data-fidelity term with a fractional constrained PDE. In addition, we adopt a non-smooth primal-dual algorithm to resolve the obtained proximal linearized minimization problem. The non-convex fidelity term is used to handle the high-frequency of the impulse noise component, while the fractional operator enables the efficient denoising of smooth areas, avoiding also the staircasing effect that appears on the relevant variational denoising models. Moreover, the proposed primal-dual algorithm helps in preserving fine structures and texture with good convergence rate. Numerical experiments, including ultrasound images, show that the proposed non-convex constrained PDE produces better denoising results compared to the state-of-the-art denoising models.

LR-Net: Low-Rank Spatial-Spectral Network for Hyperspectral Image Denoising.

Due to the physical limitations of the imaging devices, hyperspectral images (HSIs) are commonly distorted by a mixture of Gaussian noise, impulse noise, stripes, and dead lines, leading to the decline in the performance of unmixing, classification, and other subsequent applications. In this paper, we propose a novel end-to-end low-rank spatial-spectral network (LR-Net) for the removal of the hybrid noise in HSIs. By integrating the low-rank physical property into a deep convolutional neural network (DCNN), the proposed LR-Net simultaneously enjoys the strong feature representation ability from DCNN and the implicit physical constraint of clean HSIs. Firstly, spatial-spectral atrous blocks (SSABs) are built to exploit spatial-spectral features of HSIs. Secondly, these spatial-spectral features are forwarded to a multi-atrous block (MAB) to aggregate the context in different receptive fields. Thirdly, the contextual features and spatial-spectral features from different levels are concatenated before being fed into a plug-and-play low-rank module (LRM) for feature reconstruction. With the help of the LRM, the workflow of low-rank matrix reconstruction can be streamlined in a differentiable manner. Finally, the low-rank features are utilized to capture the latent semantic relationships of the HSIs to recover clean HSIs. Extensive experiments on both simulated and real-world datasets were conducted. The experimental results show that the LR-Net outperforms other state-of-the-art denoising methods in terms of evaluation metrics and visual assessments. Particularly, through the collaborative integration of DCNNs and the low-rank property, the LR-Net shows strong stability and capacity for generalization.

Performance evaluation of de-noised medical images after removing speckled noise by wavelet transform

In the healthcare community, the quality of the medical image is of prime concern to make accurate observations for diagnosis. Different types of noise such as Gaussian noise, impulse noise and spe...

Mixed Noise Removal Using Adaptive Median Based Non-Local Rank Minimization

In this paper, we present an innovative mechanism for image restoration problems in which the image is corrupted by a mixture of additive white Gaussian noise (AWGN) and impulse noise (IN). Mixed noise removal is much more challenging problem in contrast to the problems where either only one type of noise model (either Gaussian or impulse) is involved. Several well-known and efficient algorithms exist to effectively remove either Gaussian noise or Impulse noise, independently. However, in practice, noise may occur as a mixture of such noise models. Thus, the existing techniques devised to handle individual types of noise may not perform well. Moreover, the complexity of the problem hinges on the fact that the removal of either type of noise from the given image affects the noise statistics in the residual image. Therefore, a rigorous mechanism is required which not only infers altered noise statistics but also removes the residual noise in an effective manner. In this regard, an innovative approach is introduced to restore the underlying image in three key steps. Firstly, the intensity values, affected by impulsive noise, are identified by analyzing noise statistics with the help of adaptive median filtering. The identified intensity values are then aggregated by exploiting nonlocal data redundancy prior. Thus the first step enables the remaining noise to follow the zero mean Gaussian distribution in the median filtered image. Secondly, we estimate Gaussian noise in the resulting image, which acts as a key parameter in the subsequent singular value thresholding process for rank minimization. Finally, a reduced rank optimization applied to the pre-processed image obtained in the first step. The experimental results indicate that the proposed AMNLRA (Adaptive Median based Non-local Low Rank Approximation) approach can effectively tackle mixed noise complexity as compared to numerous state of the art algorithms.

A new nonlocal means based framework for mixed noise removal

Many image-denoising approaches seek to remove either additive white Gaussian noise (AWGN) or impulse noise (IN), because both types are easier to process when considered separately. However, images can be corrupted by a mixture of AWGN and IN during image acquisition and transmission. The major difficulty of mixed noise removal arises through the complex distribution of noise, which cannot be fitted by a simple parametric model. In this paper, a new nonlocal means based framework (NMF) is proposed. A median-type filter is used to detect the locations of outlier pixels; these pixels are then replaced by their nonlocal means, which makes the mixed noise distribution approximately Gaussian. To prove the effectiveness of our NMF, a low rank approximation combined with NMF (LRNM) model is presented for mixed noise removal. In the LRNM, we group similar nonlocal patches in a matrix and apply a low rank approximation to reconstruct the clean image. Gradient regularization is added to better preserve the image texture details. A convolutional neural network (CNN) combined with the NMF (NMF-CNN) is also presented, to prove the generality of the NMF. Experimental results show that LRNM and NMF-CNN achieve a strong mixed noise removal performance and also produce visually pleasing denoising results.

DeGAN: Mixed noise removal via generative adversarial networks

Restoration of images corrupted by mixed noise (e.g., additive white Gaussian noise and impulse noise) is very difficult due to the complexity of the mixed noise distribution. Various mixed noise removal models involve the preprocessing based on outlier detection. However, the performance of these models largely depends on the accuracy of pixel location detection of outliers, and artifacts and missing image details are prone to occur when the mixture noise is strong. In this paper, a new denoising model based on generative adversarial network (DeGAN) is proposed to remove mixed noise in images. The proposed model combines generator, discriminator, and feature extractor networks. Through the mutual game between the generator and discriminator networks combined with additional training from the feature extractor network, the generator network implements a direct mapping from the noisy image domain to the noise-free image domain. In addition, we design a new joint loss function to incorporate information from image features and human visual perception into the mixed noise elimination task, which further improves the image quality and the visual effect. Abundant experiments show that the performance of our model is better than the state-of-the-art mixed noise removal methods in three different types of mixed noise scenarios, and the joint loss function does improve the denoising performance.

Integrated time-frequency wavelet analysis and impulse response filtering on SASW test for rigid pavement stiffness prediction

This paper employs an improved continuous wavelet transform (CWT) technique of Gaussian derivative function and impulse response filtering (IRF) in seismic surface wave analysis to improve data analysis in the Spectral Analysis of Surface Wave (SASW) method. Two procedures were used: first, the response spectrum of interest was chosen using a time–frequency wavelet spectrogram. Then, noisy distortions were eliminated by utilizing a time–frequency wavelet and impulse response filtering. The outcomes show that the SASW method is able to identify the surface wave velocity which coincides with the dynamic stiffness parameters of Portland Cement Concrete (PCC) slabs. The values of surface wave velocity increased during the curing stage, and in situ measurement of wave velocity could be helpful in determining the degree of curing. A good congruence has been demonstrated between the stiffness of PCC obtained from SASW measurements vis a vis that obtained using the American Concrete Institute (ACI) formulation.

Alpha Stable Distribution Based FARIMA Modeling and Forecasting for Network Traffic Data

Through research on network traffic in recent years, it is found that actual network traffic not only has long correlation but also has heavy-tailed characteristics. The Alpha stable distribution provides a very useful theoretical tool for such processes. According to the nature of the Alpha stable distribution, we need to improve the relevant parameter value method of the Fractional Autoregressive Integrated Moving Average model and improve the prediction accuracy of the model. In this paper, the Alpha stable distribution based Fractional Autoregressive Integrated Moving Average modelling method is introduced, and the validation of the method is analyzed using Fractional Gaussian Noise time series and impulse noise corrupted Fractional Gaussian Noise time series. Finally, the Alpha stable distribution based Fractional Autoregressive Integrated Moving Average model is applied to BC-p Aug89.TL data provided by Bell Labs. The analysis shows that the improved Fractional Autoregressive Integrated Moving Average model has a better prediction effect on actual network traffic and is a more representative research method.

Effect of image noise on the classification of skin lesions using deep convolutional neural networks

Skin lesions are in a category of disease that is both common in humans and a major cause of death. The classification accuracy of skin lesions is a crucial determinant of the success rate of curing lethal diseases. Deep Convolutional Neural Networks (CNNs) are now the most prevalent computer algorithms for the purpose of disease classification. As with all algorithms, CNNs are sensitive to noise from imaging devices, which often contaminates the quality of the images that are fed into them. In this paper, a deep CNN (Inception-v3) is used to study the effect of image noise on the classification of skin lesions. Gaussian noise, impulse noise, and noise made up of a compound of the two are added to an image dataset, namely the Dermofit Image Library from the University of Edinburgh. Evaluations, based on t-distributed Stochastic Neighbor Embedding (t-SNE) visualization, Receiver Operating Characteristic (ROC) analysis, and saliency maps, demonstrate the reliability of the Inception-v3 deep CNN in classifying noisy skin lesion images.

Mixed image denoising using weighted coding and non-local similarity

Denoising an image is a heuristic and objective process. Still, underlying noise that is predominant in the images reduces the quality. Additive white Gaussian noise (AWGN) and impulse noise are the most exploited types of noise. For a specified amount of density, a combination of AWGN and impulse noise may distract the entire signal causing a loss in the magnitude. This paper presents a denoising model by exploiting such a combination that uses an overcomplete dictionary by sparse based denoising scheme with suitable regularization terms. A weight matrix is defined to optimize the operation at specific locations of the image. Finally, the use of non-local similarity features improves the quality of reconstructed images. The weight matrix maps the regions where the effect of multiple noise sources is present. The results proved the superiority of the proposed technique. Simulation of the proposed technique on many images with different quantities of noise produced an improvement of up to 2 dB when the noise effect is more when compared to the state-of-the-art techniques.

BER Performance of Space–Time Parallel ICI Cancellation of OFDM in MIMO Power Line Communications

Most of the studies on power line communication (PLC) are focused on single-input-single output (SISO)-PLC. There have been recent empirical and/or theoretical research with the focus on multiple-input-multiple-output (MIMO)-PLC. This article analyzes the effects of correlation between different paths in MIMO-PLC on the performance of bit error rate (BER) and the channel capacity in the PLC system. Orthogonal frequency division multiplexing (OFDM) is an effective method to mitigate the effect of the frequency selective multipath fading channel in the PLC system. However, OFDM is susceptible to the imperfect orthogonality among its subcarriers caused by the frequency offset at the receiver. Intercarrier interference cancellation technique such as parallel cancellation (PC) scheme is implemented in MIMO-PLC scenario to study the effect of correlation based on the latest research in MIMO-PLC. 2 × 1 and 2 × 2 space-time (ST)-OFDM and 2 × 2 STPC-OFDM channel models are investigated for the performance of the BER and channel capacity in additive impulsive Gaussian noise via computer simulations. It shows that the BER and channel capacity of both 2 × 1 and 2 × 2 STPC-OFDM outperforms 2 × 1 and 2 × 2 ST-OFDM, respectively, regardless of the correlation between different paths in MIMO-PLC.

Hyperspectral Mixed Noise Removal By $\ell _1$-Norm-Based Subspace Representation

This article introduces a new hyperspectral image (HSI) denoising method that is able to cope with additive mixed noise, i.e., mixture of Gaussian noise, impulse noise, and stripes, which usually corrupt hyperspectral images in the acquisition process. The proposed method fully exploits a compact and sparse HSI representation based on its low-rank and self-similarity characteristics. In order to deal with mixed noise having a complex statistical distribution, we propose to use the robust $\ell _1$ data fidelity instead of using the $\ell _2$ data fidelity, which is commonly employed for Gaussian noise removal. In a series of experiments with simulated and real datasets, the proposed method competes with state-of-the-art methods, yielding better results for mixed noise removal.

Hyperspectral Image Denoising via Subspace Low-rank Representation and Spatial–spectral Total Variation

Abstract Hyperspectral images (HSIs) acquired actually often contain various types of noise, such as Gaussian noise, impulse noise, and dead lines. On the basis of land covers, the spectral vectors in HSI can be separated into different classifications, which means the spectral space can be regarded as a union of several low-rank (LR) subspaces rather than a single LR subspace. Recently, LR constraint has been widely applied for denoising HSI. However, those LR-based methods do not constrain the intrinsic structure of spectral space. And these methods cannot make better use of the spatial or spectral features in an HSI cube. In this article, a framework named subspace low-rank representation combined with spatial‐spectral total variation regularization (SLRR-SSTV) is proposed for HSI denoising, where the SLRR is introduced to more precisely satisfy the low-rank property of spectral space, and the SSTV regularization is involved for the spatial and spectral smoothness enhancement. An inexact augmented Lagrange multiplier method by alternative iteration is employed for the SLRR-SSTV model solution. Both simulated and real HSI experiment results demonstrate that the proposed method can achieve a state-of-the-art performance in HSI denoising.

Интегральное представление решения задачи о дифракции акустического импульса в секторе с углом 2Pi/n и его численная аппроксимация

Интегральное представление решения задачи о дифракции акустического импульса в секторе с углом 2Pi/n и его численная аппроксимация

Численное вычисление решений задач о распаде гауссового импульса и дифракции на углу 2π/n

Численное вычисление решений задач о распаде гауссового импульса и дифракции на углу 2π/n

Performance Evaluation of Sc-IDMA & Of DM- IDMA in Impulsive Media

In this paper, we analyzed the working phenomenon of Single and Multi carrier IDMA in Non Gaussian Impulsive medium and also compared their relative performances. The performance comparison is evaluated under the following constraints; by varying the iteration count, impulsive constant, control parameters and no. of users etc. The multi user detection for these schemes can be realized with complexity (per user) strictly independent of number of users. The simulation result concludes that multicarrier IDMA outperforms the single carrier IDMA in impulsive non Gaussian channel as a medium.

Block-Structured Compressed Spectrum Sensing With Gaussian Mixture Noise Distribution

In real cognitive radio systems, the additive noise does not always follow Gaussian distribution, e.g., man-made noise and impulse noise. This letter addresses the problem of sparse spectrum sensing when the additive noise follows Gaussian mixture distribution. What is more, the key parameter of the distribution is unknown. By introducing a prior variable that can control the block sparse structure of the solution, the prior knowledge of the block structure of the signal of the primary users is effectively explored. All of the unknown variables are calculated in iterative manner with closed form based on the theory of vibrational message passing. Simulation results show that the proposed algorithm is robust to Gaussian mixture noise and can obtain better performance.

Hyperspectral Image Denoising via Matrix Factorization and Deep Prior Regularization.

Deep learning has been successfully introduced for 2D-image denoising, but it is still unsatisfactory for hyperspectral image (HSI) denosing due to the unacceptable computational complexity of the end-to-end training process and the difficulty of building a universal 3D-image training dataset. In this paper, instead of developing an end-to-end deep learning denoising network, we propose a hyperspectral image denoising framework for the removal of mixed Gaussian impulse noise, in which the denoising problem is modeled as a convolutional neural network (CNN) constrained non-negative matrix factorization problem. Using the proximal alternating linearized minimization, the optimization can be divided into three steps: the update of the spectral matrix, the update of the abundance matrix and the estimation of the sparse noise. Then, we design the CNN architecture and proposed two training schemes, which can allow the CNN to be trained with a 2D-image dataset. Compared with the state-of-the-art denoising methods, the proposed method has relatively good performance on the removal of the Gaussian and mixed Gaussian impulse noises. More importantly, the proposed model can be only trained once by a 2D-image dataset, but can be used to denoise HSIs with different numbers of channel bands.

Adaptation Strategies for Applying AWGN-Based Denoiser to Realistic Noise

Discriminative learning based denoising model trained with Additive White Gaussian Noise (AWGN) performs well on synthesized noise. However, realistic noise can be spatialvariant, signal-dependent and a mixture of complicated noises. In this paper, we explore multiple strategies for applying an AWGN-based denoiser to realistic noise. Specifically, we trained a deep network integrating noise estimating and denoiser with mixed Gaussian (AWGN) and Random Value Impulse Noise (RVIN). To adapt the model to realistic noises, we investigated multi-channel, multi-scale and super-resolution approaches. Our preliminary results demonstrated the effectiveness of the newly-proposed noise model and adaptation strategies.

Hyperspectral Images Denoising via Nonconvex Regularized Low-Rank and Sparse Matrix Decomposition.

Hyperspectral images (HSIs) are often degraded by a mixture of various types of noise during the imaging process, including Gaussian noise, impulse noise, and stripes. Such complex noise could plague the subsequent HSIs processing. Generally, most HSI denoising methods formulate sparsity optimization problems with convex norm constraints, which over-penalize large entries of vectors, and may result in a biased solution. In this paper, a nonconvex regularized low-rank and sparse matrix decomposition (NonRLRS) method is proposed for HSI denoising, which can simultaneously remove the Gaussian noise, impulse noise, dead lines, and stripes. The NonRLRS aims to decompose the degraded HSI, expressed in a matrix form, into low-rank and sparse components with a robust formulation. To enhance the sparsity in both the intrinsic low-rank structure and the sparse corruptions, a novel nonconvex regularizer named as normalized ε -penalty, is presented, which can adaptively shrink each entry. In addition, an effective algorithm based on the majorization minimization (MM) is developed to solve the resulting nonconvex optimization problem. Specifically, the MM algorithm first substitutes the nonconvex objective function with the surrogate upper-bound in each iteration, and then minimizes the constructed surrogate function, which enables the nonconvex problem to be solved in the framework of reweighted technique. Experimental results on both simulated and real data demonstrate the effectiveness of the proposed method.