A New Method for TSVD Regularization Truncated Parameter Selection

Wu, Zemin; Bian, Shaofeng; Chen, Xiang; Tong, Yude

doi:10.1155/2013/161834

Cited by 11 publications

(5 citation statements)

References 22 publications

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“…TSVD regularization, on the other hand, has a greater ability to suppress noise. The mathematical principle underlying TSVD is given as follows ( Wu et al, 2013 ).

k is the truncation parameter, and like Tikhonov, it may be found using the L-BAA method.…”

Section: Methodsmentioning

confidence: 99%

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Solving the inverse problem in electrocardiography imaging for atrial fibrillation using various time-frequency decomposition techniques based on empirical mode decomposition: A comparative study

Zhang

Lian

2022

Front. Physiol.

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Electrocardiographic imaging (ECGI) can aid in identifying the driving sources that cause and sustain atrial fibrillation (AF). Traditional regularization strategies for addressing the ECGI inverse problem are not currently concerned about the multi-scale analysis of the inverse problem, and these techniques are not clinically reliable. We have previously investigated the solution based on uniform phase mode decomposition (UPEMD-based) to the ECGI inverse problem. Numerous other methods for the time-frequency analysis derived from empirical mode decomposition (EMD-based) have not been applied to the inverse problem in ECGI. By applying many EMD-based solutions to the ECGI inverse problem and evaluating the performance of these solutions, we hope to find a more efficient EMD-based solution to the ECGI inverse problem. In this study, five AF simulation datasets and two real datasets from AF patients derived from a clinical ablation procedure are employed to evaluate the operating efficiency of several EMD-based solutions. The Pearson’s correlation coefficient (CC), the relative difference measurement star (RDMS) of the computed epicardial dominant frequency (DF) map and driver probability (DP) map, and the distance (Dis) between the estimated and referenced most probable driving sources are used to evaluate the application of various EMD-based solutions in ECGI. The results show that for DF maps on all simulation datasets, the CC of UPEMD-based and improved UPEMD (IUPEMD)-based techniques are both greater than 0.95 and the CC of the empirical wavelet transform (EWT)-based solution is greater than 0.889, and the RDMS of UPEMD-based and IUPEMD-based approaches is less than 0.3 overall and the RDMS of EWT-based method is less than 0.48, performing better than other EMD-based solutions; for DP maps, the CC of UPEMD-based and IUPEMD-based techniques are close to 0.5, the CC of EWT-based is 0.449, and the CC of the remaining EMD-based techniques on the SAF and CAF is all below 0.1; the RDMS of UPEMD-based and IUPEMD-based are 0.06∼0.9 less than that of other EMD-based methods for all the simulation datasets overall. On two authentic AF datasets, the Dis between the first 10 real and estimated maximum DF positions of UPEMD-based and EWT-based methods are 212∼1440 less than that of others, demonstrating these two EMD-based solutions are superior and are suggested for clinical application in solving the ECGI inverse problem. On all datasets, EWT-based algorithms deconstruct the signal in the shortest time (no more than 0.12s), followed by UPEMD-based solutions (less than 0.81s), showing that these two schemes are more efficient than others.

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“…TSVD regularization, on the other hand, has a greater ability to suppress noise. The mathematical principle underlying TSVD is given as follows ( Wu et al, 2013 ).

k is the truncation parameter, and like Tikhonov, it may be found using the L-BAA method.…”

Section: Methodsmentioning

confidence: 99%

“…TSVD regularization, on the other hand, has a greater ability to suppress noise. The mathematical principle underlying TSVD is given as follows (Wu et al, 2013).…”

Section: Inverse Problemmentioning

confidence: 99%

Solving the inverse problem in electrocardiography imaging for atrial fibrillation using various time-frequency decomposition techniques based on empirical mode decomposition: A comparative study

Zhang

Lian

2022

Front. Physiol.

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“…While, if the iteration continues to the solution x = A −1 B, which is referred to the asymptotic convergence, the solution will be less accurate. This is what occurs in regularization methods with fixed regularization parameters [7][8][9][10][11][12][13][14][15], which leads to a naive solution and, in some cases, may even diverge.…”

Section: Landweber Regularizationmentioning

confidence: 99%

“…Impact force reconstruction methods are usually ill-posed, which results in sensitivity to measurement noises. To deal with the ill-posedness, several regularization techniques are exploited in the literature, such as the Tikhonov method [7,8], Truncated Singular Value Decomposition (TSVD) [9], and Bayesian regularization [10,11]. Finding an optimum regularization parameter plays an important role in the regularization performance, for which various techniques like Generalized Cross Value (GCV) [12], L-curve [13], l 1 and l 2 norm [14,15], etc., are proposed.…”

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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“…2) TSVD: has also been proposed [30], [31] aiming to overcome the ill-posing character of signal models like the one in (6). To do this, TSVD uses a better defined transfer matrix than H, denoted by H k .…”

Section: A Matrix Notation and Regularizationmentioning

confidence: 99%

Generalization and Regularization for Inverse Cardiac Estimators

Meseguer

Everss

Gutierrez-Fernandez-Calvillo

et al. 2022

IEEE Trans. Biomed. Eng.

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Electrocardiographic Imaging (ECGI) aims to estimate the intracardiac potentials noninvasively, hence allowing the clinicians to better visualize and understand many arrhythmia mechanisms. Most of the estimators of epicardial potentials use a signal model based on an estimated spatial transfer matrix together with Tikhonov regularization techniques, which works well specially in simulations, but it can give limited accuracy in some real data. Based on the quasielectrostatic potential superposition principle, we propose a simple signal model that supports the implementation of principled out-of-sample algorithms for several of the most widely used regularization criteria in ECGI problems, hence improving the generalization capabilities of several of the current estimation methods. Experiments on simple cases (cylindrical and Gaussian shapes scrutinizing fast and slow changes, respectively) and on real data (examples of torso tank measurements available from Utah University, and an animal torso and epicardium measurements available from Maastricht University, both in the EDGAR public repository) show that the superposition-based out-of-sample tuning of regularization parameters promotes stabilized estimation errors of the unknown source potentials, while slightly increasing Manuscript

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A New Method for TSVD Regularization Truncated Parameter Selection

Cited by 11 publications

References 22 publications

Solving the inverse problem in electrocardiography imaging for atrial fibrillation using various time-frequency decomposition techniques based on empirical mode decomposition: A comparative study

Solving the inverse problem in electrocardiography imaging for atrial fibrillation using various time-frequency decomposition techniques based on empirical mode decomposition: A comparative study

Iterative-Based Impact Force Identification on a Bridge Concrete Deck

Generalization and Regularization for Inverse Cardiac Estimators

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