The reservoir stimulation technology based on horizontal-well hydraulic fracturing has become one of the key means for efficient development of shale gas reservoir. Accurately describing the geometric shape and statistical characteristics of fracture...
The modeling of many problems of practical interest leads to nonlinear ill-posed equations (for example, the parameter identification problem (see the Numerical section)). In this article, we introduce a new source condition (SC) and a new parameter...
Inspired by the concept of regular local rings in classical algebra, in this article we initiate the study of the regular parameter elements in a commutative local Noetherian hyperring. These elements provide a deep connection between the dimension o...
The electrocardiogram (ECG) is the standard method in clinical practice to non-invasively analyze the electrical activity of the heart, from electrodes placed on the body’s surface. The ECG can provide a cardiologist with relevant information t...
In dynamic MRI, sufficient temporal resolution can often only be obtained using imaging protocols which produce undersampled data for each image in the time series. This has led to the popularity of compressed sensing (CS) based reconstructions. One...
This study addresses the inverse problem of parameter identification in mathematical models of tumor growth under limited and noisy experimental data. Three classical growth models—logistic, Richards, and Gompertz—are investigated in the...
Recovering the relaxation spectrum, a fundamental rheological characteristic of polymers, from experiment data requires special identification methods since it is a difficult ill-posed inverse problem. Recently, a new approach relating the identifica...
We consider choice of the regularization parameter in Tikhonov method if the noise level of the data is unknown. One of the best rules for the heuristic parameter choice is the quasi-optimality criterion where the parameter is chosen as the global mi...
Synthetic aperture imaging radiometers (SAIRs) are powerful passive microwave systems for high-resolution imaging by use of synthetic aperture technique. However, the ill-posed inverse problem for SAIRs makes it difficult to reconstruct the high-prec...
In this paper, we investigate the regularization of the backward problem for a diffusion process with a time-fractional derivative. We propose a novel double-parameter regularization scheme that integrates the quasi-reversibility method for the gover...
Various types of heterogeneous observations can be combined within a parameter estimation process using spherical radial basis functions (SRBFs) for regional gravity field refinement. In this process, regularization is in most cases inevitable, and c...
We present an adaptive method for fine-tuning hyperparameters in edge-preserving regularization for PET image reconstruction. For edge-preserving regularization, in addition to the smoothing parameter that balances data fidelity and regularization, o...
The regularization parameter plays an important role in regularization-based electrical tomography (ET) algorithms, but the existing methods generally cannot determine the parameter. Moreover, these methods are not real-time since a thorough search m...
The accurate identification of kinematic parameters is crucial for improving the positioning accuracy of industrial robots, particularly in advanced manufacturing and automation. However, limited measurement space in practical applications often lead...
Time–frequency distributions (TFDs) are crucial for analyzing non-stationary signals. Compressive sensing (CS) in the ambiguity domain offers an approach for TFD reconstruction with high performance, but selecting the optimal regularization par...
Sparsity-based fault diagnosis methods have achieved great success. However, fault classification is still challenging because of neglected potential knowledge. This paper proposes a combined sparse representation deep learning (SR-DEEP) method for r...
The multi-laminated controlled release system has been widely used in the modern pharmaceutical industry because of its simple structure and safety, which can control the drug release behavior by regulating its internal parameters. To achieve three d...
Increase in downhole mining prompts the need to develop effective methods for maintenance of shafts. Currently, grouting behind the shaft wall is the main approach used for prevention of water seepage into the shaft. Several factors determine the gro...
The Padé-based method for subgroup parameter calculation in resonance self-shielding analysis is ill-posed: the truncated overdetermined system, the Vandermonde-type coefficient matrix, and the unenforced pole–residue structure jointly p...
The main difficulty posed by the parameter inversion of partial differential equations lies in the presence of numerous local minima in the cost function. Inversion fails to converge to the global minimum point unless the initial estimate is close to...
Catastrophic forgetting is a major challenge for deep learning models when they are incrementally trained on a sequence of new data. Reducing this forgetting in image and video data has been the primary research focus, but less attention has been giv...
In this paper, an adaptation method for adjusting the scaling parameters of an unscented Kalman filter (UKF) is proposed to improve the estimation performance of the filter in dynamic conditions. The proposed adaptation method is based on a sequentia...
This study investigates tri-periodic Horadam-type recurrence systems from both algebraic and computational perspectives. Algebraically, by adapting standard discrete Floquet-type and monodromy matrix viewpoints to the tri-periodic setting, the sequen...
Ill-posed problems arise in many areas of science and engineering. Tikhonov is a usual regularization which replaces the original problem by a minimization problem with a fidelity term and a regularization term. In this paper, a tensor t-production s...
Finding the best configuration of a neural network’s hyper-parameters may take too long to be feasible using an exhaustive search, especially when the cardinality of the search space has a big combinatorial number of possible solutions with var...
The study presents a robust methodology for simultaneous state and parameter estimation in nonlinear thermal systems, demonstrated on a counter-current heat exchanger model operating with nitrogen under industrial conditions. To address challenges of...
Vibration monitoring is one of the most effective approaches for bearing fault diagnosis. Within this category of techniques, sparsity constraint-based regularization has received considerable attention for its capability to accurately extract repeti...
This paper presents new developments concerning the biparametric Mittag-Leffler function,
In the fields of continuous casting and the roll stepped cooling, the heat transfer coefficient is piecewise linear. However, few papers discuss the solution of the backward heat conduction problem in this situation. Therefore, the aim of this paper...
This paper studies an inverse problem associated with the time-fractional Schrödinger equation in a field-free potential. To address the severe ill-posedness of the problem, a mollification regularization method with truncated kernels is employe...
This paper considers a Cauchy problem for the multi-dimensional modified Helmholtz equation with inhomogeneous Dirichlet and Neumann data. The Cauchy problem is severely ill-posed, and a general mollification method is introduced to solve the problem...
The presence of a nearby boundary is likely to be important in the life cycle and evolution of motile flagellate bacteria. This has led many authors to employ numerical simulations to model near-surface bacterial motion and compute hydrodynamic bound...
In this paper, an edge detection method based on the regularized Laplacian operation is given. The Laplacian operation has been used extensively as a second-order edge detector due to its variable separability and rotation symmetry. Since the image d...
In this paper, we introduced a new source condition and a new parameter-choice strategy which also gives the known best error estimate. To obtain the results we used the assumptions used in earlier studies. Further, we studied the proposed new parame...
This paper presents two new models for solving image the deblurring problem in the presence of impulse noise. One involves a high-order total variation (TV) regularizer term in the corrected total variation L1 (CTVL1) model and is named high-order co...
This work addresses the problem of non-blind image deblurring for arbitrary input noise. The problem arises in the context of sensors with strong chromatic aberrations, as well as in standard cameras, in low-light and high-speed scenarios. A short de...
Since the classical iterative methods for solving nonlinear ill-posed problems are locally convergent, this paper constructs a robust and widely convergent method for identifying parameter based on homotopy algorithm, and investigates this method’s c...
Noise in an image can affect one’s extraction of image information, therefore, image denoising is an important image pre-processing process. Many of the existing models have a large number of estimated parameters, which increases the time compl...
A new scheme for forming partially regular microreliefs by rotational rolling is proposed. A new transcendental curve-shaped, partially regular microrelief (of a trochoid type) is discussed; the shape and geometric parameters of its grooves are subst...
The modeling of developable surfaces is considered a very important application in plat-metal-based industries. Relating to the purpose, this discussion aims to obtain some formulas for constructing the regular developable Bézier patches, in w...
In this paper, a mixed-order image denoising algorithm containing fractional-order and high-order regularization terms is proposed, which effectively suppresses the staircase effect generated by the TV model and its variants while better preserving t...
The inversion of potential field data has widely utilized the generalized cross-validation (GCV) and the unbiased predictive risk estimator (UPRE) methods to determine the regularization parameter. However, these two methods are time-consuming and it...
Sparse signal processing theory has been applied to synthetic aperture radar (SAR) imaging. In compressive sensing (CS), the sparsity is usually considered as a known parameter. However, it is unknown practically. For many functions of CS, we need to...
In this article, an inverse problem with regards to the Laplace equation with non-homogeneous Neumann boundary conditions in a three-dimensional case is investigated. To deal with this problem, a regularization method (mollification method) with the...
Single-cell RNA-seq (scRNA-seq) is a powerful tool to measure the expression patterns of individual cells and discover heterogeneity and functional diversity among cell populations. Due to variability, it is challenging to analyze such data efficient...
Pyramidal neurons and interneurons play critical roles in regulating the neuronal activities in the mammalian cortex, where they exhibit different firing patterns. Pyramidal neurons mainly exhibit regular-spiking firing patterns, while interneurons h...
The Rational Function Model (RFM) is composed of numerous highly correlated Rational Polynomial Coefficients (RPCs), establishing a mathematical relationship between two-dimensional images and three-dimensional spatial coordinates. Due to the existen...
Various models were developed in the past to simulate different hydrological processes. However, discrepancies between simulated and observed values are still significant and pose a challenge to many researchers. Models contain many parameters that c...
Tautenhahn (2002) studied the Lavrentiev regularization method (LRM) to approximate a stable solution for the ill-posed nonlinear equation
The use of Raman and high-spectral lidars enables measurements of a stratospheric aerosol extinction profile independent of backscatter, and a multi-wavelength (MW) lidar can obtain additional information that can aid in retrieving the microphysical...
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