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Bernstein Filter: a new solver for mean curvature regularized models

Abstract: 

The mean curvature has been shown a proper regularization in various ill-posed inverse problems in signal processing. Traditional solvers are based on either gradient descent methods or Euler Lagrange Equation. However, it is not clear if this mean curvature regularization term itself is convex or not. In this paper, we first prove that the mean curvature regularization is convex if the dimension of imaging domain is not
larger than seven. With this convexity, all optimization methods lead to the same global optimal solution. Based on this convexity and Bernstein theorem, we propose an efficient filter solver, which can implicitly minimize the mean curvature.Our experiments show that this filter is at least two orders of magnitude faster than traditional solvers.

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Paper Details

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Submitted On:
11 April 2016 - 3:46am
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Type:
Poster
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Document Year:
2016
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[1] , "Bernstein Filter: a new solver for mean curvature regularized models", IEEE SigPort, 2016. [Online]. Available: http://sigport.org/640. Accessed: Jul. 11, 2020.
@article{640-16,
url = {http://sigport.org/640},
author = { },
publisher = {IEEE SigPort},
title = {Bernstein Filter: a new solver for mean curvature regularized models},
year = {2016} }
TY - EJOUR
T1 - Bernstein Filter: a new solver for mean curvature regularized models
AU -
PY - 2016
PB - IEEE SigPort
UR - http://sigport.org/640
ER -
. (2016). Bernstein Filter: a new solver for mean curvature regularized models. IEEE SigPort. http://sigport.org/640
, 2016. Bernstein Filter: a new solver for mean curvature regularized models. Available at: http://sigport.org/640.
. (2016). "Bernstein Filter: a new solver for mean curvature regularized models." Web.
1. . Bernstein Filter: a new solver for mean curvature regularized models [Internet]. IEEE SigPort; 2016. Available from : http://sigport.org/640