The Experts below are selected from a list of 327 Experts worldwide ranked by ideXlab platform
Piotr Fryzlewicz - One of the best experts on this subject based on the ideXlab platform.
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Multiscale interpretation of Taut String estimation and its connection to Unbalanced Haar wavelets
Statistics and Computing, 2011Co-Authors: Piotr FryzlewiczAbstract:We compare two state-of-the-art non-linear techniques for nonparametric function estimation via piecewise constant approximation: the Taut String and the Unbalanced Haar methods. While it is well-known that the latter is multiscale, it is not obvious that the former can also be interpreted as multiscale. We provide a unified multiscale representation for both methods, which offers an insight into the relationship between them as well as suggesting lessons both methods can learn from each other.
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multiscale interpretation of Taut String estimation and its connection to unbalanced haar wavelets
Statistics and Computing, 2011Co-Authors: Piotr FryzlewiczAbstract:We compare two state-of-the-art non-linear techniques for nonparametric function estimation via piecewise constant approximation: the Taut String and the Unbalanced Haar methods. While it is well-known that the latter is multiscale, it is not obvious that the former can also be interpreted as multiscale. We provide a unified multiscale representation for both methods, which offers an insight into the relationship between them as well as suggesting lessons both methods can learn from each other.
Eric Setterqvist - One of the best experts on this subject based on the ideXlab platform.
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Invariant $\varphi$-Minimal Sets and Total Variation Denoising on Graphs
Siam Journal on Imaging Sciences, 2019Co-Authors: Clemens Kirisits, Otmar Scherzer, Eric SetterqvistAbstract:Total variation flow, total variation regularization, and the Taut String algorithm are known to be equivalent filters for one-dimensional discrete signals. In addition, the filtered signal simulta...
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Real-time communication systems based on Taut Strings
Journal of Communications and Networks, 2018Co-Authors: Eric Setterqvist, Robert ForchheimerAbstract:We consider buffered real-time communication over channels with time-dependent capacities which are known in advance. The real-time constraint is imposed in terms of limited transmission time between sender and receiver. For a network consisting of a single channel it is shown that there is a coding rate strategy, geometrically characterized as a Taut String, which minimizes the average distortion with respect to all convex distortion-rate functions. Utilizing the Taut String characterization further, an algorithm that computes the optimal coding rate strategy is provided. We then consider more general networks with several connected channels in parallel or series with intermediate buffers. It is shown that also for these networks there is a coding rate strategy, geometrically characterized as a Taut String, which minimizes the average distortion with respect to all convex distortion-rate functions. The optimal offline strategy provides a benchmark for the evaluation of different coding rate strategies. Further, it guides us in the construction of a simple but rather efficient strategy for channels in the online setting which alternates between a good and a bad state.
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Taut Strings and Real Interpolation
2016Co-Authors: Eric SetterqvistAbstract:The Taut String problem concerns finding the function with the shortest graph length, i.e. the Taut String, in a certain set of continuous piecewise linear functions. It has appeared in a broad ra ...
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Energy of Taut Strings accompanying Wiener process
Stochastic Processes and their Applications, 2015Co-Authors: Mikhail Lifshits, Eric SetterqvistAbstract:Let W be a Wiener process. For r>0 and T>0 let IW(T,r)2 denote the minimal value of the energy ∫0Th′(t)2dt taken among all absolutely continuous functions h(⋅) defined on [0,T], starting at zero and satisfying W(t)−r≤h(t)≤W(t)+r,0≤t≤T. The function minimizing energy is a Taut String, a classical object well known in Variational Calculus, in Mathematical Statistics, and in a broad range of applications. We show that there exists a constant C∈(0,∞) such that for any q>0rT1/2IW(T,r)⟶LqC,as rT1/2→0, and for any fixed r>0, rT1/2IW(T,r)⟶a.s.C,as T→∞. Although precise value of C remains unknown, we give various theoretical bounds for it, as well as rather precise results of computer simulation.
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Energy of Taut Strings accompanying Wiener process
arXiv: Probability, 2014Co-Authors: Mikhail Lifshits, Eric SetterqvistAbstract:Let $W$ be a Wiener process. The function $h(\cdot)$ minmizing energy $\int_0^T h'(t)^2\, dt$ among all functions satisfying $W(t)-r \le h(t) \le W(t)+ r$ on an interval $[0,T]$ is called Taut String. This is a classical object well known in Variational Calculus, Mathematical Statistics, etc. We show that the energy of this Taut String on large intervals is equivalent to $C^2 T\, /\, r^2$ where $C$ is some finite positive constant. While the precise value of $C$ remains unknown, we give various theoretical bounds for it as well as rather precise results of computer simulation. While the Taut String clearly depends on entire trajectory of $W$, we also consider an adaptive version of the problem by giving a construction (Markovian pursuit) of a random function based only on the past values of $W$ and having minimal asymptotic energy. The solution, an optimal pursuit strategy, quite surprisingly turns out to be related with a classical minimization problem for Fisher information on the bounded interval.
Angelo Luongo - One of the best experts on this subject based on the ideXlab platform.
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Semi-analytical approaches for the nonlinear dynamics of a Taut String subject to a moving load
Nonlinear Dynamics, 2019Co-Authors: Manuel Ferretti, Giuseppe Piccardo, Angelo LuongoAbstract:The nonlinear behavior induced by a moving force on the dynamics of a nonlinear Taut String is investigated. In these cases, classic perturbation solutions are only applicable to the weakly nonlinear problem and pertain to small values of dimensionless parameters governing the system. A change of coordinate that is dependent on the nonlinear quasi-static response of the String enables the formulation of a new set of governing equations for an incremental dynamic variable. These new equations are obtained using a closed-form expression for the nonlinear quasi-static displacement of the String. The solution to the linearized form of the governing equations allows us to compute the effective dynamic response even in the presence of strong nonlinearities, for which String dynamic tensions can reach values over twice the static ones. The proposed procedure also shows good reduction characteristics and permits a description of the dynamic response using a small number of eigenfunctions. Applications of the procedure show that, unless the speed of the moving load is sufficiently large, the nonlinear behavior of the String is captured by the quasi-static solution, whereas the dynamics are captured by the linearized equations of motion about this state.
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solution to the problem of a mass traveling on a Taut String via integral equation
Advances in Mathematical Physics, 2019Co-Authors: Manuel Ferretti, Angelo LuongoAbstract:The problem of a massive Taut String, traveled by a heavy point mass, moving with an assigned law, is formulated in a linear context. Displacements are assumed to be transverse, and the dynamic tension is neglected. The equations governing the moving boundary problem are derived via a variational principle, in which the geometric compatibility between the point mass and the String is enforced via a Lagrange multiplier, having the meaning of transverse reactive force. The equations are rearranged in the form of a unique Volterra integral equation in the reactive force, which is solved numerically. A classical Galerkin solution is implemented for comparison. Numerical results throw light on the physics of the phenomenon and confirm the effectiveness of the algorithm.
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Statics of Shallow Inclined Elastic Cables under General Vertical Loads: A Perturbation Approach
Mathematics, 2018Co-Authors: Angelo Luongo, Daniele ZulliAbstract:The static problem for elastic shallow cables suspended at points at different levels under general vertical loads is addressed. The cases of both suspended and Taut cables are considered. The funicular equation and the compatibility condition, well known in literature, are here shortly re-derived, and the commonly accepted simplified hypotheses are recalled. Furthermore, with the aim of obtaining simple asymptotic expressions with a desired degree of accuracy, a perturbation method is designed, using the Taut String solution as the generator system. The method is able to solve the static problem for any distributions of vertical loads and shows that the usual, simplified analysis is just the first step of the perturbation procedure proposed here.
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Static Perturbation Analysis of Inclined Shallow Elastic Cables under general 3D-loads
Curved and Layered Structures, 2016Co-Authors: Angelo Luongo, Daniele ZulliAbstract:Abstract Inclined, shallow, elastic cables under static 3D loads, arbitrarily distributed, are studied. Cables having natural length both larger or smaller than the distance between the supports (i.e. suspended or Taut cables, respectively), are considered. Kinematically exact equations are derived, and projected onto an orthonormal basis intrinsic to the chord. A perturbation procedure is proposed, which extrapolates the solution relevant to the Taut String, up to the desired order, and leads to a closed-form solution. Lower-order solutions are consistent with the hypotheses normally adopted in technical environment. Emphasis is given to the mechanical interpretation of the cable behavior. The asymptotic solution is compared to the explicit (not in closed-form) solution of the literature.
David Mascareñas - One of the best experts on this subject based on the ideXlab platform.
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Estimation of full-field, full-order experimental modal model of cable vibration from digital video measurements with physics-guided unsupervised machine learning and computer vision
Structural Control and Health Monitoring, 2019Co-Authors: Yongchao Yang, Lorenzo Sanchez, Alexander Roeder, John Bowlan, C Farrar, Jared Crochet, Huiying Zhang, David MascareñasAbstract:Cables are critical components for a variety of structures such as stay cables and suspenders of cable‐stayed bridges and suspension bridges. When in operational service, they are vulnerable to cumulative fatigue damage induced by dynamic loads (e.g., the cyclic vehicle loads and wind excitation). To accurately analyze and predict their dynamics behaviors and performance that could be spatially local and temporal transient, it is essential to perform high‐resolution vibration measurements, from which their dynamics properties are identified and, subsequently, a high spatial resolution, full‐modal‐order dynamics model of cable vibration can be established. This study develops a physics‐guided, unsupervised machine learning‐based video processing approach that can blindly and efficiently extract the full‐field (as many points as the pixel number of the video frame) modal parameters of cable vibration using only the video of an operating (output‐only) cable. In particular, by incorporating the physics of cable vibration (Taut String model), a novel automated modal motion filtering method is proposed to enable autonomous identification of full‐order (as many modes as possible) dynamic parameters, including those weakly excited modes that used to be challenging to identify in operational modal analysis. Therefore, a full‐field, full‐order modal model of cable vibration is established by the proposed method. Furthermore, this new approach provides a low‐cost and noncontact technique to estimate the cable tension using only the video of the vibrating cable where the fundamental frequency is automatically and efficiently estimated to compute the cable tension according to the Taut String equation. Laboratory experiments on a bench‐scale cable are conducted to validate the developed approach.
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Establishment of Full-Field, Full-Order Dynamic Model of Cable Vibration by Video Motion Manipulations
Special Topics in Structural Dynamics Volume 6, 2017Co-Authors: Lorenzo Sanchez, Alexander Roeder, John Bowlan, Jared Crochet, Yongchao Yang, Huiying Zhang, Charles R. Farrar, David MascareñasAbstract:In-service cables such as stay cables and suspenders of cable-stayed bridges and suspension bridges, are subjected to dynamic loads (e.g., the vehicle loads and wind excitation). Performing vibration measurements and subsequently identifying the dynamic properties and establishing a dynamic model of cable vibration are essential for their dynamic analysis, condition assessment, and performance prediction. For example, based on the Taut-String theory, the cable tension, as a critical indicator of cable performance and health state, can be computed using its frequency that can be identified from the measured cable vibration responses. Traditional contact-type wired or wireless sensors, such as accelerometers and strain gauge sensors, require physically attaching to the structure for vibration measurements, which could induce the mass effect. In addition, installing these sensors on structures is costly, time-consuming, and allows instrumentations at a limited number of places. On the other hand, digital video cameras have emerged as a cost effective and agile non-contact vibration measurement method, offering high-resolution, simultaneous, measurements. Recently, digital video camera measurements processed by advanced computer vision and machine learning algorithms have been successfully used for experimental and operational full-field vibration measurement and modal analysis. This study develops a video measurement and processing based technique that can autonomously and blindly extract the full-field dynamic parameters of cable vibration from the video measurements. In addition, by exploiting the Taut String theory, full-order (as many modes as possible) dynamic parameters are also extracted. Therefore, a full-field, full-order dynamic (modal) model of cable vibration is established. Laboratory experiments are conducted to validate the developed approach.
Otmar Scherzer - One of the best experts on this subject based on the ideXlab platform.
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Invariant $\varphi$-Minimal Sets and Total Variation Denoising on Graphs
Siam Journal on Imaging Sciences, 2019Co-Authors: Clemens Kirisits, Otmar Scherzer, Eric SetterqvistAbstract:Total variation flow, total variation regularization, and the Taut String algorithm are known to be equivalent filters for one-dimensional discrete signals. In addition, the filtered signal simulta...
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Bivariate density estimation using BV regularisation
Computational Statistics & Data Analysis, 2007Co-Authors: Andreas Obereder, Otmar Scherzer, Arne KovacAbstract:The problem of bivariate density estimation is studied with the aim of finding the density function with the smallest number of local extreme values which is adequate with the given data. Adequacy is defined via Kuiper metrics. The concept of the Taut-String algorithm which provides adequate approximations with a small number of local extrema is generalised for analysing two- and higher dimensional data, using Delaunay triangulation and diffusion filtering. Results are based on equivalence relations in one dimension between the Taut-String algorithm and the method of solving the discrete total variation flow equation. The generalisation and some modifications are developed and the performance for density estimation is shown.
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Taut-String Algorithm and Regularization Programs with G-Norm Data Fit
Journal of Mathematical Imaging and Vision, 2005Co-Authors: Otmar ScherzerAbstract:In this paper we derive a unified framework for the Taut-String algorithm and regularization with G -norm data fit. The G -norm data fit criterion (popularized in image processing by Y. Meyer) has been paid considerable interest in regularization models for pattern recognition. The first numerical work based on G -norm data fit has been proposed by Osher and Vese. The Taut-String algorithm has been developed in statistics (Mammen and van de Geer and Davies and Kovac) for denoising of one dimensional sample data of a discontinuous function. Recently Hinterberger et al. proposed an extension of the Taut-String algorithm to higher dimensional data by introducing the concept of tube methods. Here we highlight common features between regularization programs with a G -norm data fit term and Taut-String algorithms (respectively tube methods). This links the areas of statistics, regularization theory, and image processing.
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g norm properties of bounded variation regularization
Communications in Mathematical Sciences, 2004Co-Authors: Stanley Osher, Otmar ScherzerAbstract:Recently Y. Meyer derived a characterization of the minimizer of the Rudin-Osher- Fatemi functional in a functional analytical framework. In statistics the discrete version of this functional is used to analyze one dimensional data and belongs to the class of nonparametric regres- sion models. In this work we generalize the functional analytical results of Meyer and apply them to a class of regression models, such as quantile, robust, logistic regression, for the analysis of multi- dimensional data. The characterization of Y. Meyer and our generalization is based on G-norm properties of the data and the minimizer. A geometric point of view of regression minimization is provided. whereDudenotes the total variation semi-norm of u and α> 0. The minimizer is called the bounded variation regularized solution. The Taut-String algorithm consists in finding a String of minimal length in a tube (with radius α) around the primitive of f . The differentiated String is the Taut-String reconstruction and corresponds to the minimizer of the ROF-model. Generalizing these ideas to higher dimensions is complicated by the fact that there is no obvious analog to primitives in higher space dimensions. We overcome this difficulty by solving Laplace's equation with right hand side f (i.e. integrate twice), and differentiating. The tube with radius α around the derivative of the potential specifies all functions u which satisfyu − fGs ≤ α (see also (21)). In this paper we show that the bounded variation regularized solutions (in any number of space dimensions) are contained in a tube of radius α .F or several other regression models in statistics, such as robust, quantile, and logistic regression (reformulated in a Banach space setting for analyzing multi-dimensional data) the
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Tube Methods for BV Regularization
Journal of Mathematical Imaging and Vision, 2003Co-Authors: Walter Hinterberger, Michael Hintermüller, Karl Kunisch, Markus Von Oehsen, Otmar ScherzerAbstract:In this paper tube methods for reconstructing discontinuous data from noisy and blurred observation data are considered. It is shown that discrete bounded variation (BV)-regularization (commonly used in inverse problems and image processing) and the Taut-String algorithm (commonly used in statistics) select reconstructions in a tube. A version of the Taut-String algorithm applicable for higher dimensional data is proposed. This formulation results in a bilateral contact problem which can be solved very efficiently using an active set strategy. As a by-product it is shown that the Lagrange multiplier of the active set strategy is an efficient parameter for edge detection.
