Vector Extrapolation Based Landweber Method for Discrete Ill‐Posed Problems

Zhao, Xi-Le; Huang, Ting‐Zhu; Gu, Xian-Ming; Deng, Liang-Jian

doi:10.1155/2017/1375716

Cited by 8 publications

(4 citation statements)

References 25 publications

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“…Therefore, we intend to extend the RcdMathLib with machine learning or digital signal processing algorithms. We also aim to extend the package with an additional algorithm for solving nonlinear problems called the Landweber method [ 65 ].…”

Section: Discussionmentioning

confidence: 99%

RcdMathLib: An Open Source Software Library for Computing on Resource-Limited Devices

Kasmi

Norrdine

Schiller

et al. 2021

Sensors

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We developped an open source library called RcdMathLib for solving multivariate linear and nonlinear systems. RcdMathLib supports on-the-fly computing on low-cost and resource-constrained devices, e.g., microcontrollers. The decentralized processing is a step towards ubiquitous computing enabling the implementation of Internet of Things (IoT) applications. RcdMathLib is modular- and layer-based, whereby different modules allow for algebraic operations such as vector and matrix operations or decompositions. RcdMathLib also comprises a utilities-module providing sorting and filtering algorithms as well as methods generating random variables. It enables solving linear and nonlinear equations based on efficient decomposition approaches such as the Singular Value Decomposition (SVD) algorithm. The open source library also provides optimization methods such as Gauss–Newton and Levenberg–Marquardt algorithms for solving problems of regression smoothing and curve fitting. Furthermore, a positioning module permits computing positions of IoT devices using algorithms for instance trilateration. This module also enables the optimization of the position by performing a method to reduce multipath errors on the mobile device. The library is implemented and tested on resource-limited IoT as well as on full-fledged operating systems. The open source software library is hosted on a GitLab repository.

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Section: Discussionmentioning

confidence: 99%

RcdMathLib: An Open Source Software Library for Computing on Resource-Limited Devices

Kasmi

Norrdine

Schiller

et al. 2021

Sensors

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“…The repaired photos appear blocky as a result. To mitigate the staircase effects in restored images, one solution is to employ total fractional-order variation (TFOV)-based models [26][27][28][29][30][31][32]. These models have been proposed as an alternative approach to address the limitations of the TV model and reduce the undesirable staircase artifacts.…”

Section: Related Workmentioning

confidence: 99%

Total Fractional-Order Variation-Based Constraint Image Deblurring Problem

2023

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When deblurring an image, ensuring that the restored intensities are strictly non-negative is crucial. However, current numerical techniques often fail to consistently produce favorable results, leading to negative intensities that contribute to significant dark regions in the restored images. To address this, our study proposes a mathematical model for non-blind image deblurring based on total fractional-order variational principles. Our proposed model not only guarantees strictly positive intensity values but also imposes limits on the intensities within a specified range. By removing negative intensities or constraining them within the prescribed range, we can significantly enhance the quality of deblurred images. The key concept in this paper involves converting the constrained total fractional-order variational-based image deblurring problem into an unconstrained one through the introduction of the augmented Lagrangian method. To facilitate this conversion and improve convergence, we describe new numerical algorithms and introduce a novel circulant preconditioned matrix. This matrix effectively overcomes the slow convergence typically encountered when using the conjugate gradient method within the augmented Lagrangian framework. Our proposed approach is validated through computational tests, demonstrating its effectiveness and viability in practical applications.

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“…Due to their faster convergence, Krylov subspace methods have recently gained more attention compared with the Landweber and Kaczmarz techniques [25]. Nevertheless, due to more semi-convergence behavior, the Krylov subspace method is prone to poor solution accuracy without appropriate stopping criteria [26]. On the other hand, the Landweber method is still superior in terms of simplicity and stability, which makes it more suitable in some real-world applications [27,28].…”

Section: Introductionmentioning

confidence: 99%

Iterative-Based Impact Force Identification on a Bridge Concrete Deck

Rashidi,

Tashakori,

Kalhori

et al. 2023

Sensors

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Steel-reinforced concrete decks are prominently utilized in various civil structures such as bridges and railways, where they are susceptible to unforeseen impact forces during their operational lifespan. The precise identification of the impact events holds a pivotal role in the robust health monitoring of these structures. However, direct measurement is not usually possible due to structural limitations that restrict arbitrary sensor placement. To address this challenge, inverse identification emerges as a plausible solution, albeit afflicted by the issue of ill-posedness. In tackling such ill-conditioned challenges, the iterative regularization technique known as the Landweber method proves valuable. This technique leads to a more reliable and accurate solution compared with traditional direct regularization methods and it is, additionally, more suitable for large-scale problems due to the alleviated computation burden. This paper employs the Landweber method to perform a comprehensive impact force identification encompassing impact localization and impact time–history reconstruction. The incorporation of a low-pass filter within the Landweber-based identification procedure is proposed to augment the reconstruction process. Moreover, a standardized reconstruction error metric is presented, offering a more effective means of accuracy assessment. A detailed discussion on sensor placement and the optimal number of regularization iterations is presented. To automatedly localize the impact force, a Gaussian profile is proposed, against which reconstructed impact forces are compared. The efficacy of the proposed techniques is illustrated by utilizing the experimental data acquired from a bridge concrete deck reinforced with a steel beam.

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Vector Extrapolation Based Landweber Method for Discrete Ill‐Posed Problems

Cited by 8 publications

References 25 publications

RcdMathLib: An Open Source Software Library for Computing on Resource-Limited Devices

RcdMathLib: An Open Source Software Library for Computing on Resource-Limited Devices

Total Fractional-Order Variation-Based Constraint Image Deblurring Problem

Iterative-Based Impact Force Identification on a Bridge Concrete Deck

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