Restoration Problem Research Articles

An inertial conjugate gradient projection method for large-scale nonlinear equations and its application in the image restoration problems

Based on the acceleration effect of the inertial extrapolation technique on the convergence of iterative sequences, the number of algorithms incorporating this technique has gradually increased in recent years. Currently, there is a relative paucity of studies focusing on the Polak-Ribière-Polyak (PRP) conjugate gradient algorithm that integrate the inertial extrapolation technique. In this article, we introduce an inertial three-term PRP conjugate gradient projection method by incorporating an inertial extrapolation step into the three-term PRP algorithm, where the search direction exhibits sufficient descent and trust region characteristics. The search rule employs a derivative-free technique. Under suitable hypotheses, the proposed algorithm demonstrates global convergence. Numerical results indicate the superiority and competitiveness of this innovative method. Furthermore, its effectiveness in addressing image restoration problems underscores the practicality of this algorithm.

MODEL OF MAXIMAL WEIGHTS INVERSE CHAINS FOR THE ANALYSIS OF THE INFLUENCE FACTORS OF THE SOFTWARE COMPLEXES SUPPORT

Context. The problem of identification, formation and restoration of the boundaries of influencing factors, lost as a result of the implementation of multi-layer perceptron models into the models of subjective perception of the object of software complexes support, as well as the applied practical problem of primary monitoring of the frequency manifestation of a given influencing factor in the post-real-time mode, is considered. The object of research is the influencing factors of support of software complexes. Objective – the goal of the work is to develop a model of inverse chains of maximum weights for the analysis of influencing factors of the software complexes support. Method. A model of maximal weights inverse chains for the analysis of the influence factors of the software complexes support was developed for the analysis of the influencing factors of the software complexes support. The developed model provides possibility to identify and form feedback chains of maximum weights for the identification and further analysis of influencing factors that are reflected into the results of the object perception (the supported software complex or its support processes), by the relevant subjects of interaction which directly or indirectly interact with it. Results. Results of the resolved applied practical problem of primary monitoring of the frequency manifestation of a given influencing factor in the post-real-time mode have been provided as an example of the applied practical use of the developed model. The output results of the developed models functioning – are the reverse chains of maximum weights. In the future, the results obtained by the developed model are used to solve the applied-scientific problem of identification, formation and restoration of the boundaries of influencing factors, lost as a result of the implementation of the appropriate models of multilayer perceptron inside the models of subjective perception of the software complexes support. So the developed model of maximal weights inverse chains for the analysis of the influence factors of the software complexes support resolves this applied-scientific problem, initially caused by the implementation of the corresponding multilayer perceptron models inside the model of the subjective perception of the object of software complexessupport. The developed model provides the possibility of carrying out a qualitative analysis of the transformation of the input characteristics of the object of support into the output resulting characteristics of its subjective perception. Conclusions. Developed model allows to resolve the described problems. At the same time, the developed model improves the classical understanding of multilayer perceptron artificial neural networks, as it introduces an additional value to the neurons of hidden layers, which (starting from now) are able to perform a completely new role of influencing factors markers, while in the classical understanding of multilayer perceptron artificial neural networks they did not perform any functions other than arithmetic to ensure the possibility of correct learning and functioning of a multilayer perceptron artificial neural networks.

О проекте атласа «Биоразнообразие России»

The paper considers the relevance and possibility of developing a new cartographic work—the “Biodiversity of Russia” atlas. The aim of the work is to present the fundamental role of biodiversity in the development of nature and its importance as a national treasure, as a basis for sustainability and prosperity of Russia—a huge part of our planet. The atlas is intended to combine the efforts of various specialists to summarize modern scientific data on the biological diversity of the country’s territory. Sections of the atlas will reflect the country’s biodiversity at different levels of biota organization, including genetic, species and broadly ecosystem (soils, wetlands, forests, landscapes, biomes) diversity, based on the use of geoinformation technologies and various means of content visualization, with the use of high-quality photographs in order to achieve the greatest informativeness and visibility. The problems of biodiversity protection and restoration are discussed in detail: loss of species, Red Books, the system of specially protected natural areas in Russia and its representativeness, the share of red-listed species in the total number of species in different regions of the Russian Federation. A special problem is the situation with biodiversity assessment and protection in new regions of the country. The development of the Atlas will provide a new body of scientific knowledge about the natural component of the country, its diversity, which will allow scientifically justified organization of both the use and protection of biological diversity. Purposeful unification of such complex material in one publication will give a new impetus to the development of research in the area under consideration. The visibility and accessibility of the publication will contribute to the realization of the importance of the biodiversity problem and the need to participate in its conservation.

A Practical Contrastive Learning Framework for Single-Image Super-Resolution.

Contrastive learning has achieved remarkable success on various high-level tasks, but there are fewer contrastive learning-based methods proposed for low-level tasks. It is challenging to adopt vanilla contrastive learning technologies proposed for high-level visual tasks to low-level image restoration problems straightly. Because the acquired high-level global visual representations are insufficient for low-level tasks requiring rich texture and context information. In this article, we investigate the contrastive learning-based single-image super-resolution (SISR) from two perspectives: positive and negative sample construction and feature embedding. The existing methods take naive sample construction approaches (e.g., considering the low-quality input as a negative sample and the ground truth as a positive sample) and adopt a prior model (e.g., pretrained very deep convolutional networks proposed by visual geometry group (VGG) model) to obtain the feature embedding. To this end, we propose a practical contrastive learning framework for SISR (PCL-SR). We involve the generation of many informative positive and hard negative samples in frequency space. Instead of utilizing an additional pretrained network, we design a simple but effective embedding network inherited from the discriminator network, which is more task-friendly. Compared with the existing benchmark methods, we retrain them by our proposed PCL-SR framework and achieve superior performance. Extensive experiments have been conducted to show the effectiveness and technical contributions of our proposed PCL-SR thorough ablation studies. The code and resulting models will be released via https://github.com/Aitical/PCL-SISR.

MDTNet: Partial transformer with degradation-aware module for restoring old photos with multiple degradations

Old photos preserve the memories of the old days and have special meanings in life. However, they often suffer from severe and complex degradations, such as cracks, dirt, and noise. Old photo restoration is thus a meaningful but challenging task. Most of the current deep learning methods to repair corrupted old photos focus on one single type of degradation or limited number of degradations. The lack of proper old photo datasets makes the digital restoration problem even more challenging. In this paper, we propose MDTNet, which is a novel transformer-based method for restoring old photos with multiple degradations. MDTNet is an efficient end-to-end transformer architecture with only a single encoder and a decoder to complete the restoration. Specifically, a novel partial transformer encoder is designed with partial multi-head self-attention to extract local-global context information from the valid masked area, which represents the unbroken area. In addition, a degradation-aware module is proposed in the decoder to automatically learn different degradation information, to improve the effect of multiple degradation restoration. Moreover, a synthetic old photo dataset — the SynOld dataset — was built, which simulates the multiple degradations of real old photos. Experimental results show that the proposed method outperforms the state-of-the-art methods on both public datasets and the custom-developed dataset. The code is available at https://github.com/YuanZhaoc/MDTNet.

New hybrid conjugate gradient method for nonlinear optimization with application to image restoration problems

New hybrid conjugate gradient method for nonlinear optimization with application to image restoration problems

A novel variable neighborhood descent algorithm for service restoration in radial electrical distribution networks

Abstract This paper presents a variable neighborhood descent algorithm for the service restoration problem (SRP) in electrical distribution systems. The restoration problem appears when a permanent fault occurs in the system. The fault must be localized and isolated from the rest of the system. As a consequence of the isolation, the downstream area is de-energized and requires restoration. The variable neighborhood descent algorithm features its ability to solve the SRP for radial distribution systems and introduces a strategy that helps to deal with the system’s radiality. Tests are performed using a 53-node test system. The results show that the proposed algorithm can efficiently solve the SRP in a distribution system, and as a deterministic algorithm, the results can be used to help nondeterministic algorithms.

Modified Double Inertial Extragradient-like Approaches for Convex Bilevel Optimization Problems with VIP and CFPP Constraints

Convex bilevel optimization problems (CBOPs) exhibit a vital impact on the decision-making process under the hierarchical setting when image restoration plays a key role in signal processing and computer vision. In this paper, a modified double inertial extragradient-like approach with a line search procedure is introduced to tackle the CBOP with constraints of the CFPP and VIP, where the CFPP and VIP represent a common fixed point problem and a variational inequality problem, respectively. The strong convergence analysis of the proposed algorithm is discussed under certain mild assumptions, where it constitutes both sections that possess a mutual symmetry structure to a certain extent. As an application, our proposed algorithm is exploited for treating the image restoration problem, i.e., the LASSO problem with the constraints of fractional programming and fixed-point problems. The illustrative instance highlights the specific advantages and potential infect of the our proposed algorithm over the existing algorithms in the literature, particularly in the domain of image restoration.

A New Hybrid Descent Algorithm for Large-Scale Nonconvex Optimization and Application to Some Image Restoration Problems

Conjugate gradient methods are widely used and attractive for large-scale unconstrained smooth optimization problems, with simple computation, low memory requirements, and interesting theoretical information on the features of curvature. Based on the strongly convergent property of the Dai–Yuan method and attractive numerical performance of the Hestenes–Stiefel method, a new hybrid descent conjugate gradient method is proposed in this paper. The proposed method satisfies the sufficient descent property independent of the accuracy of the line search strategies. Under the standard conditions, the trust region property and the global convergence are established, respectively. Numerical results of 61 problems with 9 large-scale dimensions and 46 ill-conditioned matrix problems reveal that the proposed method is more effective, robust, and reliable than the other methods. Additionally, the hybrid method also demonstrates reliable results for some image restoration problems.

Spatially adaptive oscillation total generalized variation for image restoration with structured textures

Cartoon and texture are the main components of an image, and decomposing them has gained much attention in various image restoration tasks. In this paper, we propose a novel infimal convolution type model based on total generalized variation (TGV) and spatially adaptive oscillation TGV to address cartoon-texture restoration problems. The proposed spatially adaptive oscillation TGV regularizer is capable of capturing structured textures with different orientations and frequencies in localized regions. Additionally, we incorporate the second-order tensor TGV to regularize the orientation and frequency parameter. The lower semicontinuity of the new functional is established and the existence of the solutions to the proposed model is analyzed. Furthermore, we discuss suitable discretizations of the proposed model, and introduce the alternating minimization algorithm where each subproblem can be implemented by the primal-dual method. Numerical experiments on image decomposition, denoising and inpainting demonstrate that the proposed model excels in preserving textures and is competitive against existing variational and learning-based models.

Image restoration in frequency space using complex-valued CNNs.

Real-valued convolutional neural networks (RV-CNNs) in the spatial domain have outperformed classical approaches in many image restoration tasks such as image denoising and super-resolution. Fourier analysis of the results produced by these spatial domain models reveals the limitations of these models in properly processing the full frequency spectrum. This lack of complete spectral information can result in missing textural and structural elements. To address this limitation, we explore the potential of complex-valued convolutional neural networks (CV-CNNs) for image restoration tasks. CV-CNNs have shown remarkable performance in tasks such as image classification and segmentation. However, CV-CNNs for image restoration problems in the frequency domain have not been fully investigated to address the aforementioned issues. Here, we propose several novel CV-CNN-based models equipped with complex-valued attention gates for image denoising and super-resolution in the frequency domains. We also show that our CV-CNN-based models outperform their real-valued counterparts for denoising super-resolution structured illumination microscopy (SR-SIM) and conventional image datasets. Furthermore, the experimental results show that our proposed CV-CNN-based models preserve the frequency spectrum better than their real-valued counterparts in the denoising task. Based on these findings, we conclude that CV-CNN-based methods provide a plausible and beneficial deep learning approach for image restoration in the frequency domain.

Ai Art In Mobile: Topic Modeling Of User Reviews For Generative Ai Applications

The generative AI concept, which enables users to create text, image, and video content through prompts, is revolutionizing the content side and AI applications in marketing. Despite the increasing popularity of generative AI applications, the market perception regarding generative AI remains underexplored. This study aims to explore the generative AI market perception through the context of mobile applications with the help of user reviews. The study follows a structured approach including identifying the generative AI mobile applications, assessing the context through rating scores and install amounts of mobile applications, and using a topic modeling approach (BerTopic) for online reviews to identify the topics included in the conversation. 8159 user reviews from 22 mobile applications are used as sample of the study and the average rating score for the sample found as 4,06 which signals a positive perception of market. The study concludes top ten topics as; “Dissatisfaction About Amount of Advertisements in app”, “NSFW Content and Moderation”, “Praise of Application”, “Functionality Problems & Crashes”, “Payment Necessity and Trial Problems”, “In-App Purchase Restoration Problems”, “Specific Feature in App”, “Chat Function”, “Credit System” and “Excess of Ads”. The study reveals the main issues of Ai Art mobile applications for marketing decision-making processes.

INNOVATIVE MEANS OF NORMALIZING PHYSICAL FACTORS THE ENVIRONMENT IN THE PROCESSES OF RECONSTRUCTION AND RESTORATION HISTORICAL HERITAGE OBJECTS

The problems of reconstruction and restoration of historical buildings and structures are relevant all over the world. It is especially important for Ukraine, where a large number of historical buildings and buildings of architectural value have been destroyed or damaged by military operations. The developed composite materials allow, due to their small thickness, to reduce the levels of electromagnetic fields and noise to values that meet modern international standards. A particularly important result is the reduction of low-frequency noise levels (by 12–30dB), which is practically not absorbed by building materials and structures. LED sources ultraviolet radiation can be used in the presence of people for at least 8 hours without reaching the maximum permissible exposure level of 30J/m2 according to SBM-2015. The use of LED ultraviolet radiation sources allows to increase the concentration of ions in deionized air to the standard concentration (500 cm-3) within 10 minutes according to SBM-2015 and disinfect the environment.

The BiCG Algorithm for Solving the Minimal Frobenius Norm Solution of Generalized Sylvester Tensor Equation over the Quaternions

In this paper, we develop an effective iterative algorithm to solve a generalized Sylvester tensor equation over quaternions which includes several well-studied matrix/tensor equations as special cases. We discuss the convergence of this algorithm within a finite number of iterations, assuming negligible round-off errors for any initial tensor. Moreover, we demonstrate the unique minimal Frobenius norm solution achievable by selecting specific types of initial tensors. Additionally, numerical examples are presented to illustrate the practicality and validity of our proposed algorithm. These examples include demonstrating the algorithm’s effectiveness in addressing three-dimensional microscopic heat transport and color video restoration problems.

An Adaptive Missing Data Restoration Method for UAV Confrontation Based on Deep Regression Model

Completing missions with autonomous decision-making unmanned aerial vehicles (UAV) is a development direction for future battlefields. UAV make decisions based on battlefield situation information collected by sensors and can quickly and accurately perform complex tasks such as path planning, cooperative reconnaissance, cooperative pursuit and attacks. Obtaining real-time situation information of enemy is the basis for realizing autonomous decision-making of the UAV. However, in practice, due to internal sensor failure or interference of enemy, the acquired situation information is prone to be missing, which affects the training and decision-making of autonomous UAV. In this paper, an adaptive missing situation data restoration method for UAV confrontation is proposed. The UAV confrontation situation data are acquired through JSBSim, an open-source UAV simulation platform. By fusing temporal convolutional network and long short-term memory sequences, we establish a deep regression method for missing data restoration and introduce an adaptive mechanism to reduce the training time of the restoration model in response to dynamic changes in the enemy’s strategy during UAV confrontation. In addition, we evaluate the reliability of the proposed method by comparing with different baseline models under different degrees of data missing conditions. The performance of our method is quantified by five metrics. The performance of our proposed method is better than the other benchmark algorithms. The experimental results show that the proposed method can solve the missing data restoration problem and provide reliable situation data while effectively reducing the training time of the restoration model.

A novel double inertial viscosity algorithm for convex bilevel optimization problems applied to image restoration problems

Convex bilevel optimization holds a crucial role in the decision-making process in a hierarchical setting, while image restoration plays a critical role in signal processing and computer vision. In this paper, a new double inertial viscosity approximation method with a linesearch technique is introduced for solving convex bilevel optimization problems and then its strong convergence is analyzed under moderate conditions. As an application, our proposed algorithm is employed for solving image restoration problems. The experiment results highlight the specific advantages and potential infect of the algorithm over the existing algorithms in the literature, particularly in the domain of image restoration.

Моделі відновлення транспортно-логістичної інфраструктури скотарства на деокупованих територіях україни

In the conditions of de-occupation and restoration of the territories of Ukraine, an important task is the restoration of the transport and logistics infrastructure for the efficient functioning of the livestock industry. The study covers the analysis of existing problems related to the destruction of infrastructure due to military actions and proposes a set of models that contribute to the rapid and efficient recovery of this industry. The proposed models in the article are aimed at restoring production capacities, improving the efficiency of logistics processes, and ensuring the sustainable development of cattle breeding in the de-occupied territories of Ukraine. A comprehensive approach to solving the problems of infrastructure restoration will not only restore economic activity but also contribute to the long-term development of the regions. The de-occupation of the territories of Ukraine affected by military operations creates new challenges for the recovery of various sectors of the economy, including cattle breeding. The transport and logistics infrastructure, which is critical to the functioning of this industry, has suffered significant destruction. Therefore, restoring this infrastructure is critically important for ensuring the region’s food security, economic growth, and stability. Optimizing logistics routes is an essential component of infrastructure recovery. New realities of safety and accessibility must be considered, including alternative delivery routes and the use of local resources. Restoring the transport and logistics infrastructure of cattle breeding in the de-occupied territories of Ukraine is extremely important for the economic revival of the regions. The application of complex recovery models, considering modern technologies and innovative approaches, will ensure the sustainable development of agriculture and raise the standard of living of the local population. In the above-mentioned scientific study, all the main challenges and critical limitations related to the restoration and development of the transport infrastructure of Ukraine are highlighted. Keywords: transport and logistics chains, de-occupied territories, economic management, transport infrastructure, model, technologies, strategy.

A collaborative restoration strategy of resilient distribution system with the support of electric bus clusters

The widespread deployment of electric buses (EBs) offers substantial flexibility resources to support the service restoration and enhance the resilience of distribution system (DS). Therefore, this paper presents a comprehensive and collaborative service restoration strategy for resilient DS, considering the support of EBs. First, the restoration flexibility model for EBs is derived, which quantifies the restoration capability of EBs by dividing effective EB clusters. This model is integrated into the DS restoration process. Then, a two-step collaborative restoration method of DS is proposed with the aim of minimizing the load curtailment cost. The first step addresses the restoration planning problem to determine the dispatch decisions for EB clusters. Based on above planning solutions, the second step focuses on the real-time restoration problem of DS, obtaining optimal restoration results through coordinating EB clusters and other local resources. In this stage, the impact of natural disasters on the EB cluster dispatch in transportation system is considered, and a rolling optimization method is employed to deal with uncertainties from renewables, load, and EB cluster dispatch time. Finally, numerical simulations are conducted using the modified IEEE 33-bus distribution test system and a 29-node transportation system to verify the effectiveness of the proposed restoration method.

An IDFPM-based algorithm without Lipschitz continuity to constrained nonlinear equations for sparse signal and blurred image restoration problems

The derivative-free projection method (DFPM) is widely used to solve constrained nonlinear equations. To guarantee the convergence of the derivative-free projection method, the mapping should be Lipschitz continuous, which is a strict requirement in theory. Hence, it is interesting to design the new DFPM that possesses nice convergence under weaker theoretical hypothesis. In this paper, we propose an inertial DFPM-based algorithm (named IDFPM), in which the inertial extrapolation step is embedded in the design for the search direction. The global convergence of the proposed algorithm is obtained without the Lipschitz continuity of the mapping. Numerical experiments are carried out for two kinds of problems. The one consists of eight test problems from classical literature and the compressed sensing model. The numerical results show that the proposed algorithm is promising.

Novel Conjugate Gradient Methods for Image Restoration

The image restoration problem can be solved with the right techniques and tools. Although the quality of images may be lowered throughout the data collecting procedure, there are ways to do so. Clarity may be enhanced as a result of the procedure. It is the goal of image restoration to restore the original image from the damaged data. Here are some examples of applications in forensic research, picture restoration, medical imaging, astronomical imaging, and more. It can be advantageous to enhance image quality as much as possible, which justifies the expense and difficulty of the restoration methods. The conjugate gradient method is a numerical optimization technique that places emphasis on the conjugate of the coefficient in order to determine the optimal solution. The current study introduces a novel quadratic function-based coefficient conjugate gradient methodology for the removal of impulse noise from pictures. Global convergence has been shown to occur with the suggested method. The numerical results indicate that the proposed methods have high efficiency and global convergence in image restoration problems compared to the Fletcher-Reevess (FR) method.