Splitting with Near-Circulant Linear Systems: Applications to Total Variation CT and PET
From MaRDI portal
Publication:5214831
DOI10.1137/18M1224003zbMath1448.92113arXiv1810.13100OpenAlexW3005097570MaRDI QIDQ5214831
Ernest K. Ryu, Seyoon Ko, Joong-Ho Won
Publication date: 5 February 2020
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1810.13100
convergence analysisalternating direction method of multipliersDouglas-Rachford splittingprimal-dual hybrid gradientcirculant linear systemsvariational image denoising
Convex programming (90C25) Biomedical imaging and signal processing (92C55) Computational methods for problems pertaining to biology (92-08)
Related Items
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Nonlinear total variation based noise removal algorithms
- On the ergodic convergence rates of a first-order primal-dual algorithm
- Attouch-Théra duality revisited: Paramonotonicity and operator splitting
- A three-operator splitting scheme and its optimization applications
- Preconditioned Douglas-Rachford algorithms for TV- and TGV-regularized variational imaging problems
- A dual algorithm for the solution of nonlinear variational problems via finite element approximation
- Circulant and skew-circulant splitting methods for Toeplitz systems.
- A nonstationary accelerating alternating direction method for frame-based Poissonian image deblurring
- A first-order primal-dual algorithm for convex problems with applications to imaging
- On the equivalence of the primal-dual hybrid gradient method and Douglas-Rachford splitting
- On the convergence rate improvement of a primal-dual splitting algorithm for solving monotone inclusion problems
- On the Douglas-Rachford algorithm
- On the global and linear convergence of the generalized alternating direction method of multipliers
- The Mathematics of Computerized Tomography
- Regularization Preconditioners for Frame-Based Image Deblurring with Reduced Boundary Artifacts
- Convergence Rate Analysis of Primal-Dual Splitting Schemes
- A General Framework for a Class of First Order Primal-Dual Algorithms for Convex Optimization in Imaging Science
- Theoretically Exact Filtered Backprojection-Type Inversion Algorithm for Spiral CT
- The Split Bregman Method for L1-Regularized Problems
- The Numerical Solution of Parabolic and Elliptic Differential Equations
- On the Numerical Solution of Heat Conduction Problems in Two and Three Space Variables
- A Proposal for Toeplitz Matrix Calculations
- An Optimal Circulant Preconditioner for Toeplitz Systems
- Splitting Algorithms for the Sum of Two Nonlinear Operators
- The Discrete Cosine Transform
- Conjugate-gradient preconditioning methods for shift-variant PET image reconstruction
- A Fast Algorithm for Deblurring Models with Neumann Boundary Conditions
- Conjugate Gradient Methods for Toeplitz Systems
- Primal-Dual Decomposition by Operator Splitting and Applications to Image Deblurring
- Discrete Cosine Transform
- A Statistical Model for Positron Emission Tomography
- Preconditioned Douglas--Rachford Splitting Methods for Convex-concave Saddle-point Problems
- Multiway Splitting Method for Toeplitz Matrix Vector Product
- A fast algorithm for solving circulant tensor systems
- Deconvolving Images With Unknown Boundaries Using the Alternating Direction Method of Multipliers
- A Nonlinear Alternating Direction Method
- Convex Analysis
- Mean Value Methods in Iteration
- Convex analysis and monotone operator theory in Hilbert spaces
