The Use of L-Curve and U-Curve in Inverse Electromagnetic Modelling

Krawczyk-Stańdo, D.; Rudnicki, Marek

doi:10.1007/978-3-540-78490-6_9

Cited by 16 publications

(14 citation statements)

References 7 publications

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“…However, it may fail to find an appropriate λ when the point of the maximum curvature is difficult to detect [15,16], and the reconstructed images may tend to be oversmooth in some cases [17,19]. In previous studies, the U-curve method has been proposed and tested in some numerical applications [18,19] and FDOT problems [20]. In this study, the feasibility of the U-curve criterion for DFMT problems is investigated, and the performances are compared with those of the L-curve method.…”

Section: Discussionmentioning

confidence: 99%

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Automatic selection of regularization parameters for dynamic fluorescence molecular tomography: a comparison of L-curve and U-curve methods

Chen¹,

Su²,

Zhou³

et al. 2016

Biomed. Opt. Express

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Dynamic fluorescence molecular tomography (FMT) is a promising technique for the study of the metabolic process of fluorescent agents in the biological body in vivo, and the quality of the parametric images relies heavily on the accuracy of the reconstructed FMT images. In typical dynamic FMT implementations, the imaged object is continuously monitored for more than 50 minutes. During each minute, a set of the fluorescent measurements is acquired and the corresponding FMT image is reconstructed. It is difficult to manually set the regularization parameter in the reconstruction of each FMT image. In this paper, the parametric images obtained with the L-curve and U-curve methods are quantitatively evaluated through numerical simulations, phantom experiments and in vivo experiments. The results illustrate that the U-curve method obtains better accuracy, stronger robustness and higher noise-resistance in parametric imaging. Therefore, it is a promising approach to automatic selection of the regularization parameters for dynamic FMT.

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Section: Discussionmentioning

confidence: 99%

“…As an alternative to L-curve, the U-curve method has been proposed [18,19], and its feasibility for FMT problems has been studied [20]. It has been proved that the U-curve always has a local minimum [18].…”

Section: Introductionmentioning

confidence: 99%

Automatic selection of regularization parameters for dynamic fluorescence molecular tomography: a comparison of L-curve and U-curve methods

Chen¹,

Su²,

Zhou³

et al. 2016

Biomed. Opt. Express

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“…This explains the recent emergence of automated methods of selecting α that do not require a priori information about the solution, in particular, the L-curve method [23], the U-curve method [4] and the generalized cross-validation method [6]. Detailed information about them can also be found in monograph [8] and paper [15]. However, the practice of inverse problems solving, as it is also shown in [30], has demonstrated many situations where the implementation of these methods is linked to some mathematical challenges arising, for instance, from absence of a clearly defined angle in the L-curve or a local minimum of the U-curve in the interval of definition of the values of regularization parameter α.…”

Section: Fig 4 Algorithm For Non-stationary Loads Identificationmentioning

confidence: 99%

Identification of dynamic loads applied to an elastically deformed element of constructions

Lachmayer

Yanchevskyi

Mozgova

et al. 2018

ACM

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The technique has been presented for time-dependence identification of several independent beetwen each other loads distributed over a given area of a structure with arbitrary topology by using quantity values more convenient for measurements. In the assumption that the structure's response linearly depends on the loads, the considered problem, which belongs to the class of boundary inverse problems in the mechanics of solids, is reduced to a system of linear algebraic equations for coefficients that approximate the sought-for influences. The system is solved using a regularizing algorithm providing stability of results to random errors in initial data and calculation errors. Concrete calculations, substantiating the efficiency of the presented technique, have been performed as with theoretical data to identify two non-stationary loads applied to a wheel carrier of a race car as with experimental data to restore an impact force applied to a round plate with fixed boundary. To calculate values of a system's elements corresponding to values of measured quantities under unit loads, the finite element method was used. The suggested technique can be used for designing structures with complex geometry based on criterias of their dynamic (fatigue) strength, etc.

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“…Some of the common methods to determine the regularization parameter in inverse problems are the L-curve method of Hansen (1992Hansen ( , 2000 and U -curve method of KrawczykStańDo and Rudnicki (2007) and Krawczyk-Stado and Rudnicki (2008). After trials with both methods we selected the U -curve method.…”

Section: Selection Of the Regularization Parametermentioning

confidence: 99%

Regularization destriping of remote sensing imagery

Basnayake¹,

Bollt²,

Tufillaro³

et al. 2017

Nonlin. Processes Geophys.

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Abstract. We illustrate the utility of variational destriping for ocean color images from both multispectral and hyperspectral sensors. In particular, we examine data from a filter spectrometer, the Visible Infrared Imaging Radiometer Suite (VIIRS) on the Suomi National Polar Partnership (NPP) orbiter, and an airborne grating spectrometer, the Jet Population Laboratory's (JPL) hyperspectral Portable Remote Imaging Spectrometer (PRISM) sensor. We solve the destriping problem using a variational regularization method by giving weights spatially to preserve the other features of the image during the destriping process. The target functional penalizes "the neighborhood of stripes" (strictly, directionally uniform features) while promoting data fidelity, and the functional is minimized by solving the Euler-Lagrange equations with an explicit finite-difference scheme. We show the accuracy of our method from a benchmark data set which represents the sea surface temperature off the coast of Oregon, USA. Technical details, such as how to impose continuity across data gaps using inpainting, are also described.

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The Use of L-Curve and U-Curve in Inverse Electromagnetic Modelling

Cited by 16 publications

References 7 publications

Automatic selection of regularization parameters for dynamic fluorescence molecular tomography: a comparison of L-curve and U-curve methods

Automatic selection of regularization parameters for dynamic fluorescence molecular tomography: a comparison of L-curve and U-curve methods

Identification of dynamic loads applied to an elastically deformed element of constructions

Regularization destriping of remote sensing imagery

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