Aspects of Total Variation Regularized L[sup 1] Function Approximation

By Tony F. Chan, Selim Esedoglu. SIAM Journal on Applied Mathematics, 2005

760 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fe030c0db583577e004fed119645944488137e0c

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Citations in the corpus

Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models (2006, methodology): “On the other hand, it might be possible to cook up special given images f and special values λ for which there are nonbinary minimizers; for instance, in the case of the convex formulation (7) of the related geometry problem (4), the simple example of a disk as the given shape leads to nonbinary sol”
DIRICHLET PROBLEMS FOR THE 1-LAPLACE OPERATOR, INCLUDING THE EIGENVALUE PROBLEM (2007, methodology): “In [10] the existence of a minimizer is shown for r = 1 and a comparison of r = 2 with r = 1 is given.”
Structure-Texture Image Decomposition—Modeling, Algorithms, and Parameter Selection (2006, methodology): “This model has recently been studied mathematically in the continuous case in Chan and Esedoglu (2004).”
A Globally Optimal Algorithm for Robust TV-L1 Range Image Integration (2007, background): “Using the L(1) norm in conjunction with TV regularization has many other consequences, but we mention only one important qualitative result from [9]: the regularization induced by the TV-L(1) energy is pure geometric, i.”
Convex optimization problem prototyping for image reconstruction in computed tomography with the Chambolle-Pock algorithm (2011, methodology): “We also employ 0 X and 1 X to mean a vector from the space X with all components set to 0 and 1, respectively.”
An Efficient TVL1 Algorithm for Deblurring Multichannel Images Corrupted by Impulsive Noise (2009, methodology): “Recently, geometric properties of the TVL1 model, which uses TV with the above 1-fidelity term, were analyzed in [10].”
Total variation models for variable lighting face recognition (2006, methodology): “[3], [26], [ 9 ] is particularly suited for separating large-scale and small-scalefacialcomponents.Weintroducethismodelandanalyze the properties that are related to our purpose.”
Recent Developments in Total Variation Image Restoration (2004, background): “Indeed, the following statement has been proved in [10]: Let u(x) be a minimizer of (6) for f(x) = 1S(x).”
A Combined First and Second Order Variational Approach for Image Reconstruction (2012, neutral): “As it has been shown in [55] and also studied in [24] and [36], the L1 norm in the fidelity term leads to efficient restorations of images that have been corrupted by impulse noise.”
Salt-and-pepper noise removal by median-type noise detectors and detail-preserving regularization (2005, background): “If one wishes to smooth out all the noisy patches, one has to increase β, see [7] for the role of β.”
Fast Global Minimization of the Active Contour/Snake Model (2007, methodology): “Chan and Esedo¯ glu studied in [ 29 ] the differences between the ROF model and the ROF model that uses the L 1 -norm as a fidelity measure.”
Nonlocal Operators with Applications to Image Processing (2008, background): “It is also known to keep intact large structures without reducing contrast (as oppose to the TV − L 2 case) while eliminating the smaller scales [14].”
A Fast Algorithm for Edge-Preserving Variational Multichannel Image Restoration (2009, background): “[1, 9, 26]) instead of the square of the 2-norm as in (1.”
Diagonal preconditioning for first order primal-dual algorithms in convex optimization (2011, background): “TV-L(1) image denoising The TV-L(1) model [12, 6] is a popular image denoising model.”