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A First-Order Primal-Dual Algorithm for Convex Problems with Applications to Imaging
  • A. ChambolleT. Pock
  • Mathematics, Computer Science
    Journal of Mathematical Imaging and Vision
  • 1 May 2011
TLDR
A first-order primal-dual algorithm for non-smooth convex optimization problems with known saddle-point structure can achieve O(1/N2) convergence on problems, where the primal or the dual objective is uniformly convex, and it can show linear convergence, i.e. O(ωN) for some ω∈(0,1), on smooth problems.
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Total Generalized Variation
The novel concept of total generalized variation of a function $u$ is introduced, and some of its essential properties are proved. Differently from the bounded variation seminorm, the new concept…
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A Duality Based Approach for Realtime TV-L1 Optical Flow
TLDR
This work presents a novel approach to solve the TV-L1 formulation, which is based on a dual formulation of the TV energy and employs an efficient point-wise thresholding step.
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Trainable Nonlinear Reaction Diffusion: A Flexible Framework for Fast and Effective Image Restoration
  • Yunjin ChenT. Pock
  • Computer Science
    IEEE Transactions on Pattern Analysis and Machine…
  • 12 August 2015
TLDR
This work proposes a dynamic nonlinear reaction diffusion model with time-dependent parameters, which preserves the structural simplicity of diffusion models and take only a small number of diffusion steps, which makes the inference procedure extremely fast.
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Learning a variational network for reconstruction of accelerated MRI data
To allow fast and high‐quality reconstruction of clinical accelerated multi‐coil MR data by learning a variational network that combines the mathematical structure of variational models with deep…
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PROST: Parallel robust online simple tracking
TLDR
This work shows that augmenting an on-line learning method with complementary tracking approaches can lead to more stable results, and uses a simple template model as a non-adaptive and thus stable component, a novel optical-flow-based mean-shift tracker as highly adaptive element and anon-line random forest as moderately adaptive appearance-based learner.
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Diagonal preconditioning for first order primal-dual algorithms in convex optimization
  • T. PockA. Chambolle
  • Computer Science
    International Conference on Computer Vision
  • 6 November 2011
TLDR
This paper proposes simple and easy to compute diagonal preconditioners for the first-order primal-dual algorithm for which convergence of the algorithm is guaranteed without the need to compute any step size parameters.
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An Improved Algorithm for TV-L 1 Optical Flow
TLDR
This work proposes an improvement variant of the original duality based TV-L 1 optical flow algorithm that can preserve discontinuities in the flow field by employing total variation (TV) regularization and integrates a median filter into the numerical scheme to further increase the robustness to sampling artefacts in the image data.
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On the ergodic convergence rates of a first-order primal–dual algorithm
TLDR
The proofs of convergence for a first order primal–dual algorithm for convex optimization is revisited, with simpler proofs and more complete results that can deal with explicit terms and nonlinear proximity operators in spaces with quite general norms.
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An introduction to continuous optimization for imaging
TLDR
The state of the art in continuous optimization methods for such problems, and particular emphasis on optimal first-order schemes that can deal with typical non-smooth and large-scale objective functions used in imaging problems are described.
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