Noise-free Data Research Articles

Modeling and Hybrid Inversion of Mineral Deposits Using the Dipping Dike Model with Finite Depth Extent

The dipping dike model has shown to be a useful approximation for mineral deposits. To make this model more realistic, we include the thickness, which yields the depth to the bottom, as an additional parameter. The magnetic anomaly is obtained by combining the anomalies of two infinite dikes, so that the resulting expression is simpler than the classical prismatic models with polygonal cross section. We employ a Metropolis-Hasting (MH) algorithm coupled with the Levenberg-Marquardt (LM) method to invert magnetic profiles assuming a model of multiple dike-like sources. We use a few iterations of the LM method to improve the candidate solutions at the end of each random walk generated by MH. The following parameters are obtained: depth to the top, thickness, half-width, horizontal location of the top center, geological dip, in addition to two effective parameters that depend on the intensity of magnetization and the directions of the induced and remanent fields. For synthetic anomalies, both noise-free and noisy magnetic data are considered, with examples presented for each scenario. These examples highlight the discrepancy between models with finite and infinite sources. They also illustrate the higher accuracy of the hybrid MH-LM method over the pure MH approach. Moreover, two field examples related to mineral exploration have been considered: the Pima copper mine, United States, where the relative differences between the parameters obtained by our algorithm and those known from drilling are not higher than 10%, and a magnetic profile over iron ore deposits located in Laje, northeast Brazil, where the inverted parameters were useful for detailing previous studies.

An Overview of Systems-Theoretic Guarantees in Data-Driven Model Predictive Control

The development of control methods based on data has seen a surge of interest in recent years. When applying data-driven controllers in real-world applications, providing theoretical guarantees for the closed-loop system is of crucial importance to ensure reliable operation. In this review, we provide an overview of data-driven model predictive control (MPC) methods for controlling unknown systems with guarantees on systems-theoretic properties such as stability, robustness, and constraint satisfaction. The considered approaches rely on the fundamental lemma from behavioral theory in order to predict input–output trajectories directly from data. We cover various setups, ranging from linear systems and noise-free data to more realistic formulations with noise and nonlinearities, and we provide an overview of different techniques to ensure guarantees for the closed-loop system. Moreover, we discuss avenues for future research that may further improve the theoretical understanding and practical applicability of data-driven MPC.

Particle swarm optimization method for parameter selecting in Tikhonov regularization method for solving inverse problems

In this article the Tikhonov method used as a regularization technique for solving the inverse problem liner operator equation of the first kind with noisy and noise-free data. We also provide the Tikhonov method's essential analysis for tackling inverse problems. Following that, we go over how to choose the Tikhonov regularization parameter by implementing the Particle Swarm Optimization (PSO) technique. The effectiveness of combining these two approaches particle swarm optimization and Tikhonov is demonstrated to be highly practicable.

Development and Validation of a Real-Time Service Model for Noise Removal and Arrhythmia Classification Using Electrocardiogram Signals.

Arrhythmias range from mild nuisances to potentially fatal conditions, detectable through electrocardiograms (ECGs). With advancements in wearable technology, ECGs can now be monitored on-the-go, although these devices often capture noisy data, complicating accurate arrhythmia detection. This study aims to create a new deep learning model that utilizes generative adversarial networks (GANs) for effective noise removal and ResNet for precise arrhythmia classification from wearable ECG data. We developed a deep learning model that cleans ECG measurements from wearable devices and detects arrhythmias using refined data. We pretrained our model using the MIT-BIH Arrhythmia and Noise databases. Least squares GANs were used for noise reduction, maintaining the integrity of the original ECG signal, while a residual network classified the type of arrhythmia. After initial training, we applied transfer learning with actual ECG data. Our noise removal model significantly enhanced data clarity, achieving over 30 dB in a signal-to-noise ratio. The arrhythmia detection model was highly accurate, with an F1-score of 99.10% for noise-free data. The developed model is capable of real-time, accurate arrhythmia detection using wearable ECG devices, allowing for immediate patient notification and facilitating timely medical response.

SimNFND: A Forward-Looking Sonar Denoising Model Trained on Simulated Noise-Free and Noisy Data

Given the propagation characteristics of sound waves and the complexity of the underwater environment, denoising forward-looking sonar image data presents a formidable challenge. Existing studies often add noise to sonar images and then explore methods for its removal. This approach neglects the inherent complex noise in sonar images, resulting in inaccurate evaluations of traditional denoising methods and poor learning of noise characteristics by deep learning models. To address the lack of high-quality data for FLS denoising model training, we propose a simulation algorithm for forward-looking sonar data based on RGBD data. By utilizing rendering techniques and noise simulation algorithms, high-quality noise-free and noisy sonar data can be rapidly generated from existing RGBD data. Based on these data, we optimize the loss function and training process of the FLS denoising model, achieving significant improvements in noise removal and feature preservation compared to other methods. Finally, this paper performs both qualitative and quantitative analyses of the algorithm’s performance using real and simulated sonar data. Compared to the latest FLS denoising models based on traditional methods and deep learning techniques, our method demonstrates significant advantages in denoising capability. All inference results for the Marine Debris Dataset (MDD) have been made open source, facilitating subsequent research and comparison.

Noise propagation in linear stationary iterations

AbstractWe consider a stationary iteration for solving a linear system of arbitrary order. The method includes, e.g. Kaczmarz iteration, the Landweber iteration and the SOR (Gauss-Seidel) iteration. A study of the behavior of the iterates, both theoretically and experimentally, is performed. In particular we compare the behavior with and without noise in the data. The results give insight into the interplay between noise free and noisy iterates. For comparision we also included a Krylov type method CGLS in the experiments. As expected CGLS works well for noise free data but also tends to amplify the noise faster than the other methods, thus making it more critical when to stop the iterations.

SECRET: Statistical Emulation for Computational Reverse Engineering and Translation with applications in healthcare

There have been impressive advances in the physical and mathematical modelling of complex physiological systems in the last few decades, with the potential to revolutionise personalised healthcare with patient-specific evidence-based diagnosis, risk assessment and treatment decision support using digital twins. However, practical progress and genuine clinical impact hinge on successful model calibration, parameter estimation and uncertainty quantification, which calls for novel innovative adaptions and methodological extensions of contemporary state-of-the-art inference techniques from Statistics and Machine Learning. In the present study, we focus on two computational fluid-dynamics (CFD) models of the blood systemic and pulmonary circulation. We discuss state-of-the-art emulation techniques based on deep learning and Gaussian processes, which are coupled with established inference techniques based on greedy optimisation, simulated annealing, Markov Chain Monte Carlo, History Matching and rejection sampling for computationally fast inference of unknown parameters of the CFD models from blood flow and pressure data. The inference task was set as a competitive challenge which the participants had to conduct within a limited time frame representative of clinical requirements. The performance of the methods was assessed independently and objectively by the challenge organisers, based on a ground truth that was unknown to the method developers. Our results indicate that for the systemic challenge, in which an idealised case of noise-free data was considered, the relative deviation from the ground-truth in parameter space ranges from 10−5% (highest-performing method) to 3% (lowest-performing method). For the pulmonary challenge, for which noisy data was generated, the performance ranges from 0.9% to 7% deviation for the parameter posterior mean, and from 35% to 570% deviation for the parameter posterior variance.

Ground-truth-free Deep Learning for 3-D Seismic Denoising and Reconstruction with Channel Attention Mechanism

Seismic denoising methods using supervised methods rely on a large number of high-quality paired training datasets to reach satisfactory performances. There are two ways to generate labels for network training: one is to simulate the synthetic data using the wave equation, and the other is to utilize denoised data obtained via conventional methods. However, using these labels will limit the networks' noise attenuation performance compared with using large volumes of noise-free data as labels. Here, we propose a ground-truth-free way for three-dimensional (3-D) seismic data processing. First, we use the 3-D patch scheme to divide the noisy seismic data into many fixed-size blocks and then flatten the obtained 3-D patches to expand the training set and capture more higher-order waveform characteristics from the input noisy data. Next, the obtained training dataset is sent into the proposed deep learning (DL) network, where the encoder blocks compress the feature map to extract the waveform features, and the decoder blocks reconstruct the denoised feature map. Notably, the convolutional bottleneck attention module (CBAM) and efficient channel attention (ECA) module are applied to guide the network to focus on signal fluctuation features with fewer network parameters. In addition, the concatenation mechanism is used to enable deep networks to reuse shallow-layer waveform features and mitigate overfitting during training. Finally, the unpatching scheme is used to reconstruct the denoised 3-D seismic data. Numerical experiments demonstrate that the proposed method outperforms benchmark approaches in terms of signal-to-noise ratio (SNR) improvement and useful signal preservation.

A stacking-based fault forecasting study for power transmission lines under different weather conditions

Timely diagnosis and defect warning in power systems, related to the probability of a fault occurring, may be achieved by examining the correlations between various factors and evaluating the collected information. To check the performance of the machine learning models, a large amount of data is required in various operating conditions to feed as input to the algorithms. The primary focus of the conducted work is on the defect warning process, with additional studies discussing fault identification, type determination, and location. The stacking-based method is considered the main learning approach; however, the separate outcomes for the three single base methods, i.e., RF, SVM, and XGBoost, along with some other popular and strong algorithms have also been presented. In the warning study section, the proposed stacking approach achieved a minimum accuracy of 99.31 % while taking into consideration the noisy samples, and it has achieved a maximum accuracy of 100 % for all weather conditions with noise-free data. The fault identification component achieves an accuracy of 100 %, whereas the type determination part achieves an accuracy of 99.98 %. More details and results are provided in the paper. The modeling and simulations in this work were implemented in Python and MATLAB.

Numerical analysis of the effects of pores on propagating guided waves

The present numerical study aims to analyze the effect of pores on propagating guided waves while outlining the relevance of pore formation and its significance to structural properties. The primary focus of this study was on the pores present in planar carbon fiber-reinforced polymer (CFRP) parts. The wavefield data were generated by applying the elastodynamic finite integration technique (EFIT) solver AE3D, allowing for a systematic analysis based on fully controllable configurations and noise-free data. An isotropic material model was used to simplify the modeling of the anisotropic CFRP by assuming the averaged quasi-isotropic properties of the CFRP in all directions. More than 220 specimens containing single pores or four basic configurations of pore accumulations were modeled and analyzed in terms of their effect on the out-of-plane component of the propagating guided waves. Analysis of the guided wavefield data focused on the direction-dependent maximum amplitude differences and deviations in the wavefield energy. Mode- and wavenumber-specific amplitude loss along the centerline was analyzed using a matrix pencil algorithm. Finally, principal component analysis (PCA) was conducted to examine deviations caused by the presence of pores. Analysis of the wavefield effects of the pores for each specific configuration showed good differentiation between the considered pore volume groups. At the same time, the effects of the pores were shown to be significantly dependent on the pore configuration in terms of orientation and morphological properties. Associated with this, the intersecting outcome ranges for different pore volume groups were evident when all the pore configurations were considered simultaneously.

Accelerated, physics-inspired inference of skeletal muscle microstructure from diffusion-weighted MRI.

Muscle health is a critical component of overall health and quality of life. However, current measures of skeletal muscle health take limited account of microstructural variations within muscle, which play a crucial role in mediating muscle function. To address this, we present a physics-inspired, machine learning-based framework for the non-invasive estimation of microstructural organization in skeletal muscle from diffusion-weighted MRI (dMRI) in an uncertainty-aware manner. To reduce the computational expense associated with direct numerical simulations of dMRI physics, a polynomial meta-model is developed that accurately represents the input/output relationships of a high-fidelity numerical model. This meta-model is used to develop a Gaussian process (GP) model that provides voxel-wise estimates and confidence intervals of microstructure organization in skeletal muscle. Given noise-free data, the GP model accurately estimates microstructural parameters. In the presence of noise, the diameter, intracellular diffusion coefficient, and membrane permeability are accurately estimated with narrow confidence intervals, while volume fraction and extracellular diffusion coefficient are poorly estimated and exhibit wide confidence intervals. A reduced-acquisition GP model, consisting of one-third the diffusion-encoding measurements, is shown to predict parameters with similar accuracy to the original model. The fiber diameter and volume fraction estimated by the reduced GP model is validated via histology, with both parameters accurately estimated, demonstrating the capability of the proposed framework as a promising non-invasive tool for assessing skeletal muscle health and function.

Adaptive merging migration

Velocity errors and data noise are inevitable for seismic imaging of field data sets in current production; therefore, it is desirable to improve the seismic images as part of the migration process to mitigate the influence of such errors and noise. To address this, we develop a new method of adaptive merging migration (AMM). Our method can produce migrated sections of equal quality to conventional migration methods given a correct velocity model and noise-free data. In addition, it can ameliorate the seismic image quality when applied with erroneous migration velocity models or noisy seismic data. AMM uses an efficient recursive Radon transform to generate multiple p-component images, representing migrated sections associated with different local plane slopes. It then adaptively merges the subsections from those p-component images that are less distorted by velocity errors or noise into the whole image. Such merging is implemented by computing adaptive weights followed by a selective stacking. We use three synthetic velocity models and one field data set to evaluate the AMM performance on isolated Gaussian velocity errors, inaccurate smoothed velocities, velocity errors around high-contrast and short-wavelength interfaces, and noisy seismic data. Numerical tests conducted on synthetic and field data sets validate that AMM can effectively improve the seismic image quality in the presence of different types of velocity errors and data noise.

Method-level Bug Prediction: Problems and Promises

Fixing software bugs can be colossally expensive, especially if they are discovered in the later phases of the software development life cycle. As such, bug prediction has been a classic problem for the research community. As of now, the Google Scholar site generates ∼113,000 hits if searched with the “bug prediction” phrase. Despite this staggering effort by the research community, bug prediction research is criticized for not being decisively adopted in practice. A significant problem of the existing research is the granularity level (i.e., class/file level) at which bug prediction is historically studied. Practitioners find it difficult and time-consuming to locate bugs at the class/file level granularity. Consequently, method-level bug prediction has become popular in the past decade. We ask, are these method-level bug prediction models ready for industry use? Unfortunately, the answer is no . The reported high accuracies of these models dwindle significantly if we evaluate them in different realistic time-sensitive contexts. It may seem hopeless at first, but, encouragingly, we show that future method-level bug prediction can be improved significantly. In general, we show how to reliably evaluate future method-level bug prediction models and how to improve them by focusing on four different improvement avenues: building noise-free bug data, addressing concept drift, selecting similar training projects, and developing a mixture of models. Our findings are based on three publicly available method-level bug datasets and a newly built bug dataset of 774,051 Java methods originating from 49 open-source software projects.

Results of the 2023 ISBI challenge to reduce GABA-edited MRS acquisition time.

Use a conference challenge format to compare machine learning-based gamma-aminobutyric acid (GABA)-edited magnetic resonance spectroscopy (MRS) reconstruction models using one-quarter of the transients typically acquired during a complete scan. There were three tracks: Track 1: simulated data, Track 2: identical acquisition parameters with in vivo data, and Track 3: different acquisition parameters with in vivo data. The mean squared error, signal-to-noise ratio, linewidth, and a proposed shape score metric were used to quantify model performance. Challenge organizers provided open access to a baseline model, simulated noise-free data, guides for adding synthetic noise, and in vivo data. Three submissions were compared. A covariance matrix convolutional neural network model was most successful for Track 1. A vision transformer model operating on a spectrogram data representation was most successful for Tracks 2 and 3. Deep learning (DL) reconstructions with 80 transients achieved equivalent or better SNR, linewidth and fit error compared to conventional 320 transient reconstructions. However, some DL models optimized linewidth and SNR without actually improving overall spectral quality, indicating a need for more robust metrics. DL-based reconstruction pipelines have the promise to reduce the number of transients required for GABA-edited MRS.

Impulse Noise Image Restoration Using Nonconvex Variational Model and Difference of Convex Functions Algorithm.

In this article, the problem of impulse noise image restoration is investigated. A typical way to eliminate impulse noise is to use an L1 norm data fitting term and a total variation (TV) regularization. However, a convex optimization method designed in this way always yields staircase artifacts. In addition, the L1 norm fitting term tends to penalize corrupted and noise-free data equally, and is not robust to impulse noise. In order to seek a solution of high recovery quality, we propose a new variational model that integrates the nonconvex data fitting term and the nonconvex TV regularization. The usage of the nonconvex TV regularizer helps to eliminate the staircase artifacts. Moreover, the nonconvex fidelity term can detect impulse noise effectively in the way that it is enforced when the observed data is slightly corrupted, while is less enforced for the severely corrupted pixels. A novel difference of convex functions algorithm is also developed to solve the variational model. Using the variational method, we prove that the sequence generated by the proposed algorithm converges to a stationary point of the nonconvex objective function. Experimental results show that our proposed algorithm is efficient and compares favorably with state-of-the-art methods.

A deep learning framework for suppressing prestack seismic random noise without noise-free labels

Random noise attenuation is significant in seismic data processing. Supervised deep learning-based denoising methods have been widely developed and applied in recent years. In practice, it is often time-consuming and laborious to obtain noise-free data for supervised learning. Therefore, we propose a novel deep learning framework to denoise prestack seismic data without clean labels, which trains a high-resolution residual neural network (SRResnet) with noisy data for input and the same valid data with different noise for output. Since valid signals in noisy sample pairs are spatially correlated and random noise is spatially independent and unpredictable, the model can learn the features of valid data while suppressing random noise. Noisy data targets are generated by a simple conventional method without fine-tuning parameters. The initial estimates allow signal or noise leakage as the network does not require clean labels. The Monte Carlo strategy is applied to select training patches for increasing valid patches and expanding training datasets. Transfer learning is used to improve the generalization of real data processing. The synthetic and real data tests perform better than the commonly used state-of-the-art denoising methods.

Learning From an Artificial Neural Network in Phylogenetics.

We show that an iterative ansatz of deep learning and human intelligence guided simplification may lead to surprisingly simple solutions for a difficult problem in phylogenetics. Distinguishing Farris and Felsenstein trees is a longstanding problem in phylogenetic tree reconstruction. The Artificial Neural Network F-zoneNN solves this problem for 4-taxon alignments evolved under the Jukes-Cantor model. It distinguishes between Farris and Felsenstein trees, but owing to its complexity, lacks transparency in its mechanism of discernment. Based on the simplification of F-zoneNN and alignment properties we constructed the function FarFelDiscerner. In contrast to F-zoneNN, FarFelDiscerner's decision process is understandable. Moreover, FarFelDiscerner is significantly simpler than F-zoneNN. Despite its simplicity this function infers the tree-type almost perfectly on noise-free data, and also performs well on simulated noisy alignments of finite length. We applied FarFelDiscerner to the historical Holometabola alignments where it places Strepsiptera with beetles, concordant with the current scientific view.

KiDS-1000 cosmology: Combined second- and third-order shear statistics

Aims. In this work, we perform the first cosmological parameter analysis of the fourth release of Kilo Degree Survey (KiDS-1000) data with second- and third-order shear statistics. This paper builds on a series of studies aimed at describing the roadmap to third-order shear statistics. Methods. We derived and tested a combined model of the second-order shear statistic, namely, the COSEBIs and the third-order aperture mass statistics 〈ℳap3〉 in a tomographic set-up. We validated our pipeline with N-body mock simulations of the KiDS-1000 data release. To model the second- and third-order statistics, we used the latest version of HMCODE2020 for the power spectrum and BIHALOFIT for the bispectrum. Furthermore, we used an analytic description to model intrinsic alignments and hydro-dynamical simulations to model the effect of baryonic feedback processes. Lastly, we decreased the dimension of the data vector significantly by considering only equal smoothing radii for the 〈ℳap3〉 part of the data vector. This makes it possible to carry out a data analysis of the KiDS-1000 data release using a combined analysis of COSEBIs and third-order shear statistics. Results. We first validated the accuracy of our modelling by analysing a noise-free mock data vector, assuming the KiDS-1000 error budget, finding a shift in the maximum of the posterior distribution of the matter density parameter, ΔΩm < 0.02 σΩm, and of the structure growth parameter, ΔS8 < 0.05 σS8. Lastly, we performed the first KiDS-1000 cosmological analysis using a combined analysis of second- and third-order shear statistics, where we constrained Ωm = 0.248−0.055+0.062 and S8 = σ8√(Ωm/0.3 )= 0.772 ± 0.022. The geometric average on the errors of Ωm and S8 of the combined statistics decreases, compared to the second-order statistic, by a factor of 2.2.

Oscillatory differentiation dynamics fundamentally restricts the resolution of pseudotime reconstruction algorithms.

The challenge to understand differentiation and cell lineages in development has resulted in many bioinformatics software tools, notably those working with gene expression data obtained via single-cell RNA sequencing obtained at snapshots in time. Reconstruction methods for trajectories often proceed by dimension reduction, data clustering and then computation of a tree graph in which edges indicate closely related clusters. Cell lineages can then be deduced by following paths through the tree. In the case of multi-potent cells undergoing differentiation, this trajectory reconstruction involves the reconstruction of multiple distinct lineages corresponding to commitment to each of a set of distinct fates. Recent work suggests that there may be cases in which the cell differentiation process involves trajectories that explore, in a dynamic and oscillatory fashion, propensity to differentiate into a number of possible cell fates before commitment finally occurs. Here, we show theoretically that the presence of such oscillations provides intrinsic constraints on the quality and resolution of the trajectory reconstruction process, even for idealized noise-free data. These constraints point to inherent common limitations of current methodologies and serve both to provide additional challenge in the development of software tools and also may help to understand features observed in recent experiments.

A branch-and-bound algorithm with growing datasets for large-scale parameter estimation

The solution of nonconvex parameter estimation problems with deterministic global optimization methods is desirable but challenging, especially if large measurement datasets are considered. We propose to exploit the structure of this class of optimization problems to enable their solution with the spatial branch-and-bound algorithm. In detail, we start with a reduced dataset in the root node and progressively augment it, converging to the full dataset. We show for nonlinear programs (NLPs) that our algorithm converges to the global solution of the original problem considering the full dataset. The implementation of the algorithm extends our open-source solver MAiNGO. A numerical case study with a mixed-integer nonlinear program (MINLP) from chemical engineering and a dynamic optimization problem from biochemistry both using noise-free measurement data emphasizes the potential for savings of computational effort with our proposed approach.