Local Regularity Research Articles

Inversion algorithm determining sharp boundaries in electrical resistivity tomography

Blurred resistivity boundaries resulting from smoothness-regularized inversions of electrical resistivity tomography (ERT) data can lead to inaccurate interpretations of sharp boundary structures. To address this issue, various ERT inversion algorithms have introduced localized adjustments (localized discontinuities) in the regularization operator at positions where sharp boundaries are anticipated. Current approaches rely on prior information about sharp boundary locations, obtained from complementary geophysical, geological, and drilling data, to determine the positions and weights for these regularization adjustments. However, such prior information is frequently insufficient, limiting the application of localized regularization adjustments. Accordingly, we developed a sharp boundary inversion (SBI) algorithm using the Akaike Bayesian Information Criterion (ABIC) that determines the optimal positions and weights for localized regularization adjustments by testing various configurations and selecting the one that minimizes ABIC. A synthetic modeling study demonstrated that the SBI algorithm correctly delineated the sharp boundaries of a conductor. Its application to field data demonstrated that it delineated the sharp boundaries of a utility tunnel, and the size and horizontal position of the recovered tunnel were consistent with the estimated dimensions from the blueprint. As it does not rely heavily on prior information, the SBI algorithm can be applied to a wide range of geophysical survey data, even when prior knowledge of sharp boundary locations is limited.

Predicted missing information biases ensemble perception of temporally ordered facial expressions

By observing dynamically changing facial expressions, humans can use a specialized capacity known as ensemble coding to effortlessly obtain a summary representation of an individual’s emotional state. However, few studies have examined whether the missing expression informed by the statistical regularity in the changing facial expressions can be sampled and then influence the perceptual averaging process. In Experiment 1a and 1b, we manipulated the amount of prior information from local regularity by varying the position of the missing expression in the temporal sequence (1a: Neutral to Disgust and/or Disgust to Neutral,1b: Neutral to Happy and/or Happy to Neutral) within a trial. Results showed that ensemble estimates were towards the mean of expressions including both the presented and the missing faces, only when sufficient predictability (e.g. a missing expression in the late position) informed by local regularity. In Experiment 2, we added prior information from global regularities to help boost the predictability of an early missing expression by keeping the emotional direction consistent in a block. However, estimates were not towards the mean of expressions including both the presented and the missing expressions as expected. Although the generalizability may be limited, these findings suggest that prior information at different levels of hierarchical predictive coding may exert qualitatively different influences on the perceptual averaging of temporally ordered facial expressions with missing items.

The Kohn–Laplace Equation on Abstract CR Manifolds: Local Regularity

The Kohn–Laplace Equation on Abstract CR Manifolds: Local Regularity

Multi-stage dehazing network: Where haze perception unit meets global and local progressive contrastive regularization

Multi-stage dehazing network: Where haze perception unit meets global and local progressive contrastive regularization

A retinex inspired deep image prior model for despeckling and deblurring of aerial and satellite images using proximal gradient method

ABSTRACT Unsupervised learning models, particularly in the remote sensing domain, have gained significant attention in recent years. Various degradations in the satellite images, primarily occurring during acquisition, pose a substantial hurdle in obtaining reliable ground truth and extensive training data. The Deep Image Prior model (DIP) addresses these issues by performing restoration tasks using a single image, relying on the implicit regularization inherent in the network architecture. In this paper, we propose a novel approach, integrating the DIP model within the retinex framework to restore aerial and satellite images from the Gamma distributed speckles and linear shift-invariant Gaussian blur along with contrast enhancement using the alternating proximal gradient descent ascent (PGDA) method. Our proposed methodology combines implicit regularization with explicit total variational (TV) regularization, incorporating automated estimation of local regularization parameters. The data-fidelity component in the optimization function is formulated using the Bayesian Maximum A posteriori (MAP) estimate, assuming the speckles follow the Gamma distribution. Demonstration of despeckling and deblurring alone and in addition as a combined task is carried out on aerial and Synthetic Aperture Radar (SAR) images with different resolutions and polarization from various sources. Results obtained are compared with various state-of-the-art despeckling and deblurring models using distinct image quality metrics such as Equivalent Number of Looks (ENL), Contrast to Noise Ratio (CNR), Edge Preserving Index (EPI), Entropy, Global Contrast Factor (GCF), Natural Image Quality Evaluator (NIQE), Blind/Referenceless Image Spatial Quality Evaluator (BRISQUE) and Bradley-Terry (B-T) score based on the various factors. The quality of restored images depicted superior performance of the proposed method over the existing models under study.

Joint extraction of entity and relation based on Fine-tuning BERT for Long Biomedical literatures

Abstract Motivation Joint extraction of entity and relation is an important research direction in Information Extraction. The number of scientific and technological biomedical literature is rapidly increasing, so automatically extracting entities and their relations from these literatures are key tasks to promote the progress of biomedical research. Results The joint extraction of entity and relation model achieves both intra-sentence extraction and cross-sentence extraction, alleviating the problem of long-distance information dependence in long literature. Joint extraction of entity and relation model incorporates a variety of advanced deep learning techniques in this paper: (1) a fine-tuning BERT text classification pre-training model, (2) Graph Convolutional Network learning method, (3) Robust Learning Against Textual Label Noise with Self-Mixup Training, (4) Local regularization Conditional Random Fields. The model implements the following functions: identifying entities from complex biomedical literature effectively, extracting triples within and across sentences, reducing the effect of noisy data during training, and improving the robustness and accuracy of the model. The experiment results prove that the model performs well on the self-built BM_GBD dataset and public datasets, enabling precise large language model enhanced knowledge graph construction for biomedical tasks. Availability and implementation The model and partial code are available on GitHub at https://github.com/zhaix922/Joint-extraction-of-entity-and-relation.

Local regularity for nonlocal double phase equations in the Heisenberg group

We prove interior boundedness and Hölder continuity for the weak solutions of nonlocal double phase equations in the Heisenberg group $\mathbb{H}^n$ . This solves a problem raised by Palatucci and Piccinini et al. in 2022 and 2023 for the nonlinear integro-differential problems in Heisenberg setting. Our proof of the a priori estimates bases on De Giorgi–Nash–Moser theory, where the important ingredients are Caccioppoli-type inequality and Logarithmic estimate. To achieve this goal, we establish a new and crucial Sobolev–Poincaré type inequality in local domain, which may be of independent interest and potential applications.

Fully multivariate detrended fluctuation analysis using Mahalanobis norm with application to multivariate signal denoising

Detrended fluctuation analysis (DFA) has become an important tool for the long-range correlation and local regularity fluctuation analysis of nonstationary time series data. While the method is well-established and well-understood for single time series data, its extensions for multivariate data (comprising multiple channels) are still emerging. A major challenge in that regard is to incorporate inherent inter-channel dependencies within the DFA analysis. We propose a novel method to address that challenge through Mahalanobis distance (MD) norm that provides an analytical way to incorporate covariance matrix within the computation of the proposed multichannel fluctuation function. Through analytical analysis and experimental results, we show that incorporation of cross-channel correlations within the fluctuation function makes the rendered long-range correlation analysis more accurate for the multivariate correlated data. Next, we next demonstrate the utility of the proposed generic multichannel DFA (GMDFA) within the multivariate signal denoising problem(s). To this end, our denoising approach first obtains data driven multiscale signal representation by multi-stage use of multivariate variational mode decomposition (MVMD) method. Then, proposed GMDFA is used to reject the predominantly noisy modes based on their randomness scores.

Locally Adaptive Shrinkage Priors for Trends and Breaks in Count Time Series

Nonstationary count time series characterized by features such as abrupt changes and fluctuations about the trend arise in many scientific domains including biophysics, ecology, energy, epidemiology, and social science domains. Current approaches for integer-valued time series lack the flexibility to capture local transient features while more flexible models for continuous data types are inadequate for universal applications to integer-valued responses such as settings with small counts. We present a modeling framework, the negative binomial Bayesian trend filter (NB-BTF), that offers an adaptive model-based solution to capturing multiscale features with valid integer-valued inference for trend filtering. The framework is a hierarchical Bayesian model with a dynamic global-local shrinkage process. The flexibility of the global-local process allows for the necessary local regularization while the temporal dependence induces a locally smooth trend. In simulation, the NB-BTF outperforms a number of alternative trend filtering methods. Then, we demonstrate the method on weekly power outage frequency in Massachusetts townships. Power outage frequency is characterized by a persistent low level trend with occasional spikes. These illustrations show the estimation of a smooth, nonstationary trend with adequate uncertainty quantification.

Farmers market food safety: A comprehensive review of training needs in the U.S.

Farmers markets offer an apparently easy way for small-scale or hobbyist food producers to sell fresh produce, meat, and poultry from their farms or dis­tribute value-added products, but they may be unaware of the foodborne illness risks associated with both fresh produce and derivative products, as well as of their local food safety requirements. Food guidance and rules vary from state to state and market to market, making it difficult for indi­viduals to navigate the various regulatory levels. Even if a local food producer is exempt from these rules due to their amount of sales, they will still benefit greatly from resources and educational tools that increase awareness and knowledge of food safety best practices. This review discusses current knowledge of and guidelines for food safety in farmers markets based on peer-reviewed and grey literature as well as published guidelines and recommendations. We examine facilities and supplies, regulatory measures, education and train­ing, and Good Farmers Market Practices as pre­ventive measures to enhance food safety in farmers markets, which are critical to local and regional food systems. Overall, we identified various barri­ers to implementing farmers market food safety standards and practices in this scoping review; removing these barriers will require the participa­tion of local regularity authorities, market managers, vendors, and consumers.

Nonlinear subspace clustering by functional link neural networks

Nonlinear subspace clustering based on a feed-forward neural network has been demonstrated to provide better clustering accuracy than some advanced subspace clustering algorithms. While this approach demonstrates impressive outcomes, it involves a balance between effectiveness and computational cost. In this study, we employ a functional link neural network to transform data samples into a nonlinear domain. Subsequently, we acquire a self-representation matrix through a learning mechanism that builds upon the mapped samples. As the functional link neural network is a single-layer neural network, our proposed method achieves high computational efficiency while ensuring desirable clustering performance. By incorporating the local similarity regularization to enhance the grouping effect, our proposed method further improves the quality of the clustering results. We name our method as Functional Link Neural Network Subspace Clustering (FLNNSC). Furthermore, we propose a convex combination subspace clustering scheme that combines a linear subspace clustering method with the functional link neural network subspace clustering approach. This combination method is named as Convex Combination Subspace Clustering (CCSC), which allows for a dynamic balance between linear and nonlinear representations. Extensive experiments conducted on four widely used datasets, including Extended Yale B, USPS, COIL20, and ORL, demonstrate that both FLNNSC and CCSC outperform several state-of-art subspace clustering methods in terms of clustering accuracy. Our affinity graph experiments reveal that FLNNSC exhibits clear block diagonal structures. We provide recommendations for hyperparameters in FLNNSC by performing a parameter sensitivity analysis, and empirically verify the convergence of FLNNSC. Additionally, we show that FLNNSC has a lower computational cost compared to two high-performing methods.

Robust estimation of structural orientation parameters and 2D/3D local anisotropic Tikhonov regularization

Understanding the orientation of geologic structures is crucial for analyzing the complexity of the earths’ subsurface. For instance, information about geologic structure orientation can be incorporated into local anisotropic regularization methods as a valuable tool to stabilize the solution of inverse problems and produce geologically plausible solutions. We introduce a new variational method that uses the alternating direction method of multipliers within an alternating minimization scheme to jointly estimate orientation and model parameters in 2D and 3D inverse problems. Specifically, our approach adaptively integrates recovered information about structural orientation, enhancing the effectiveness of anisotropic Tikhonov regularization in recovering geophysical parameters. The paper also discusses the automatic tuning of algorithmic parameters to maximize the new method’s performance. Our algorithm is tested across diverse 2D and 3D examples, including structure-oriented denoising and trace interpolation. The results indicate that the algorithm is robust in solving the considered large and challenging problems, alongside efficiently estimating the associated tilt field in 2D cases and the dip, strike, and tilt fields in 3D cases. Synthetic and field examples show that our anisotropic regularization method produces a model with enhanced resolution and provides a more accurate representation of the true structures.

A super-resolution algorithm of Ghost Imaging using CNN with Grouped orthonormalization algorithm Constraint

Ghost imaging (GI) is capable of reconstructing images under low-light conditions by single-pixel measurements. However, improving image resolution often requires extensive single-pixel sampling, limiting practical applications. Here we propose a super-resolution algorithm of GI using Convolutional neural network with Grouped orthonormalization algorithm Constraint (GICGC), which aims to reconstruct images at super-resolution with strong local regularities and self-similarity. The proposed algorithm, a versatile approach, has been demonstrated to outperform several other widely used GI algorithms in terms of spatial resolution and sampling rate. Our findings are supported by rigorous benchmark tests and experimental validations in challenging environments, including multimode fibers. The imaging experimental results demonstrate that GICGC achieves superior performance in reconstructing image linewidth and contrast, effectively doubling resolution capability by approximately 2.1 times, indicating significant potential in biomedical imaging and other fields. We believe this study represents a novel breakthrough in universal super-resolution ghost imaging and paves the way for its practical applications.

Local regularity for the space-homogenous Landau equation with very soft potentials

Local regularity for the space-homogenous Landau equation with very soft potentials

Multi-Scale Classification and Contrastive Regularization: Weakly Supervised Large-Scale 3D Point Cloud Semantic Segmentation

With the proliferation of large-scale 3D point cloud datasets, the high cost of per-point annotation has spurred the development of weakly supervised semantic segmentation methods. Current popular research mainly focuses on single-scale classification, which fails to address the significant feature scale differences between background and objects in large scenes. Therefore, we propose MCCR (Multi-scale Classification and Contrastive Regularization), an end-to-end semantic segmentation framework for large-scale 3D scenes under weak supervision. MCCR first aggregates features and applies random downsampling to the input data. Then, it captures the local features of a random point based on multi-layer features and the input coordinates. These features are then fed into the network to obtain the initial and final prediction results, and MCCR iteratively trains the model using strategies such as contrastive learning. Notably, MCCR combines multi-scale classification with contrastive regularization to fully exploit multi-scale features and weakly labeled information. We investigate both point-level and local contrastive regularization to leverage point cloud augmentor and local semantic information and introduce a Decoupling Layer to guide the loss optimization in different spaces. Results on three popular large-scale datasets, S3DIS, SemanticKITTI and SensatUrban, demonstrate that our model achieves state-of-the-art (SOTA) performance on large-scale outdoor datasets with only 0.1% labeled points for supervision, while maintaining strong performance on indoor datasets.

Lipschitz regularity of a weakly coupled vectorial almost-minimizers for the p-Laplacian

For a given constant λ>0 and a bounded Lipschitz domain D⊂Rn (n≥2), we establish that almost-minimizers of the functionalJ(v;D)=∫D∑i=1m|∇vi(x)|p+λχ{|v|>0}(x)dx,1<p<∞, where v=(v1,⋯,vm), and m∈N, exhibit optimal Lipschitz continuity in compact sets of D. Furthermore, assuming p≥2 and employing a distinctly different methodology, we tackle the issue of boundary Lipschitz regularity for v. This approach simultaneously yields an alternative proof for the optimal local Lipschitz regularity for the interior case.

The Rate of Convergence of Bregman Proximal Methods: Local Geometry Versus Regularity Versus Sharpness

The Rate of Convergence of Bregman Proximal Methods: Local Geometry Versus Regularity Versus Sharpness

Determining coefficients for a fractional p-Laplace equation from exterior measurements

We consider an inverse problem of determining the coefficients of a fractional p -Laplace equation in the exterior domain. Assuming suitable local regularity of the coefficients in the exterior domain, we offer an explicit reconstruction formula in the region where the exterior measurements are performed. This formula is then used to establish a global uniqueness result for real-analytic coefficients. In addition, we also derive a stability estimate for the unique determination of the coefficients in the exterior measurement set.

Discretization of Non-uniform Rational B-Spline (NURBS) Models for Meshless Isogeometric Analysis

We present an algorithm for fast generation of quasi-uniform and variable-spacing nodes on domains whose boundaries are represented as computer-aided design (CAD) models, more specifically non-uniform rational B-splines (NURBS). This new algorithm enables the solution of partial differential equations within the volumes enclosed by these CAD models using (collocation-based) meshless numerical discretizations. Our hierarchical algorithm first generates quasi-uniform node sets directly on the NURBS surfaces representing the domain boundary, then uses the NURBS representation in conjunction with the surface nodes to generate nodes within the volume enclosed by the NURBS surface. We provide evidence for the quality of these node sets by analyzing them in terms of local regularity and separation distances. Finally, we demonstrate that these node sets are well-suited (both in terms of accuracy and numerical stability) for meshless radial basis function generated finite differences discretizations of the Poisson, Navier-Cauchy, and heat equations. Our algorithm constitutes an important step in bridging the field of node generation for meshless discretizations with isogeometric analysis.

Generalized local Morrey regularity of elliptic systems

Generalized local Morrey regularity of elliptic systems