# An Algorithm for Total Variation Minimization and Applications

@article{Chambolle2004AnAF, title={An Algorithm for Total Variation Minimization and Applications}, author={A. Chambolle}, journal={Journal of Mathematical Imaging and Vision}, year={2004}, volume={20}, pages={89-97} }

We propose an algorithm for minimizing the total variation of an image, and provide a proof of convergence. We show applications to image denoising, zooming, and the computation of the mean curvature motion of interfaces.

## 969 Citations

### On Semismooth Newton’s Methods for Total Variation Minimization

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Based on the theory on semismooth operators,Semismooth Newton’s methods for total variation minimization are studied to show the effectiveness of the proposed algorithms.

### Total variational image denoising. Influence of noise distribution: Comparison analysis

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In this paper we review the total variation image denoising schemes and highlight the various approaches to tune the employed regularization parameters. An experimental set-up, which uses both the…

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The discretization of a bilaterally constrained total variation minimization problem with conforming low order finite elements is analyzed and three iterative schemes are proposed which differ in the…

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A functional is derived whose minimizer corresponds to the denoised image the authors want to recover and the existence of a minimizer is proved, and the capability of the model is shown on some numerical examples.

### Restoration and Zoom of Irregularly Sampled, Blurred, and Noisy Images by Accurate Total Variation Minimization with Local Constraints

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We propose an algorithm to solve a problem in image restoration which considers several different aspects of it, namely irregular sampling, denoising, deconvolution, and zooming. Our algorithm is b...

### Fast algorithm for total variation minimization

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This paper proposes a method that accelerates the convergence speed of the Chambolle's algorithm based on introduction of 4-directional TV criterion and 4-dimesional dual vector.

### Mixed regularization method for image restoration

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A new mixed regularization method for image recovery is presented based on the combination of the bounded variation regularization and the quadratic H-k regularization, which gives significant improvement over standard single regularizations.

### Convergence of a Central Difference Discretization of ROF Model for Image Denoising

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We study a central difference discretization of Rudin-Osher-Fetami model for image de-noising. We show that the discrete solution uk converges to the continuous solution u in L2 norm and a rate of…

### Implementation of total variation regularization algorithm on CELL processor

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This study has implemented the TV algorithm on the CELL processor by using various special programming techniques and an optimum software design to overcome the long computational time resulting from iterative calculations.

### An Image Level Set Method for Denoising

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A new algorithm based on image level set and partial differential equations (PDE) operator that can serve a definite purpose in reducing more types of noise (Gaussian, Poisson and Salt & Pepper noise).

## References

SHOWING 1-10 OF 22 REFERENCES

### Global Total Variation Minimization

- Computer ScienceSIAM J. Numer. Anal.
- 1999

This paper presents an alternative approach of the total variation minimization problem, a practical algorithm which handles digital image data and experimental results, and gives a short development of the bounded variation (BV) background.

### An algorithm for Mean Curvature Motion

- Computer Science
- 2004

The algorithm is a variant of the variational approach of Almgren, Taylor and Wang and it is shown that it approximates, as the time--step goes to zero, the generalized motion.

### Convergence of an Iterative Method for Total Variation Denoising

- Mathematics
- 1997

In total variation denoising, one attempts to remove noise from a signal or image by solving a nonlinear minimization problem involving a total variation criterion. Several approaches based on this…

### Iterative Methods for Total Variation Denoising

- Computer ScienceSIAM J. Sci. Comput.
- 1996

A fixed point algorithm for minimizing a TV penalized least squares functional is presented and compared with existing minimization schemes, and a variant of the cell-centered finite difference multigrid method of Ewing and Shen is implemented for solving the (large, sparse) linear subproblems.

### A computational algorithm for minimizing total variation in image restoration

- MathematicsIEEE Trans. Image Process.
- 1996

A reliable and efficient computational algorithm for restoring blurred and noisy images that can be used in an adaptive/interactive manner in situations when knowledge of the noise variance is either unavailable or unreliable is proposed.

### Image recovery via total variation minimization and related problems

- Computer Science
- 1997

A variant of the original TV minimization problem that handles correctly some situations where TV fails is proposed, and an alternative approach whose purpose is to handle the minimization of the minimum of several convex functionals is proposed.

### Total variation based interpolation

- Mathematics9th European Signal Processing Conference (EUSIPCO 1998)
- 1998

An reversible interpolation method for signals or images, in the sense that the original image can be deduced from its interpolation by a sub-sampling, to minimise a regularisation functional defined in space domain, with a constraint defined in the frequency domain.

### A Nonlinear Primal-Dual Method for Total Variation-Based Image Restoration

- MathematicsSIAM J. Sci. Comput.
- 1999

A new method for solving total variation (TV) minimization problems in image restoration by introducing an additional variable for the flux quantity appearing in the gradient of the objective function, which can be interpreted as the normal vector to the level sets of the image u.

### Edge Direction Preserving Image Zooming: A Mathematical and Numerical Analysis

- MathematicsSIAM J. Numer. Anal.
- 2001

This paper focuses on linear methods, gives a general framework to design them, and shows that the preservation of 1D structures pleads in favor of the cancellation of the periodization of the image spectrum, and studies variational nonlinear methods.