Nonmonotone and Monotone Active-Set Methods for Image Restoration, Part 2: Numerical Results

Kärkkäinen, Tommi; Majava, K.

doi:10.1023/a:1004607123926

Cited by 14 publications

(30 citation statements)

References 9 publications

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“…For example, the method cannot preserve image contrast, the corners get easily smeared, and the so-called staircase effect turns smooth surfaces into piecewise constant regions [13,46,60,123,142]. In addition, please see the numerical experiments presented in [45,47,99,111].…”

Section: Definition 52 (Space Of Functions Of Bounded Variation) Thementioning

confidence: 99%

See 1 more Smart Citation

A New Augmented Lagrangian Approach for $L^1$-mean Curvature Image Denoising

Myllykoski¹,

Glowinski²,

Kärkkäinen³

et al. 2015

SIAM J. Imaging Sci.

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Section: Definition 52 (Space Of Functions Of Bounded Variation) Thementioning

confidence: 99%

“…Similar approaches have been compared and analyzed in [113]. In particular, the active-set methods have received moderate attention in this context [99,110,111,113], and a semi-adaptive approach was presented in [112]. -Modify the fidelity term such that…”

Section: Definition 52 (Space Of Functions Of Bounded Variation) Thementioning

confidence: 99%

A New Augmented Lagrangian Approach for $L^1$-mean Curvature Image Denoising

Myllykoski¹,

Glowinski²,

Kärkkäinen³

et al. 2015

SIAM J. Imaging Sci.

Self Cite

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“…), creating somewhat Funnecessary_ jumps in coefficients. See [26,34] for theoretical arguments on problems with including .…”

Section: Total Variation Regularization and Solutionmentioning

confidence: 99%

“…The active set method. This is a discrete approach [8,25,26] solving the EulerYLagrange equation which implements a related idea to the above combined method i.e. treat active sets (jruj ¼ 0) differently from inactive sets.…”

Section: Remarkmentioning

confidence: 99%

On a nonlinear multigrid algorithm with primal relaxation for the image total variation minimisation

Chan

Chen

2006

Numer Algor

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Digital image restoration has drawn much attention in the recent years and a lot of research has been done on effective variational partial differential equation models and their theoretical studies. However there remains an urgent need to develop fast and robust iterative solvers, as the underlying problem sizes are large. This paper proposes a fast multigrid method using primal relaxations. The basic primal relaxation is known to get stuck at a Flocal_ non-stationary minimum of the solution, which is usually believed to be Fnonsmooth_. Our idea is to utilize coarse level corrections, overcoming the deadlock of a basic primal relaxation scheme. A further refinement is to allow non-regular coarse levels to correct the solution, which helps to improve the multilevel method. Numerical experiments on both 1D and 2D images are presented.

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“…For better improving the quality of the recovered image, several authors investigated the hybrid regularization based schemes. For instance, total bounded variation regularization model [28], total variation and Besov regularizers [23], a hybrid of H 1 norm and TV norm regularizers [29][30][31][32]. Moreover, to reduce the staircasing effect, Tony et.…”

Section: Introductionmentioning

confidence: 99%

Split Bregman iteration for hybrid regularization based image restoration

Zhou¹,

Li²,

Lin³

2013

Proceedings of 3rd International Conference on Multimedia Technology(ICMT-13)

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Abstract. In this paper, the hybrid regularization based scheme for image restoration is researched in detail. This strategy contains two regularization items, which helps to achieve superior image reconstruction. To quickly minimize the energy functional, we adopt the fast split Bregman iteration method. Numerical simulations distinctly demonstrate the superiority of our advanced scheme for image recovery over the traditional method.

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Nonmonotone and Monotone Active-Set Methods for Image Restoration, Part 2: Numerical Results

Cited by 14 publications

References 9 publications

A New Augmented Lagrangian Approach for $L^1$-mean Curvature Image Denoising

A New Augmented Lagrangian Approach for $L^1$-mean Curvature Image Denoising

On a nonlinear multigrid algorithm with primal relaxation for the image total variation minimisation

Split Bregman iteration for hybrid regularization based image restoration

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