Generalized Sinkhorn Iterations for Regularizing Inverse Problems Using Optimal Mass Transport
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Publication:4689648
DOI10.1137/17M111208XzbMath1401.49049arXiv1612.02273MaRDI QIDQ4689648
Publication date: 17 October 2018
Published in: SIAM Journal on Imaging Sciences (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1612.02273
inverse problemsmedical imagingproximal methodsoptimal mass transportvariable splittingSinkhorn iterations
Large-scale problems in mathematical programming (90C06) Numerical methods involving duality (49M29) Transportation, logistics and supply chain management (90B06) Special problems of linear programming (transportation, multi-index, data envelopment analysis, etc.) (90C08) Biomedical imaging and signal processing (92C55) Geometric methods (93B27) Inverse problems in optimal control (49N45) Linear optimal control problems (49N05)
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Cites Work
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- Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers
- Nonlinear total variation based noise removal algorithms
- On the relation between optimal transport and Schrödinger bridges: a stochastic control viewpoint
- Long history of the Monge-Kantorovich transportation problem
- Primal-dual splitting algorithm for solving inclusions with mixtures of composite, Lipschitzian, and parallel-sum type monotone operators
- Application of the Wasserstein metric to seismic signals
- Tomographic reconstruction from a few views: a multi-marginal optimal transport approach
- Fast multiplication of a recursive block Toeplitz matrix by a vector and its application
- Local convergence analysis of a grouped variable version of coordinate descent
- On the scaling of multidimensional matrices
- Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems
- On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
- Computing the Kantorovich distance for images
- The earth mover's distance as a metric for image retrieval
- A first-order primal-dual algorithm for convex problems with applications to imaging
- A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
- On a problem of Monge
- Optimal mass transport for registration and warping
- Dykstras algorithm with bregman projections: A convergence proof
- The Mathematics of Computerized Tomography
- Mathematical Methods in Image Reconstruction
- A Smoothed Dual Approach for Variational Wasserstein Problems
- Proximal Splitting Methods in Signal Processing
- Scaling algorithms for unbalanced optimal transport problems
- Entropic and Displacement Interpolation: A Computational Approach Using the Hilbert Metric
- An augmented Lagrangian approach to Wasserstein gradient flows and applications
- Diffeomorphic Density Matching by Optimal Information Transport
- Entropic Approximation of Wasserstein Gradient Flows
- An unconstrained convex programming view of linear programming
- Entropic Proximal Mappings with Applications to Nonlinear Programming
- Monotone Operators and the Proximal Point Algorithm
- The Variational Formulation of the Fokker--Planck Equation
- Metrics for Power Spectra: An Axiomatic Approach
- Geometric Methods for Spectral Analysis
- On the convergence rate of a forward-backward type primal-dual splitting algorithm for convex optimization problems
- Iterative Bregman Projections for Regularized Transportation Problems
- Uncertainty Bounds for Spectral Estimation
- A Douglas--Rachford Type Primal-Dual Method for Solving Inclusions with Mixtures of Composite and Parallel-Sum Type Monotone Operators
- Diagonal Equivalence to Matrices with Prescribed Row and Column Sums
- Convex analysis and monotone operator theory in Hilbert spaces
- Optimal Transport
