Unknown Noise Level Research Articles

Diffusion models for multidimensional seismic noise attenuation and superresolution

Seismic data quality proves pivotal to its interpretation, necessitating the reduction of noise and enhancement of resolution. Traditional and deep-learning-based solutions have achieved varying degrees of success on low-dimensional seismic data. We develop a deep generative solution for high-dimensional seismic data denoising and superresolution through the innovative application of denoising diffusion probabilistic models (DDPMs), which we refer to as MD Diffusion. MD Diffusion treats degraded seismic data as a conditional prior that guides the generative process, enhancing the capability to recover data from complex noise. By iteratively training an implicit probability model, we achieve a sampling speed 10 times faster than the original DDPM. Extensive training allows us to explicitly model complex seismic data distributions in synthetic data sets to transfer this knowledge to the process of recovering field data with unknown noise levels, thereby attenuating the noise and enhancing the resolution in an unsupervised manner. Quantitative metrics and qualitative results for 3D synthetic and field data demonstrate that MD Diffusion exhibits superior performance in high-dimensional seismic data denoising and superresolution compared with the UNet and seismic superresolution methods, especially in enhancing thin-layer structures and preserving fault features, and indicates the potential for application to higher-dimensional data.

Research and Implementation of Denoising Algorithm for Brain MRIs via Morphological Component Analysis and Adaptive Threshold Estimation

The inevitable noise generated in the acquisition and transmission process of MRIs seriously affects the reliability and accuracy of medical research and diagnosis. The denoising effect for Rician noise, whose distribution is related to MR image signal, is not good enough. Furthermore, the brain has a complex texture structure and a small density difference between different parts, which leads to higher quality requirements for brain MR images. To upgrade the reliability and accuracy of brain MRIs application and analysis, we designed a new and dedicated denoising algorithm (named VST–MCAATE), based on their inherent characteristics. Comparative experiments were performed on the same simulated and real brain MR datasets. The peak signal-to-noise ratio (PSNR), and mean structural similarity index measure (MSSIM) were used as objective image quality evaluation. The one-way ANOVA was used to compare the effects of denoising between different approaches. p < 0.01 was considered statistically significant. The experimental results show that the PSNR and MSSIM values of VST–MCAATE are significantly higher than state-of-the-art methods (p < 0.01), and also that residual images have no anatomical structure. The proposed denoising method has advantages in improving the quality of brain MRIs, while effectively removing the noise with a wide range of unknown noise levels without damaging texture details, and has potential clinical promise.

Synthetic Aperture Radar Image Despeckling Based on a Deep Learning Network Employing Frequency Domain Decomposition

Synthetic aperture radar (SAR) images are inevitably interspersed with speckle noise due to their coherent imaging mechanism, which greatly hinders subsequent related research and application. In recent studies, deep learning has become an effective tool for despeckling remote sensing images. However, preserving more texture details while removing speckle noise remains a challenging task in the field of SAR image despeckling. Furthermore, most despeckling algorithms are designed specifically for a specific look and seriously lack generalizability. Therefore, in order to remove speckle noise in SAR images, a novel end-to-end frequency domain decomposition network (SAR−FDD) is proposed. The method first performs frequency domain decomposition to generate high-frequency and low-frequency information. In the high-frequency branch, a mean filter is employed to effectively remove noise. Then, an interactive dual-branch framework is utilized to learn the details and structural information of SAR images, effectively reducing speckles by fully utilizing features from different frequencies. In addition, a blind denoising model is trained to handle noisy SAR images with unknown noise levels. The experimental results demonstrate that the SAR−FDD achieves good visual effects and high objective evaluation metrics on both simulated and real SAR test sets (peak signal-to-noise ratio (PSNR): 27.59 ± 1.57 and structural similarity index (SSIM): 0.78 ± 0.05 for different speckle noise levels), demonstrating its strong denoising performance and ability to preserve edge textures.

A Lightweight Ultrasound Image Denoiser Using Parallel Attention Modules and Capsule Generative Adversarial Network

The quality of ultrasound (US) imaging has been constrained by its limited contrast and resolution, inherent speckle noise, and the presence of other artifacts. Existing traditional and deep learning-based US denoising approaches have many limitations, such as reliance on manual parameter configurations, poor performance for unknown noise levels, the requirement for a large number of training data, and high computational expense. To address these challenges, we propose a novel Generative Adversarial Network (GAN) based denoiser. Capsule networks are utilized in both the generator and discriminator of the proposed GAN to capture intricate sparse features with less complexity. In addition, bias components are removed from all neurons of the generator to handle the unknown noise levels. A parallel attention module is also included in the proposed model to further enhance denoising performance. The proposed approach is trained in a semi-supervised manner and can thus be trained with fewer labeled images. Experimental evaluation on publicly available HC18 and BUSI datasets showed that the proposed approach achieved state-of-the-art denoising performance, with PSNR values of 33.86 and 34.16, and SSIM indices of 0.91 and 0.90, respectively. Moreover, experiments showed that the proposed approach is lightweight and more than twice as fast as similar denoisers.

Seismic arrival-time picking on distributed acoustic sensing data using semi-supervised learning

Distributed Acoustic Sensing (DAS) is an emerging technology for earthquake monitoring and subsurface imaging. However, its distinct characteristics, such as unknown ground coupling and high noise level, pose challenges to signal processing. Existing machine learning models optimized for conventional seismic data struggle with DAS data due to its ultra-dense spatial sampling and limited manual labels. We introduce a semi-supervised learning approach to address the phase-picking task of DAS data. We use the pre-trained PhaseNet model to generate noisy labels of P/S arrivals in DAS data and apply the Gaussian mixture model phase association (GaMMA) method to refine these noisy labels and build training datasets. We develop PhaseNet-DAS, a deep learning model designed to process 2D spatio-temporal DAS data to achieve accurate phase picking and efficient earthquake detection. Our study demonstrates a method to develop deep learning models for DAS data, unlocking the potential of integrating DAS in enhancing earthquake monitoring.

Energy-Limited Joint Source-Channel Coding of Gaussian Sources over Gaussian Channels with Unknown Noise Level.

We consider the problem of transmitting a Gaussian source with minimum mean square error distortion over an infinite-bandwidth additive white Gaussian noise channel with an unknown noise level and under an input energy constraint. We construct a universal joint source-channel coding scheme with respect to the noise level, that uses modulo-lattice modulation with multiple layers. For each layer, we employ either analog linear modulation or analog pulse-position modulation (PPM). We show that the designed scheme with linear layers requires less energy compared to existing solutions to achieve the same quadratically increasing distortion profile with the noise level; replacing the linear layers with PPM layers offers an additional improvement.

Medical Image Despeckling Using the Invertible Sparse Fuzzy Wavelet Transform with Nature-Inspired Minibatch Water Wave Swarm Optimization.

Speckle noise is a pervasive problem in medical imaging, and conventional methods for despeckling often lead to loss of edge information due to smoothing. To address this issue, we propose a novel approach that combines a nature-inspired minibatch water wave swarm optimization (NIMWVSO) framework with an invertible sparse fuzzy wavelet transform (ISFWT) in the frequency domain. The ISFWT learns a non-linear redundant transform with a perfect reconstruction property that effectively removes noise while preserving structural and edge information in medical images. The resulting threshold is then used by the NIMWVSO to further reduce multiplicative speckle noise. Our approach was evaluated using the MSTAR dataset, and objective functions were based on two contrasting reference metrics, namely the peak signal-to-noise ratio (PSNR) and the mean structural similarity index metric (MSSIM). Our results show that the suggested approach outperforms modern filters and has significant generalization ability to unknown noise levels, while also being highly interpretable. By providing a new framework for despeckling medical images, our work has the potential to improve the accuracy and reliability of medical imaging diagnosis and treatment planning.

Detection of ovarian follicles cancer cells using hybrid optimization technique with deep convolutional neural network classifier

Having one’s life threatened by a disease like ovarian cancer is the single most crucial thing in the whole world. It is difficult to achieve high performance without sacrificing computational efficiency; the results of the denoising process are not as good as they could be; the proposed models are nonconvex and involve several manually chosen parameters, which provides some leeway to boost denoising performance; the methods generally involve a complex optimisation problem in the testing stage; Here at DnCNN, we’ve developed our own version of the deep ii learning model, a discriminative learning technique. The goal was to eliminate the need for the iterative optimisation technique at the time it was being evaluated. The goal was to avoid having to go through testing altogether, thus this was done. It is highly advised to use a Deep CNN model, the efficacy of which can be evaluated by comparing it to that of more traditional filters and pre-trained DnCNN. The Deep CNN strategy has been shown to be the best solution to minimise noise when an image is destroyed by Gaussian or speckle noise with known or unknown noise levels. This is because Deep CNN uses convolutional neural networks, which are trained using data. This is because convolutional neural networks, which are the foundation of Deep CNN, are designed to learn from data and then use that learning to make predictions. Deep CNN achieves a 98.45% accuracy rate during testing, with an error rate of just 0.002%.

Denoising Generalization Performance of Channel Estimation in Multipath Time-Varying OFDM Systems

Although Orthogonal Frequency Division Multiplexing (OFDM) technology is still the key transmission waveform technology in 5G, traditional channel estimation algorithms are no longer sufficient for the high-speed multipath time-varying channels faced by both existing 5G and future 6G. In addition, the existing Deep Learning (DL) based OFDM channel estimators are only applicable to Signal-to-Noise Ratios (SNRs) in a small range, and the estimation performance of the existing algorithms is greatly limited when the channel model or the mobile speed at the receiver does not match. To solve this problem, this paper proposes a novel network model NDR-Net that can be used for channel estimation under unknown noise levels. NDR-Net consists of a Noise Level Estimate subnet (NLE), a Denoising Convolutional Neural Network subnet (DnCNN), and a Residual Learning cascade. Firstly, a rough channel estimation matrix value is obtained using the conventional channel estimation algorithm. Then it is modeled as an image and input to the NLE subnet for noise level estimation to obtain the noise interval. Then it is input to the DnCNN subnet together with the initial noisy channel image for noise reduction to obtain the pure noisy image. Finally, the residual learning is added to obtain the noiseless channel image. The simulation results show that NDR-Net can obtain better estimation results than traditional channel estimation, and it can be well adapted when the SNR, channel model, and movement speed do not match, which indicates its superior engineering practicability.

Multiple testing and variable selection along the path of the least angle regression

Abstract We investigate multiple testing and variable selection using the Least Angle Regression (LARS) algorithm in high dimensions under the assumption of Gaussian noise. LARS is known to produce a piecewise affine solution path with change points referred to as the knots of the LARS path. The key to our results is an expression in closed form of the exact joint law of a $K$-tuple of knots conditional on the variables selected by LARS, the so-called post-selection joint law of the LARS knots. Numerical experiments demonstrate the perfect fit of our findings. This paper makes three main contributions. First, we build testing procedures on variables entering the model along the LARS path in the general design case when the noise level can be unknown. These testing procedures are referred to as the Generalized $t$-Spacing tests and we prove that they have an exact non-asymptotic level (i.e. the Type I error is exactly controlled). This extends work of [ 31] where the spacing test works for consecutive knots and known variance. Second, we introduce a new exact multiple testing procedure after model selection in the general design case when the noise level may be unknown. We prove that this testing procedure has exact non-asymptotic level for general design and unknown noise level. Third, we prove exact control of the false discovery rate under orthogonal design assumption. Monte-Carlo simulations and a real data experiment are provided to illustrate our results in this case. Of independent interest, we introduce an equivalent formulation of the LARS algorithm based on a recursive function.

Interferogram blind denoising using deep residual learning for phase-shifting interferometry

The interferogram containing the noises often affects the accuracy of phase retrieval, leading to the degradation of the phase imaging quality. To address this issue, a new interferogram blind denoising (IBD) method based on deep residual learning is proposed. In the presence of unknown noise levels, during the training, the deep residual convolutional neural networks (DRCNN) in the IBD approach is able to remove the latent clean interferogram implicitly, and then gradually establish the residual mapping relation in the pixel-level between the interferogram and the noises. With a well-trained DRCNN model, this algorithm can deal not only with the single-frame interferogram efficiently but also with the multi-frame phase-shifted interferograms collaboratively, while effectively retaining interferogram features related to phase retrieval. Simulation and experimental results demonstrate the feasibility and applicability of the proposed IBD method.

Robust instance-optimal recovery of sparse signals at unknown noise levels

Abstract We consider the problem of sparse signal recovery from noisy measurements. Many of frequently used recovery methods rely on some sort of tuning depending on either noise or signal parameters. If no estimates for either of them are available, the noisy recovery problem is significantly harder. The square root LASSO and the least absolute deviation LASSO are known to be noise-blind, in the sense that the tuning parameter can be chosen independent on the noise and the signal. We generalize those recovery methods to the rLASSO and give a recovery guarantee once the tuning parameter is above a threshold. Moreover, we analyze the effect of mistuning on a theoretic level and prove the optimality of our recovery guarantee. Further, for Gaussian matrices, we give a refined analysis of the threshold of the tuning parameter and proof a new relation of the tuning parameter on the dimensions. Indeed, for a certain amount of measurements, the tuning parameter becomes independent on the sparsity. Finally, we verify that the least absolute deviation LASSO can be used with random walk matrices of uniformly at random chosen left regular biparitite graphs.

Denoising of MR and CT images using cascaded multi-supervision convolutional neural networks with progressive training

As MR Rician noise and CT low-dose perfusion noise have a complicated distribution, it is still a challenging task to automatically and accurately remove the noises existing in MR and CT images. Recently, convolutional neural networks have shown favorable performance on image denoising tasks. However, existing methods ignored the hierarchical features extracted from multi-supervision inner layers and estimated the denoised image just by the last single layer, which can not adequately reserve the details of the image. In this paper, we propose a cascaded multi-supervision convolutional neural network named CMSNet to remove the low-dose perfusion noise in CT images and the Rician noise exist in MR images. The CMSNet consists of a multi-supervision network (MSNet) followed with a Refinement network. MSNet is presented to predict the noise constrained by the supervisions from last three convolution layers, which can help acquire more accurate noise prediction and thus obtain the noise-free image. Refinement network is introduced to relief the details lost problem caused by the denoising operation. We employ a progressive training strategy, i.e., MSNet is first trained independently to predict the preliminary noise and then jointly trained with Refinement network for more accurate noise estimating, which can boost the network performance. Experiments are conducted on clinic abdominal MR and CT images, and the results show that our proposed model achieved a promising performance in terms of unknown noise level, a specific noise level on peak signal to noise ratio (PSNR) and global structure similarity index measurement (SSIM).

High-dimensional black-box optimization under uncertainty

Optimizing expensive black-box systems with limited data is an extremely challenging problem. As a resolution, we present a new surrogate optimization approach by addressing two gaps in prior research—unimportant input variables and inefficient treatment of uncertainty associated with the black-box output. We first design a new flexible non-interpolating parsimonious surrogate model using a partitioning-based multivariate adaptive regression splines approach, Tree Knot MARS (TK-MARS). The proposed model is specifically designed for optimization by capturing the structure of the function, bending at near-optimal locations, and is capable of screening unimportant input variables. Furthermore, we develop a novel replication approach called Smart-Replication, to overcome the uncertainty associated with the black-box output. The Smart-Replication approach identifies promising input points to replicate and avoids unnecessary evaluations of other data points. Smart-Replication is agnostic to the choice of a surrogate and can adapt itself to an unknown noise level. Finally to demonstrate the effectiveness of our proposed approaches we consider different complex global optimization test functions from the surrogate optimization literature. The results indicate that TK-MARS outperforms original MARS within a surrogate optimization algorithm and successfully detects important variables. The results also show that although non-interpolating surrogates can mitigate uncertainty, replication is still beneficial for optimizing highly complex black-box functions. The robustness and the quality of the final optimum solution found through Smart-Replication are competitive with that using no replications in environments with low levels of noise and using a fixed number of replications in highly noisy environments.

Efficient Tuning-Free l1-Regression of Nonnegative Compressible Signals

In compressed sensing the goal is to recover a signal from as few as possible noisy, linear measurements with the general assumption that the signal has only a few non-zero entries. The recovery can be performed by multiple different decoders, however most of them rely on some tuning. Given an estimate for the noise level a common convex approach to recover the signal is basis pursuit denoising. If the measurement matrix has the robust null space property with respect to the ℓ2-norm, basis pursuit denoising obeys stable and robust recovery guarantees. In the case of unknown noise levels, nonnegative least squares recovers non-negative signals if the measurement matrix fulfills an additional property (sometimes called the M+-criterion). However, if the measurement matrix is the biadjacency matrix of a random left regular bipartite graph it obeys with a high probability the null space property with respect to the ℓ1-norm with optimal parameters. Therefore, we discuss non-negative least absolute deviation (NNLAD), which is free of tuning parameters. For these measurement matrices, we prove a uniform, stable and robust recovery guarantee. Such guarantees are important, since binary expander matrices are sparse and thus allow for fast sketching and recovery. We will further present a method to solve the NNLAD numerically and show that this is comparable to state of the art methods. Lastly, we explain how the NNLAD can be used for viral detection in the recent COVID-19 crisis.

Deep Learning Seismic Random Noise Attenuation via Improved Residual Convolutional Neural Network

Because a high signal-to-noise ratio (SNR) is beneficial to the subsequent processing procedures, the noise attenuation is important. We propose an adaptive random noise attenuation framework based on convolutional neural networks (CNNs). The framework transforms the target function from effective signal learning to noise learning through residual learning, so as to improve the training efficiency. After sufficient training, the network transfers the learned seismic data features using a large synthetic data set to the testing of complex field data with unknown noise levels and, thus, attenuates the noise in an unsupervised way. Unsupervised noise reduction requires certain representativeness of the training data and a sufficient amount of training data sets. In the network architecture, we introduce residual learning and batch normalization (BN) to reduce the training parameters of the network, thereby shortening the time for feature learning. The activation function with leakage correction function can effectively retain negative information, and its combination with the double convolutional residual block can enhance the generalization ability and feature extraction performance of the network. In the test of synthetic data and complex field data with unknown noise levels, by comparing the noise reduction results of some classic denoising algorithms, the adaptive CNN proposed in this article can more effectively attenuate the noise and reconstruct the seismic waveform.

The Structured Smooth Adjustment for Square-root Regularization: Theory, algorithm and applications

In this paper, a novel method called Structured Smooth Adjustment for Square-root Regularization (SSASR) is proposed to simultaneously select grouped variables and encourage piecewise smoothness within each group. This approach is based on square-root regularization with a joint ℓ2,1 norm regularizer that, like the group lasso, shrinks a group of coefficients to identically zero and, additionally, involves an additional IGTV regularizer to enforce certain structural constraints – instead of pure sparsity – on the coefficients. We show the SSASR estimator can achieve optimal estimation and prediction, which is adaptive to the unknown noise level, under some mild conditions on the design matrix. To implement, an efficient algorithm termed Scaled Dual Forward–backward Splitting is proposed with proved convergence. Furthermore, we carry out an experimental evaluation on both synthetic data and real data obtained from glioblastoma multiforme samples and gray images.

A Two-Stage Reinforcement Learning Approach for Multi-UAV Collision Avoidance Under Imperfect Sensing

Unlike autonomous ground vehicles (AGVs), unmanned aerial vehicles (UAVs) have a higher dimensional configuration space, which makes the motion planning of multi-UAVs a challenging task. In addition, uncertainties and noises are more significant in UAV scenarios, which increases the difficulty of autonomous navigation for multi-UAV. In this letter, we proposed a two-stage reinforcement learning (RL) based multi-UAV collision avoidance approach without explicitly modeling the uncertainty and noise in the environment. Our goal is to train a policy to plan a collision-free trajectory by leveraging local noisy observations. However, the reinforcement learned collision avoidance policies usually suffer from high variance and low reproducibility, because unlike supervised learning, RL does not have a fixed training set with ground-truth labels. To address these issues, we introduced a two-stage training method for RL based collision avoidance. For the first stage, we optimize the policy using a supervised training method with a loss function that encourages the agent to follow the well-known reciprocal collision avoidance strategy. For the second stage, we use policy gradient to refine the policy. We validate our policy in a variety of simulated scenarios, and the extensive numerical simulations demonstrate that our policy can generate time-efficient and collision-free paths under imperfect sensing, and can well handle noisy local observations with unknown noise levels.

Image Denoising Algorithm Based on Local Adaptive Nonlinear Response Diffusion

We describe an image denoising algorithm to improve the denoising performance and the time efficiency, while keeping the edge texture of the image from being blurred. First, the algorithm discriminates the pixel whether is an edge pixel or a noise pixel according to the similarity region values of the neighborhoods, and calculates the adaptive diffusion coefficients to construct an adaptive influence function, which can control the noise and the edges to have different diffusion speeds. Then, a 5-layer feedback convolution network with 16 small filters in each layer generates the reconstructed image through convolution, diffusion and deconvolution. Last, the algorithm uses multiple noise levels training sets to train and optimize the network parameters, and generates the finial image denoising model. The experimental results show that the proposed algorithm using adaptive diffusion coefficients can maintain the edges and the smaller filter can improve the time efficiency. The algorithm also has higher denoising accuracy for images with unknown noise level by training on multiple-noise-level training sets.

A novel DeepCNN model for denoising analysis of MRI brain tumour images

Medical images must be introduced to the specialists or doctors with high accuracy for the diagnosis of critical diseases like a brain tumour. In this paper, a novel DeepCNN model is proposed to perform MRI brain tumour image denoising task and the results are compared with pre-trained DnCNN, Gaussian, adaptive, bilateral and guided filters. It is found that DeepCNN performs better than other filtering methods used. Different noise levels ranging from 5 to 50 and noises like salt and pepper, Poisson, Gaussian, and speckle noises are used to form the noisy images. Performance metrics like peak signal to noise ratio and structural similarity index are calculated and compared across all filters and noises. The proposed DeepCNN model performs well for denoising with the unknown and known noise levels. It speeds up the training process and also improves the denoising performance because of using 17 convolutional layers and batch normalisation.