Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Mathematical Programming: Series A and B
International Journal of Computer Vision
Orthonormal Vector Sets Regularization with PDE's and Applications
International Journal of Computer Vision
Numerical Methods for p-Harmonic Flows and Applications to Image Processing
SIAM Journal on Numerical Analysis
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Numerical methods for minimization problems constrained to S1 and S2
Journal of Computational Physics
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Image restoration combining a total variational filter and a fourth-order filter
Journal of Visual Communication and Image Representation
Some First-Order Algorithms for Total Variation Based Image Restoration
Journal of Mathematical Imaging and Vision
A Curvilinear Search Method for $p$-Harmonic Flows on Spheres
SIAM Journal on Imaging Sciences
The Split Bregman Method for L1-Regularized Problems
SIAM Journal on Imaging Sciences
A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
SIAM Journal on Imaging Sciences
IEEE Transactions on Image Processing
Multiphase Soft Segmentation with Total Variation and H1 Regularization
Journal of Mathematical Imaging and Vision
Operator Splittings, Bregman Methods and Frame Shrinkage in Image Processing
International Journal of Computer Vision
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
Journal of Mathematical Imaging and Vision
SIAM Journal on Imaging Sciences
A Fast Algorithm for Euler's Elastica Model Using Augmented Lagrangian Method
SIAM Journal on Imaging Sciences
Inexact Alternating Direction Methods for Image Recovery
SIAM Journal on Scientific Computing
Color TV: total variation methods for restoration of vector-valued images
IEEE Transactions on Image Processing
Color image enhancement via chromaticity diffusion
IEEE Transactions on Image Processing
Variational denoising of partly textured images by spatially varying constraints
IEEE Transactions on Image Processing
Mumford-Shah-Euler Flow with Sphere Constraint and Applications to Color Image Inpainting
SIAM Journal on Imaging Sciences
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The numerical methods of total variation (TV) model for image denoising, especially Rudin-Osher-Fatemi (ROF) model, is widely studied in the literature. However, the S^n^-^1 constrained counterpart is less addressed. The classical gradient descent method for the constrained problem is limited in two aspects: one is the small time step size to ensure stability; the other is that the data must be projected onto S^n^-^1 during evolution since the unit norm constraint is poorly satisfied. In order to avoid these drawbacks, in this paper, we propose two alternative numerical methods based on the Lagrangian multipliers and split Bregman methods. Both algorithms are efficient and easy to implement. A number of experiments demonstrate that the proposed algorithms are quite effective in denoising of data constrained on S^1 or S^2, including general direction data diffusion and chromaticity denoising.