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In this paper, we consider the Chiral nonlinear Schödinger equation (CNLSE), where the multiplicative noises term varies arbitrarily over time. This equation defines several edge states of Hall effect characteristics in quantum physics applications. We apply the sine-Gordon expansion method to produce some new stochastic solutions for the CNLSE. Some solitary and dissipative solutions were obtained in the form of rational, envelope and shock structures. We demonstrate how the multiplicative noise and model parameters affects the way the solutions behave. We provide some configurations for the both deterministic and stochastic solutions to illustrate their behaviour. It is known that noise dominates envelope growing, damping, and all wave propagation. As it is achieved, the results presented here are crucial to the development of quantum physics. The proposed methodology can be developed to solve more complex problems in applied science.

Texture is a significant component used for several applications in content-based image retrieval. Any texture classification method aims to map an anonymously textured input image to one of the existing texture classes. Extensive ranges of methods for labeling image texture were proposed earlier. However, computing the performance of these methods in the presence of various degradations is always an open area of discussion. Image noise is always a dominant factor among various image degradation factors, affecting the performance of these methods and making texture classification challenging. Therefore, it is essential to investigate the interpretation of these methods in the presence of prominent degradation factors such as noise. Applications for Segmentation-Based Fractal Texture Features (SFTF) include image classification, texture generation, and medical image analysis. They are beneficial for examining textures with intricate, erratic patterns that are difficult to characterize using conventional statistical techniques accurately. This paper assesses two texture feature extraction methods based on SFTF and statistical moment-based texture features in the presence and absence of Gaussian noise. The SFTF and statistical moments-based handcrafted features are passed to a multilayer feed-forward neural network for classification. These models are evaluated on natural textures from Kylberg Texture Dataset 1.0. The results show the superiority of segmentation-based fractal analysis over other approaches. The average accuracy rates using the SFTF are 99% and 97% in the absence and presence of Gaussian noise, respectively.

Rank-reduction methods are effective for separating random noise from the useful seismic signal based on the truncated singular value decomposition (TSVD). However, the results that the TSVD operator provides are still a mixture of noise and signal subspaces. This problem can be solved using the damped rank-reduction method by damping the singular values of noise-contaminated signals. When the seismic data include highly linear or curved events, the rank should be large enough to preserve the details of the useful signal. However, the damped rank-reduction operator becomes less powerful when using a large rank parameter. Hence, the denoised data contain significant remaining noise. More recently, the optimally damped rank-reduction method has been proposed to solve the extra noise problem as the rank value increases. The optimally damped rank-reduction operator works well for a moderately large rank, but becomes ineffective for a very large rank. We introduce an adaptive damped rank-reduction algorithm to attenuate the residual noise for a very large rank parameter. To elaborate on the proposed algorithm, we first construct a gain matrix by only using the input rank parameter, which we introduce directly into the adaptive singular-value weighting formula to make it more stable as the rank parameter becomes too large. Then, we derive a damping operator based on the improved optimal weighting operator to attenuate the residual noise. The proposed method, which can be regarded as an improved version of the optimally damped rank-reduction method, is insensitive to the input parameter. Examples of synthetic and real three-dimensional seismic data show the denoising improvement using the proposed method.

Seismic data analysis often faces the challenge of random noise contamination from various sources. To overcome this, innovative noise attenuation methods utilizing seismic signal properties are needed. This study focuses on efficiently suppressing random noise in the domain of time and frequency by accurately estimating instantaneous frequency using the single-valued group delay characteristic of seismic signals. The time-reassigned synchrosqueezing transform (TSST) and its second-order variant (TSST2) offer high-resolution time-frequency representations (TFRs) for noise suppression. Expanding on these advancements, we propose an efficient noise suppression method that integrates the adaptive thresholding model into the TSST2 framework and employs sparse representation of the TFR through low-rank estimation. This method effectively attenuates noise while preserving essential signal information. The proposed approach operates trace by trace on recorded data, initially transforming it into a sparse subspace using TSST2. The adaptive thresholding model then decomposes the resulting TFR into sparse and semi-low-rank components, achieving a high-resolution and sparse TFR for efficient separation of noise and signal. After noise suppression, the seismic data can be fully reconstructed by inversely transforming the semi-low-rank component data into the time domain. This method addresses previous limitations in noise attenuation techniques and provides a practical solution for enhancing seismic data quality.

Seismic denoising from a corrupted observation is an important part of seismic data processing which improves the signal-to-noise ratio (SNR) and resolution. In this paper, we present an effective denoising method to attenuate seismic random noise. The method takes advantage of shearlet and total generalized variation (TGV) regularization. Different regularity levels of TGV improve the quality of the final result by suppressing Gibbs artifacts caused by the shearlet. The problem is formulated as mixed constraints in a convex optimization. A Bregman algorithm is proposed to solve the proposed model. Extensive experiments based on one synthetic datum and two post-stack field data are done to compare performance. The results demonstrate that the proposed method provides superior effectiveness and preserve the structure better.

We investigate the peak-power limited (PPL) Additive White Gaussian Noise (AWGN) channels in which the signal is band-limited, and its instantaneous power cannot exceed the power P. This model is relevant to many communication systems; however, its capacity is still unknown. We use a new geometry-based approach which evaluates the maximal entropy of the transmitted signal by assessing the volume of the body, in the space of Nyquist-rate samples, comprising all the points the transmitted signal can reach. This leads to lower bounds on capacity which are tight at high Signal to Noise Ratios (SNRs). We find lower bounds on capacity, expressed as power efficiency, that were higher than the known ones by a factor of 3.3 and 8.6 in the low-pass and the band-pass cases, respectively. The gap to the upper bounds is reduced to a power ratio of 1.5. The new bounds are numerically evaluated for FDMA-style signals with limited duration and also are derived in the general case as a conjecture. The penalty in power efficiency due to the peak power constraint is roughly 6 dB at high SNRs. Further research is needed to develop effective modulation and coding for this channel.

Random noise attenuation is an important step in seismic data processing. In this paper, we propose a novel denoising approach based on compressive sensing and the curvelet transform. We formulate the random noise attenuation problem as an L1 norm regularized optimization problem. We propose to use the curvelet transform as the sparse transform in the optimization problem to regularize the sparse coefficients in order to separate signal and noise and to use the gradient projection for sparse reconstruction (GPSR) algorithm to solve the formulated optimization problem with an easy implementation and a fast convergence. We tested the performance of our proposed approach on both synthetic and field seismic data. Numerical results show that the proposed approach can effectively suppress the distortion near the edge of seismic events during the noise attenuation process and has high computational efficiency compared with the traditional curvelet thresholding and iterative soft thresholding based denoising methods. Besides, compared with f-x deconvolution, the proposed denoising method is capable of eliminating the random noise more effectively while preserving more useful signals.

Temporal random noise (TRN) in uncooled infrared detectors significantly degrades image quality. Existing denoising techniques primarily address fixed-pattern noise (FPN) and do not effectively mitigate TRN. Therefore, a novel TRN denoising approach based on total variation regularization and low-rank tensor decomposition is proposed. This method effectively suppresses temporal noise by introducing twisted tensors in both horizontal and vertical directions while preserving spatial information in diverse orientations to protect image details and textures. Additionally, the Laplacian operator-based bidirectional twisted tensor truncated nuclear norm (bt-LPTNN), is proposed, which is a norm that automatically assigns weights to different singular values based on their importance. Furthermore, a weighted spatiotemporal total variation regularization method for nonconvex tensor approximation is employed to preserve scene details. To recover spatial domain information lost during tensor estimation, robust principal component analysis is employed, and spatial information is extracted from the noise tensor. The proposed model, bt-LPTVTD, is solved using an augmented Lagrange multiplier algorithm, which outperforms several state-of-the-art algorithms. Compared to some of the latest algorithms, bt-LPTVTD demonstrates improvements across all evaluation metrics. Extensive experiments conducted using complex scenes underscore the strong adaptability and robustness of our algorithm.

Many denoising methods model noise as Gaussian noise. However, the realistic noise captured by camera devices does not satisfy Gaussian distribution. Hence, those methods do not perform well when being applied to real-world image denoising tasks. In this work, we indicate that the spatial correlation in noise and the variation of noise intensity are the main factors that impact the performance of Gaussian noise-based methods, and accordingly propose an extension of the method based on the weighted, mixed non-convex ℓp norm. The proposed method first strengthens the intensity of the noise pattern in the original denoising result through the Guided Filter, then removes the over-amplified frequency in the local area by the proposed regularization term. We prove that the optimal solution can be achieved through the sub-gradient-based iterative optimization scheme, and further reduce the computational cost by optimizing the initial values. Numerical experiments show that the proposed extending method can balance well texture preservation and noise removal, and the PSNR of the extending method’s results are greatly improved, even outperforming the recently proposed realistic noise removal methods which also include deep learning based methods.

The recent emergence of the monkeypox virus has attracted significant attention due to its serious effects, including pneumonia, retinal problems, secondary skin infections, and rectal swelling, leading to discomfort and urinary issues. Therefore, accurate identification is crucial, but the lack of comprehensive databases for each condition presents a challenge. Although Generative Adversarial Networks (GANs) show promise for improving data through augmentation, their training is hindered by differences between random noise and image structures. Because GAN-based models take random noise as input for the generators, they must acquire an adaptive function to translate this noise from randomness to meaningful visuals, leads to difficulty in training and converging. To tackle this issue, a new technique is proposed for data augmentation using a Densely Connected Decoder Encoder Generative Adversarial Network (D3EGAN). This approach combines adversarial training with variational Bayesian inference to enhance image production performance. D3EGAN uses a reversed encoder–decoder decoder–encoder framework which is pre-trained to transform random noise into more informative vectors, improving the generator’s learning ability. With this enhanced dataset, advanced deep learning models are employed such as VGG-19, ResNet50, InceptionV3, and EfficientNet to distinguish monkeypox from other diseases. Our study’s results demonstrate significant improvements in image clarity and detection accuracy, surpassing current techniques’ performance. This study highlights the effectiveness of our methodology in improving timely identification and intervention for monkeypox and related diseases, addressing a significant global health issue.