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
An Algorithm for Total Variation Minimization and Applications
Journal of Mathematical Imaging and Vision
Smooth minimization of non-smooth functions
Mathematical Programming: Series A and B
Efficient Schemes for Total Variation Minimization Under Constraints in Image Processing
SIAM Journal on Scientific Computing
Image restoration subject to a total variation constraint
IEEE Transactions on Image Processing
SIAM Journal on Scientific Computing
A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
Journal of Mathematical Imaging and Vision
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This paper proposes a new class of algorithms to compute the projection onto the set of images with a total variation bounded by a constant. The projection is computed on a dual formulation of the problem that is minimized using either a one-step gradient descent method or a multi-step Nesterov scheme. This yields iterative algorithms that compute soft thresholding of the dual vector fields. We show the convergence of the method with a convergence rate of O(1/k) for the one step method and O(1/k2) for the multi-step one, where k is the iteration number. The projection algorithm can be used as a building block in several applications, and we illusrtate it by solving linear inverse problems under total variation constraint. Numerical results show that our algorithm competes favorably with state-of-the-art TV projection methods to solve denoising, inpainting and deblurring problems.