Restoration Problem Research Articles

Distributed restoration for integrated electricity-gas-heating energy systems with an iterative loop scheme

Electricity, gas and heating networks are increasingly coupled to form an integrated energy system (IES), which is beneficial in improving the operational performance of the system during power outages. Generally, IES involves multiple energy operators, making the centralized framework impracticable. To this end, a novel distributed restoration method for IES is proposed in this paper. The IES restoration problem is formulated as a mixed-integer second-order cone programming (MISOCP) model to minimize the total load losses, which considers the coupling effects among the electricity, gas and heating networks. Then, considering the independent management and information privacy of different energy networks, the distributed restoration model is formulated by decomposing shared boundary information using the alternating direction method of multipliers (ADMM). For the sake of the non-convexity caused by binary load state variables, an iterative loop scheme is introduced in ADMM procedure. This allows us to solve a relaxed distributed model in the first stage, and perform iterative loops in the second stage, which can improve the convergence of ADMM and make the distributed solution feasible. Finally, numerical studies are conducted on 33-7-6-node IES and 123-24-32-node IES to validate the effectiveness and feasibility of the proposed method.

A socioeconomic framework for cultural heritage loss and rebuilding in post-war Ukraine: a case study learning from the Balkan experiences

ABSTRACT The war that has been raging in Ukraine since 24 February has claimed thousands of lives. The attacks by Russian forces on residential and public buildings have caused material damage on a scale not seen since the Second World War, in violation of existing international conventions. Military operations have also targeted Ukrainian cultural heritage. The conflict in the former Yugoslavia in the 1990s, which was to some extent similar, also resulted in the destruction of a large amount of immovable heritage. This article outlines promising approaches to solving the key problems of post-war heritage restoration in Ukraine, taking into account the relevant experiences of the Balkan countries. The Balkan case can provide scientific added value derived from the synthesis of the Balkan and Ukrainian experiences to increase the effectiveness of reconstruction assistance from international institutions. Practical recommendations for the establishment of an efficient post-war heritage management system are also provided.

A new hybrid approach for cold load restoration using deep learning

After an extended outage in a power system, restoration of feeders with high penetration levels of thermostatically controlled loads (TCLs) will be a challenging problem. By restoring these feeders, the demand will increase several times the normal conditions which is called the cold load pick-up (CLPU) phenomenon. This can lead to overload of equipment such as power transformers in transmission substations. In order to increase the reliability of network load supply, in transmission substations, usually several transformers are used which can be operated in parallel by closing circuit breakers on the secondary side called bus section (BS). When the restoration process is long and the loads are cold, more loads can be restored by closing the BSs and paralleling the transformers. On the other hand, it is not possible to close all the BSs simultaneously because paralleling all the transformers at the same time increases the short circuit level on the secondary side. Furthermore, in power systems, some loads are voltage-dependent and by reducing the voltage, their demand can be decreased and therefore the restoration process is expedited. Due to the increase in demand caused by CLPU, additional stress is applied to the power system, which can lead to operational constraints violation and even long-term voltage instability. Therefore, at the time of restoration of each feeder, the settings of voltage control devices are updated to avoid the violation of operational constraints and the occurrence of wider events. In this paper, in order to reduce cold load restoration time, closing the bus sections and voltage reduction are used simultaneously. Also, short circuit and operational constraints are considered. The cold load restoration problem is formulated as a mixed integer nonlinear programming and is solved using the pattern search algorithm. Since there are many decision variables and solving the problem is time-consuming, a combination of deep learning networks, pattern search algorithm and parallel computing is used to accelerate the computations.

Turning setbacks into stepping-stones for growth in conservation paleobiology

Conservation paleobiology is a cross-disciplinary field that utilizes the geohistorical record of past life on Earth to inform present-day decisions in conservation and restoration and assist in planning for future natural resource management. However, information on how past ecosystems and species responded to environmental change over decadal to millennial timescales is rarely incorporated into conservation and restoration decision-making. To heighten awareness among conservation and restoration practitioners of the relevance of geohistorical data and to bridge the gap between research and implementation in conservation paleobiology, we proposed a Research Topic titled “Integrating Conservation Biology and Paleobiology to Manage Biodiversity and Ecosystems in a Changing World”. The 21 articles subsequently published demonstrate the diversity and breadth of geohistorical information available to resource management and the challenges of translating these results into conservation practice and policy. Here we discuss the lessons we learned from editing the Research Topic and suggest a pathway forward for conservation paleobiologists who aspire to generate actionable research results to solve current problems in biodiversity conservation and ecological restoration.

Investigating the properties of mixed finite elements

The paper considers quadrature-cubic interpolation in problems of restoration of functions of two arguments. The properties of the most common finite elements Q12 (Lagrange version) and Q10 (Serendipity version) are investigated as finite elements. For more than fifty years, researchers of the finite element method have known the procedure of converting the Lagrangian model to the serendipity model. But, as is known, not all results when using this procedure satisfy users, especially proponents of physical interpretation. We are talking about the magnitude of the nodal loads of the uniform mass force of the serendipity finite element. Thus, if we consider the finite element Q10, it receives the physical inadequacy of the "spectrum" as an inheritance from the "parent" pair of Lagrangian finite elements Q8 and Q12. In Pascal's scheme, there is also a hidden connection between the finite element Q10 and the finite element Lagrangian Q12. The analysis of the inherited properties suggests that it is fundamentally possible for a Q10 substitute-base to exist in nature with the same local and integral characteristics. It turns out that the search for such a base goes beyond the capabilities of traditional modeling methods. An alternative substitute-basis Q10 was found by nonmatrix condensation of the prototype of element Q10, i.e., by using the Lagrangian model Q12. The universal nature of the non-matrix transformation of Q12 into Q10 opens up the possibility of designing a model series of mixed finite elements with physically adequate spectra of nodal loads.

Pre-conditioning CQ algorithm for solving the split feasibility problem and its application to image restoration problem

In this study, we define two pre-conditioning CQ algorithms for the split feasibility problem by using self-adaptive and line-search techniques in the real Hilbert space. One of the self-adaptive techniques is used to obtain optimal step size. These techniques do not require prior knowledge of the operator norm or estimation of the matrix norm. We also establish weak convergence theorems with respect to particular norms. As an application, numerical experiments show that the proposed algorithm is effective in image restoration problem.

Symmetry restoration and uniformly accelerated observers in Minkowski spacetime

We reassess the problem of symmetry restoration induced by observers’ acceleration within the context of interacting quantum field theories in Minkowski spacetime. We argue that the imposition of a frame-independent renormalization condition negates any observed symmetry restoration by a Rindler observer. Technically, we compute the one-loop effective potential of a λφ4 theory for an accelerated observer, employing a distinct methodology from prior investigations. Emphasizing the intricacies of the model’s renormalization, the analysis offers novel insights into the interplay between acceleration and spontaneous symmetry breaking in quantum field theory.

Modification of a conjugate gradient approach for convex constrained nonlinear monotone equations with applications in signal recovery and image restoration

Conjugate gradient (CG )methods have received widespread use in recent years for recovering damaged signals in compressive sensing. This study attempts to create a CG method that is more effective than the recent existing scheme for recovering disrupted signals. The newly created method is a modification of the method proposed by Halilu et al. (2021). Because the authors’ CG parameter can be undefined while solving general functions. As a result, to accomplish the desired result, a new CG method combined with the projection scheme of Solodov and Svaiter (1999) is presented. In addition, under mild conditions, the proposed method converges globally. Numerical experiments conducted with recent methods show the effectiveness of the proposed method. Furthermore, the proposed method is applied efficiently to address the signal recovery and image restoration problems, yielding a better result than some existing methods in the literature.

Wood is the Material of Traditional Architecture: Problems of Restoration

Wood is the Material of Traditional Architecture: Problems of Restoration

Principal Uncertainty Quantification With Spatial Correlation for Image Restoration Problems.

Uncertainty quantification for inverse problems in imaging has drawn much attention lately. Existing approaches towards this task define uncertainty regions based on probable values per pixel, while ignoring spatial correlations within the image, resulting in an exaggerated volume of uncertainty. In this paper, we propose PUQ (Principal Uncertainty Quantification) - a novel definition and corresponding analysis of uncertainty regions that takes into account spatial relationships within the image, thus providing reduced volume regions. Using recent advancements in generative models, we derive uncertainty intervals around principal components of the empirical posterior distribution, forming an ambiguity region that guarantees the inclusion of true unseen values with a user-defined confidence probability. To improve computational efficiency and interpretability, we also guarantee the recovery of true unseen values using only a few principal directions, resulting in more informative uncertainty regions. Our approach is verified through experiments on image colorization, super-resolution, and inpainting; its effectiveness is shown through comparison to baseline methods, demonstrating significantly tighter uncertainty regions.

Relaxed Inertial Projective Forward-backward Splitting Algorithms for Regularized Least Square Problems

This study presents flexible conditions of the inertial extrapolation parameter for easy implementation that is added to the algorithm in faster convergence. Modified inertial forward-backward splitting algorithms for solving variational inclusion problems are introduced to apply to solve the LASSO problem for image restoration and signal recovery, and the elastic net model for classification problem. Projection methods are used in the final step for narrowing down the search field, resulting in a better solution.

Multi-task learning with self-learning weight for image denoising

BackgroundImage denoising technology removes noise from the corrupted image by utilizing different features between image and noise. Convolutional neural network (CNN)-based algorithms have been the concern of the recent progress on diverse image restoration problems and become an efficient solution in image denoising.ObjectiveAlthough a quite number of existing CNN-based image denoising methods perform well on the simplified additive white Gaussian noise (AWGN) model, their performance often degrades severely on the real-world noisy images which are corrupted by more complicated noise.MethodsIn this paper, we utilized the multi-task learning (MTL) framework to integrate multiple loss functions for collaborative training of CNN. This approach aims to improve the denoising performance of CNNs on real-world images with non-Gaussian noise. Simultaneously, to automatically optimize the weights of individual sub-tasks within the MTL framework, we incorporated a self-learning weight layer into the CNN.ResultsExtensive experiments demonstrate that our approach effectively enhances the denoising performance of CNN-based image denoising algorithms on real-world images. It reduces excessive image smoothing, improves quantitative metrics, and enhances visual quality in the restored images.ConclusionOur method shows the effectiveness of the improved performance of denoising CNNS for real-world image denoising processing.

An Efficient Inexact Gauss–Seidel-Based Algorithm for Image Restoration with Mixed Noise

A challenge in image restoration is to recover a clear image from the blurry observation in the presence of different types of noise. There are few works addressing image deblurring under mixed noise. To handle this issue, we propose a general model based on classical wavelet tight frame regularization. We utilize a convexity-preserving term to obtain a component-wise convex model under a mild condition. Indeed, to reduce the cost of solving subproblems, the inexact Gauss–Seidel-based majorized semi-proximal alternating direction method of multipliers (sGS-imsPADMM) with relative error control is developed. Besides, the global convergence of sGS-imsPADMM is demonstrated. Numerical results for the image restoration problems show that the proposed model and solving approach are superior to some state-of-the-art methods both in numerical analysis and visual quality.

Knowledge-driven deep learning for fast MR imaging: Undersampled MR image reconstruction from supervised to un-supervised learning.

Deep learning (DL) has emerged as a leading approach in accelerating MRI. It employs deep neural networks to extract knowledge from available datasets and then applies the trained networks to reconstruct accurate images from limited measurements. Unlike natural image restoration problems, MRI involves physics-based imaging processes, unique data properties, and diverse imaging tasks. This domain knowledge needs to be integrated with data-driven approaches. Our review will introduce the significant challenges faced by such knowledge-driven DL approaches in the context of fast MRI along with several notable solutions, which include learning neural networks and addressing different imaging application scenarios. The traits and trends of these techniques have also been given which have shifted from supervised learning to semi-supervised learning, and finally, to unsupervised learning methods. In addition, MR vendors' choices of DL reconstruction have been provided along with some discussions on open questions and future directions, which are critical for the reliable imaging systems.

Image restoration for ring-array photoacoustic tomography system based on blind spatially rotational deconvolution

Ring-array photoacoustic tomography (PAT) system has been widely used in noninvasive biomedical imaging. However, the reconstructed image usually suffers from spatially rotational blur and streak artifacts due to the non-ideal imaging conditions. To improve the reconstructed image towards higher quality, we propose a concept of spatially rotational convolution to formulate the image blur process, then we build a regularized restoration problem model accordingly and design an alternating minimization algorithm which is called blind spatially rotational deconvolution to achieve the restored image. Besides, we also present an image preprocessing method based on the proposed algorithm to remove the streak artifacts. We take experiments on phantoms and in vivo biological tissues for evaluation, the results show that our approach can significantly enhance the resolution of the image obtained from ring-array PAT system and remove the streak artifacts effectively.

Pretraining a foundation model for generalizable fluorescence microscopy-based image restoration.

Fluorescence microscopy-based image restoration has received widespread attention in the life sciences and has led to significant progress, benefiting from deep learning technology. However, most current task-specific methods have limited generalizability to different fluorescence microscopy-based image restoration problems. Here, we seek to improve generalizability and explore the potential of applying a pretrained foundation model to fluorescence microscopy-based image restoration. We provide a universal fluorescence microscopy-based image restoration (UniFMIR) model to address different restoration problems, and show that UniFMIR offers higher image restoration precision, better generalization and increased versatility. Demonstrations on five tasks and 14 datasets covering a wide range of microscopy imaging modalities and biological samples demonstrate that the pretrained UniFMIR can effectively transfer knowledge to a specific situation via fine-tuning, uncover clear nanoscale biomolecular structures and facilitate high-quality imaging. This work has the potential to inspire and trigger new research highlights for fluorescence microscopy-based image restoration.

To the issue of the rights and obligations of land users in the field of land restoration

The article is devoted to the problem of legal protection of the rights and obligations of land users in the field of land restoration. The article emphasizes that a significant part of lands, regardless of their purpose, requires urgent restoration measures, however, scientific works highlight only certain aspects of legal protection and restoration of lands, as well as a comprehensive analysis of issues related to ensuring the realization of the rights and fulfillment of the obligations of owners and users of land plots for their protection and restoration actually do not exist.
 The article emphasizes that the content of legal relations consists of subjective rights and legal obligations. The viewpoints of scientists regarding the specified concepts were studied. Attention is drawn to the fact that legal relations in the field of land restoration belong to the active type of legal relations, because the provision of land restoration requires active actions on the part of the obliged entities.
 The main legal relationship for land restoration is a legal obligation that manifests itself in the active behavior of the obligated person in order to ensure the subjective rights of other subjects.
 The general rights and responsibilities of land plot users under current land legislation have been analyzed. Legal conflicts and gaps in the specified area have been studied. It was emphasized that land plots should be restored by both their owners and users in the process of their exploitation. It is proposed to make appropriate changes to the land legislation regarding the expansion and systematization of the rights and obligations of land plot users.
 The author examines the grounds for compulsory termination of rights to land plots. The author emphasizes the peculiarities of the grounds for compulsory termination of the right to use a land plot, which is the failure to eliminate the committed violations of the law by the land user.
 Some attention is paid to the problem of land restoration in the conditions of hostilities. The issue of compensation for damages caused as a result of emergency situations and armed aggression was investigated. Legislative norms aimed at determining damage and compensation for damage to owners and users of land plots have been analyzed.

Hybrid regularization inspired by total variation and deep denoiser prior for image restoration

Image restoration is a fundamental problem in computer vision, with the goal of restoring high-quality images from degraded low-quality observation images. However, the ill-posedness of restoration problem often leads to artifacts in the results. It inspires us to study the combination of prior, effectively restrict the solution space and improving the quality of the restored image. In this paper, a novel hybrid regularization method for image restoration is proposed, which adopts both internal and external image priors into a unified framework. Specifically, a new hybrid regularization model is designed. The TV model and a deep image denoiser are inserted into the restoration model using the plug-and-play framework, protecting image details while implicitly using external information for deep denoising. Moreover, in order to make the proposed hybrid regularization operable, an adaptive parameter method is proposed to adaptively balance the TV model and learned model in iteration. Experiments show that the proposed method surpasses the performance of existing image restoration techniques.

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.

Inertial Krasnosel’skiĭ-Mann iterative algorithm with step-size parameters involving nonexpansive mappings with applications to solve image restoration problems

Inertial Krasnosel’skiĭ-Mann iterative algorithm with step-size parameters involving nonexpansive mappings with applications to solve image restoration problems