The Monge–Ampère operator, as a nonlinear operator embedded in parabolic differential equations, complicates the demonstration of maximal regularity for these equations. This research uses the Riesz fractional derivative to connect the M...
Deep neural networks have shown great potential in various low-level vision tasks, leading to several state-of-the-art image denoising techniques. Training a deep neural network in a supervised fashion usually requires the collection of a great numbe...
Total variation often yields staircase artifacts in the smooth region of the image reconstruction. This paper proposes a hybrid high-order and fractional-order total variation with nonlocal regularization algorithm. The nonlocal means regularization...
We propose an adaptive weighted high frequency iterative algorithm for a fractional-order total variation (FrTV) approach with nonlocal regularization to alleviate image deterioration and to eliminate staircase artifacts, which result from the total...
X-ray computed tomography (CT) is widely used in medical applications, where many efforts have been made for decades to eliminate artifacts caused by incomplete projection. In this paper, we propose a new CT image reconstruction model based on nonloc...
This manuscript presents a study of the Stress-Driven integral Model (SDM) for the bending response of Bernoulli–Euler nanobeams. Unlike conventional approaches that reformulate the nonlocal integral problem into an equivalent differential form...
For a nonlocal initial-boundary value problem for a one-dimensional heat equation with not strongly regular boundary conditions of general type, an approximate difference scheme with weights is constructed. A correct and stable algorithm for the nume...
In this paper, we present a new regularized image reconstruction method for positron emission tomography (PET), where an adaptive weighted median regularizer is used in the context of a penalized-likelihood framework. The motivation of our work is to...
Nonlocal models are ubiquitous in all branches of science and engineering, with a rapidly expanding range of mathematical and computational applications due to the ability of such models to capture effects and phenomena that traditional models cannot...
In this work, we study a nonlocal boundary value problem for a quasilinear elliptic equation. Using the method of regularization and parameter continuation, we prove the existence and uniqueness of a regular solution to the nonlocal boundary value pr...
Subpixel mapping is a method of enhancing the spatial resolution of images, which involves dividing a mixed pixel into subpixels and assigning each subpixel to a definite land-cover class. Traditionally, subpixel mapping is based on the assumption of...
The main objective of this paper is to propose a new boundary element method (BEM) modeling for stress sensitivity of nonlocal thermo-elasto-plastic damage problems. The numerical solution of the heat conduction equation subjected to a non-local cond...
Image dehazing is a traditional task, yet it still presents arduous problems, especially in the removal of haze from the texture and edge information of an image. The state-of-the-art dehazing methods may result in the loss of some visual informative...
Hyperspectral image (HSI) possesses three intrinsic characteristics: the global correlation across spectral domain, the nonlocal self-similarity across spatial domain, and the local smooth structure across both spatial and spectral domains. This pape...
In remote sensing applications and medical imaging, one of the key points is the acquisition, real-time preprocessing and storage of information. Due to the large amount of information present in the form of images or videos, compression of these dat...
This paper presents a variant of the iterative shrinkage-thresholding (IST) algorithm, called backtracking-based adaptive IST (BAIST), for image compressive sensing (CS) reconstruction. For increasing iterations, IST usually yields a smoothing of the...
We study the regularizing effect of the zero order term in some elliptic problems, which present in the principal part a nonlocal operator, i.e., the fractional Laplacian operator. We prove the existence of bounded energy solutions, even if the data...
As an immensely important characteristic of natural images, the nonlocal self-similarity (NSS) prior has demonstrated great promise in a variety of inverse problems. Unfortunately, most current methods utilize either the internal or the external NSS...
The use of non-local self-similarity prior between image blocks can improve image reconstruction performance significantly. We propose a compressive sensing image reconstruction algorithm that combines bilateral total variation and nonlocal low-rank...
This paper focuses on image compressive sensing (CS). As the intrinsic properties of natural images, nonlocal self-similarity and sparse representation have been widely used in various image processing tasks. Most existing image CS methods apply eith...
Polarimetric synthetic aperture radar (PolSAR) has become increasingly popular in the past two decades, for it can derive multichannel features of ground objects, which contains more discriminative information compared with traditional SAR. In this p...
Hyperspectral image compressive sensing reconstruction (HSI-CSR) is an important issue in remote sensing, and has recently been investigated increasingly by the sparsity prior based approaches. However, most of the available HSI-CSR methods consider...
Hyperspectral image (HSI) acquisitions are degraded by various noises, among which additive Gaussian noise may be the worst-case, as suggested by information theory. In this paper, we present a novel tensor-based HSI denoising approach by fully ident...
Utilizing low-rank prior data in compressed sensing (CS) schemes for Landsat 8–9 remote sensing images (RSIs) has recently received widespread attention. Nevertheless, most CS algorithms focus on the sparsity of an RSI and ignore its low-rank (...
This study tackles a fourth-order inverse problem involving a cantilever beam with nonlocal conditions to simultaneously calculate the beam’s displacement and an unknown time-dependent coefficient. A finite difference approach is suggested to d...
A hyperspectral image (HSI) is often corrupted by various types of noise during image acquisition, e.g., Gaussian noise, impulse noise, stripes, deadlines, and more. Thus, as a preprocessing step, HSI denoising plays a vital role in many subsequent t...
During the imaging process, hyperspectral image (HSI) is inevitably affected by various noises, such as Gaussian noise, impulse noise, stripes or deadlines. As one of the pre-processing steps, the removal of mixed noise for HSI has a vital impact on...
Analysis of the electromechanical-size-dependent bending of piezoelectric composite structural components with flexoelectricity has been considered by many researchers because of the developments of nanotechnology and the applicability of piezoelectr...
We study the solvability of the Ionkin problem for some differential equations with one space variable. These equations include parabolic and quasiparabolic, hyperbolic and quasihyperbolic, pseudoparabolic and pseudohyperbolic, elliptic and quasielli...
The inverse problem under consideration concerns a one-dimensional parabolic equation whose thermal diffusivity takes the quadratic-in-space form
A qualitative study for a second-order boundary value problem with local or nonlocal diffusion and a cubic nonlinear reaction term, endowed with in-homogeneous Cauchy–Neumann (Robin) boundary conditions, is addressed in the present paper. Provi...
Loss of stability is studied extensively in nonlinear investigations, and classified as generic bifurcations. It requires regularity, being connected with non-locality. Such behavior comes from gradient terms in constitutive equations. Most fractiona...
During the process of signal sampling and digital imaging, hyperspectral images (HSI) inevitably suffer from the contamination of mixed noises. The fidelity and efficiency of subsequent applications are considerably reduced along with this degradatio...
In this paper, we study the traveling wave solutions for a nonlocal dispersal SIR epidemic model with standard incidence rate and nonlocal delayed transmission. The existence and nonexistence of traveling wave solutions are determined by the basic re...
We use the method of moving planes to prove the radial symmetry and monotonicity of solutions of fractional parabolic equations in the unit ball. Since the fractional Laplacian operator is a linear operator, we investigate the maximal regularity of n...
The Lax pairs of the higher-order Gerdjikov–Ivanov (HOGI) equation are extended to the multi-component formula. Then, we first derive four different types of nonlocal group reductions to this new system. To construct the solution of these four...
We provide a short introduction of new and well-known facts relating non-local operators and irregular domains. Cauchy problems and boundary value problems are considered in case non-local operators are involved. Such problems lead to anomalous behav...
Reconstructing images from multi-view projections is a crucial task both in the computer vision community and in the medical imaging community, and dynamic positron emission tomography (PET) is no exception. Unfortunately, image quality is inevitably...
An interferometric synthetic aperture radar (InSAR) phase denoising algorithm using the local sparsity of wavelet coefficients and nonlocal similarity of grouped blocks was developed. From the Bayesian perspective, the double-
Achieving high-quality reconstructions of images is the focus of research in image compressed sensing. Group sparse representation improves the quality of reconstructed images by exploiting the non-local similarity of images; however, block-matching...
High-dimensional variable selection is an important research topic in modern statistics. While methods using nonlocal priors have been thoroughly studied for variable selection in linear regression, the crucial high-dimensional model selection proper...
Seismic denoising is a core task of seismic data processing. The quality of a denoising result directly affects data analysis, inversion, imaging and other applications. For the past ten years, there have mainly been two classes of methods for seismi...
Hyperspectral unmixing is a key preprocessing technique for hyperspectral image analysis. To further improve the unmixing performance, in this paper, a nonlocal low-rank prior associated with spatial smoothness and spectral collaborative sparsity are...
Differential equations containing fractional derivatives, for both time and spatial variables, have now begun to attract the attention of mathematicians and physicists; they are used in connection with these equations as mathematical models of variou...
Alfalfa is critical to global food security, and its data is abundant in the U.S. nationally, but often scarce locally, limiting the potential performance of machine learning (ML) models in predicting alfalfa biomass yields. Training ML models on loc...
Group sparse coding (GSC) uses the non-local similarity of images as constraints, which can fully exploit the structure and group sparse features of images. However, it only imposes the sparsity on the group coefficients, which limits the effectivene...
We consider general linear multi-term Caputo fractional integro-differential equations with weakly singular kernels subject to local or non-local boundary conditions. Using an integral equation reformulation of the proposed problem, we first study th...
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This paper studies the existence, regularity, and properties of normalized ground state solutions for the mixed fractional Schrödinger equations. For subcritical cases, we establish the boundedness and Sobolev regularity of solutions, derive Poh...
This study examined quiescent optical structures in a cubic–quintic nonlinear Schrödinger model that combines intensity-dependent dispersion with a weakly nonlocal intensity-curvature response. A real phase–amplitude reduction establ...
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