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Numerical differentiation of noisy, nonsmooth, multidimensional data

Abstract: 

We consider the problem of differentiating a multivariable function specified by noisy data. Following previous work for the single-variable case, we regularize the differentiation process, by formulating it as an inverse problem with an integration operator as the forward model. Total-variation regularization avoids the noise amplification of finite-difference methods, while allowing for discontinuous solutions. Unlike the single-variable case, we use an alternating directions, method of multipliers algorithm to provide greater efficiency for large problems. We apply the method to synthetic data and to synthetic-aperture radar satellite imagery.

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Paper Details

Authors:
Rick Chartrand
Submitted On:
15 November 2017 - 7:57am
Short Link:
Type:
Presentation Slides
Event:
Presenter's Name:
Rick Chartrand
Paper Code:
GS-IVM-O.4.2
Document Year:
2017
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chartrand.pdf

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[1] Rick Chartrand, "Numerical differentiation of noisy, nonsmooth, multidimensional data", IEEE SigPort, 2017. [Online]. Available: http://sigport.org/2356. Accessed: Dec. 17, 2017.
@article{2356-17,
url = {http://sigport.org/2356},
author = {Rick Chartrand },
publisher = {IEEE SigPort},
title = {Numerical differentiation of noisy, nonsmooth, multidimensional data},
year = {2017} }
TY - EJOUR
T1 - Numerical differentiation of noisy, nonsmooth, multidimensional data
AU - Rick Chartrand
PY - 2017
PB - IEEE SigPort
UR - http://sigport.org/2356
ER -
Rick Chartrand. (2017). Numerical differentiation of noisy, nonsmooth, multidimensional data. IEEE SigPort. http://sigport.org/2356
Rick Chartrand, 2017. Numerical differentiation of noisy, nonsmooth, multidimensional data. Available at: http://sigport.org/2356.
Rick Chartrand. (2017). "Numerical differentiation of noisy, nonsmooth, multidimensional data." Web.
1. Rick Chartrand. Numerical differentiation of noisy, nonsmooth, multidimensional data [Internet]. IEEE SigPort; 2017. Available from : http://sigport.org/2356