Bernstein filter: A new solver for mean curvature regularized models

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 n...

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Bibliographic Details
Main Author: Gong, Yuanhao
Format: Conference Proceeding
Language:English
Subjects:
Bayes methods
Bernstein
convex
Convexity
Curvature
Curvature Filter
Estimation
half-window regression
Imaging
Linearity
Mathematical analysis
Mathematical model
Mathematical models
Mean Curvature
Optimization
Regularization
Signal processing
Solvers
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Summary: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.
ISSN:2379-190X
DOI:10.1109/ICASSP.2016.7471967