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Filter Design

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 not. In this paper, we first prove that the mean curvature regularization is convex if the dimension of imaging domain is not

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11 April 2016 - 3:46am
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BernsteinFilter_poster.pdf

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ICASSP.pdf

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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: Oct. 20, 2017.
@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

Edge-enhancing filters with negative weights


Edge-enhanced eigenvectors of the Laplacian with a negative weight

In [doi{10.1109/ICMEW.2014.6890711}], a~graph-based filtering of noisy images is performed by directly computing a projection of the image to be filtered onto a lower dimensional Krylov subspace of the graph Laplacian, constructed using non-negative graph weights determined by distances between image data corresponding to image pixels. We extend the construction of the graph Laplacian to the case, where some graph weights can be negative.

KGlobalSIP.pdf

PDF icon KGlobalSIP.pdf (286 downloads)

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23 February 2016 - 1:44pm
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KGlobalSIP.pdf

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[1] , "Edge-enhancing filters with negative weights", IEEE SigPort, 2015. [Online]. Available: http://sigport.org/503. Accessed: Oct. 20, 2017.
@article{503-15,
url = {http://sigport.org/503},
author = { },
publisher = {IEEE SigPort},
title = {Edge-enhancing filters with negative weights},
year = {2015} }
TY - EJOUR
T1 - Edge-enhancing filters with negative weights
AU -
PY - 2015
PB - IEEE SigPort
UR - http://sigport.org/503
ER -
. (2015). Edge-enhancing filters with negative weights. IEEE SigPort. http://sigport.org/503
, 2015. Edge-enhancing filters with negative weights. Available at: http://sigport.org/503.
. (2015). "Edge-enhancing filters with negative weights." Web.
1. . Edge-enhancing filters with negative weights [Internet]. IEEE SigPort; 2015. Available from : http://sigport.org/503

Conjugate gradient acceleration of non-linear smoothing filters


Noisy signal

The most efficient signal edge-preserving smoothing filters, e.g., for denoising, are non-linear. Thus, their acceleration is challenging and is often done in practice by tuning filters parameters, such as increasing the width of the local smoothing neighborhood, resulting in more aggressive smoothing of a single sweep at the cost of increased edge blurring. We propose an alternative technology, accelerating the original filters without tuning, by running them through a conjugate gradient method, not affecting their quality.

GlobalSIP.pdf

PDF icon GlobalSIP.pdf (288 downloads)

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Authors:
Alexander Malyshev
Submitted On:
23 February 2016 - 1:44pm
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GlobalSIP.pdf

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[1] Alexander Malyshev, "Conjugate gradient acceleration of non-linear smoothing filters", IEEE SigPort, 2015. [Online]. Available: http://sigport.org/406. Accessed: Oct. 20, 2017.
@article{406-15,
url = {http://sigport.org/406},
author = {Alexander Malyshev },
publisher = {IEEE SigPort},
title = {Conjugate gradient acceleration of non-linear smoothing filters},
year = {2015} }
TY - EJOUR
T1 - Conjugate gradient acceleration of non-linear smoothing filters
AU - Alexander Malyshev
PY - 2015
PB - IEEE SigPort
UR - http://sigport.org/406
ER -
Alexander Malyshev. (2015). Conjugate gradient acceleration of non-linear smoothing filters. IEEE SigPort. http://sigport.org/406
Alexander Malyshev, 2015. Conjugate gradient acceleration of non-linear smoothing filters. Available at: http://sigport.org/406.
Alexander Malyshev. (2015). "Conjugate gradient acceleration of non-linear smoothing filters." Web.
1. Alexander Malyshev. Conjugate gradient acceleration of non-linear smoothing filters [Internet]. IEEE SigPort; 2015. Available from : http://sigport.org/406

Accelerated graph-based spectral polynomial filters


BF, GF and CG filters on 1D signals

Graph-based spectral denoising is a low-pass filtering using the eigendecomposition of the graph Laplacian matrix of a noisy signal. Polynomial filtering avoids costly computation of the eigendecomposition by projections onto suitable Krylov subspaces. Polynomial filters can be based, e.g., on the bilateral and guided filters. We propose constructing accelerated polynomial filters by running flexible Krylov subspace based linear and eigenvalue solvers such as the Block Locally Optimal Preconditioned Conjugate Gradient (LOBPCG) method.

MLSP2015.pdf

PDF icon MLSP2015.pdf (316 downloads)

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Authors:
Alexander Malyshev
Submitted On:
23 February 2016 - 1:44pm
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MLSP2015.pdf

(316 downloads)

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[1] Alexander Malyshev, "Accelerated graph-based spectral polynomial filters", IEEE SigPort, 2015. [Online]. Available: http://sigport.org/297. Accessed: Oct. 20, 2017.
@article{297-15,
url = {http://sigport.org/297},
author = {Alexander Malyshev },
publisher = {IEEE SigPort},
title = {Accelerated graph-based spectral polynomial filters},
year = {2015} }
TY - EJOUR
T1 - Accelerated graph-based spectral polynomial filters
AU - Alexander Malyshev
PY - 2015
PB - IEEE SigPort
UR - http://sigport.org/297
ER -
Alexander Malyshev. (2015). Accelerated graph-based spectral polynomial filters. IEEE SigPort. http://sigport.org/297
Alexander Malyshev, 2015. Accelerated graph-based spectral polynomial filters. Available at: http://sigport.org/297.
Alexander Malyshev. (2015). "Accelerated graph-based spectral polynomial filters." Web.
1. Alexander Malyshev. Accelerated graph-based spectral polynomial filters [Internet]. IEEE SigPort; 2015. Available from : http://sigport.org/297

Practical Optimization Algorithms for Image Processing


Several problems in signal processing and machine learning can be casted as optimization problems. In many cases, they are of large-scale, nonlinear, have constraints, and nonsmooth in the unknown parameters. There exists plethora of fast algorithms for smooth convex optimization, but these algorithms are not readily applicable to nonsmooth problems, which has led to a considerable amount of research in this direction. In this paper, we propose a general algorithm for nonsmooth bound-constrained convex optimization problems.

posterICIP.pdf

PDF icon posterICIP.pdf (401 downloads)

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Authors:
Loic Denis, Eric Thiebaut, J-M Becker
Submitted On:
23 February 2016 - 1:43pm
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posterICIP.pdf

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[1] Loic Denis, Eric Thiebaut, J-M Becker, "Practical Optimization Algorithms for Image Processing", IEEE SigPort, 2015. [Online]. Available: http://sigport.org/223. Accessed: Oct. 20, 2017.
@article{223-15,
url = {http://sigport.org/223},
author = {Loic Denis; Eric Thiebaut; J-M Becker },
publisher = {IEEE SigPort},
title = {Practical Optimization Algorithms for Image Processing},
year = {2015} }
TY - EJOUR
T1 - Practical Optimization Algorithms for Image Processing
AU - Loic Denis; Eric Thiebaut; J-M Becker
PY - 2015
PB - IEEE SigPort
UR - http://sigport.org/223
ER -
Loic Denis, Eric Thiebaut, J-M Becker. (2015). Practical Optimization Algorithms for Image Processing. IEEE SigPort. http://sigport.org/223
Loic Denis, Eric Thiebaut, J-M Becker, 2015. Practical Optimization Algorithms for Image Processing. Available at: http://sigport.org/223.
Loic Denis, Eric Thiebaut, J-M Becker. (2015). "Practical Optimization Algorithms for Image Processing." Web.
1. Loic Denis, Eric Thiebaut, J-M Becker. Practical Optimization Algorithms for Image Processing [Internet]. IEEE SigPort; 2015. Available from : http://sigport.org/223