NDLI: Linear Estimation of Time-Warped Signals

Content Provider	IEEE Xplore Digital Library
Author	Hagege, R. Francos, J.M.
Copyright Year	1963
Abstract	We introduce a novel methodology for estimating the time-axis deformation between two observations on a time-warped signal. Since the problem of estimating the warping function is nonlinear, existing methods iteratively minimize some metric between the observation and a hypothesized deformed template. Assuming the family of possible deformations the signal may undergo admits a finite-dimensional representation, we show that there is a nonlinear mapping from the space of observations to a low-dimensional linear space, such that in this space the problem of estimating the parametric model of the warping function is solved by a linear system of equations. We call the family of estimators derived based on this representation, linear warping estimators (LWE). The new representation of the problem enables an analytic analysis of the behavior of the solution in the presence of model mismatches, which is prohibitive when iterative methods are employed. The ability to achieve this major simplification both in the solution and in analyzing its performance results from the representation of the problem in a new coordinate system which is natural to the properties of the problem, instead of representing it in the standard coordinate system imposed by the sampling mechanism. The proposed solution is unique and exact, as it provides a closed-form expression for evaluating each of the parameters of the warping model using only measurements of the amplitude information of the observed and reference signals. The solution is applicable to any elastic warping regardless of its magnitude. We analyze the behavior of the LWE in the presence of noise and obtain a minimum variance unbiased estimator for the model parameters, by finding an optimal set of nonlinear operators for mapping the original problem into a low-dimensional linear space.
Sponsorship	IEEE Information Theory Society
Starting Page	4423
Ending Page	4439
Page Count	17
File Size	5437117
File Format	PDF
ISSN	00189448
Volume Number	59
Issue Number	7
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2013-07-01
Publisher Place	U.S.A.
Access Restriction	One Nation One Subscription (ONOS)
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Estimation Noise Measurement Dictionaries Space vehicles Analytical models Standards unbiased minimum variance estimation Dynamic time warping (DTW) elastic deformations linear estimation nonlinear functionals
Content Type	Text
Resource Type	Article
Subject	Library and Information Sciences Information Systems Computer Science Applications

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4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
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