Weighted-average alternating minimization method for magnetic resonance image reconstruction based on compressive sensing

DOI10.3934/ipi.2014.8.925zbMath1302.65240OpenAlexW2328485015MaRDI QIDQ479909

Xinyan Yu, Bin Zhang, Yong-gui Zhu, Yu-Ying Shi

Publication date: 5 December 2014

Published in: Inverse Problems and Imaging (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/ipi.2014.8.925

zbMATH Keywords

compressive sensingmagnetic resonance image reconstructionweighted averagealternating minimization method

Mathematics Subject Classification ID

Numerical aspects of recurrence relations (65Q30) Numerical methods for ill-posed problems for boundary value problems involving PDEs (65N20) Modeling and interdisciplinarity (aspects of mathematics education) (97M10) Biology, chemistry, medicine (aspects of mathematics education) (97M60)

Related Items (4)

Image restoration from noisy incomplete frequency data by alternative iteration scheme ⋮ Huberization image restoration model from incomplete multiplicative noisy data ⋮ A nonlinear diffusion model for image restoration ⋮ On image restoration from random sampling noisy frequency data with regularization

Uses Software

• RecPF

Cites Work

• Unnamed Item
• Unnamed Item
• Nonlinear total variation based noise removal algorithms
• A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems
• Partial inverse of a monotone operator
• A coordinate gradient descent method for nonsmooth separable minimization
• A novel method and fast algorithm for MR image reconstruction with significantly under-sampled data
• A dual algorithm for the solution of nonlinear variational problems via finite element approximation
• Fast Multiple-Splitting Algorithms for Convex Optimization
• A New Alternating Minimization Algorithm for Total Variation Image Reconstruction
• The Split Bregman Method for L1-Regularized Problems
• On Sparse Representations in Arbitrary Redundant Bases
• Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information
• A proximal decomposition method for solving convex variational inverse problems
• General Projective Splitting Methods for Sums of Maximal Monotone Operators
• Augmented Lagrangian Method, Dual Methods and Split Bregman Iteration for ROF Model
• Uncertainty principles and ideal atomic decomposition
• Sparse Approximate Solutions to Linear Systems
• A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings
• Sparsity and incoherence in compressive sampling
• Fast Gradient-Based Algorithms for Constrained Total Variation Image Denoising and Deblurring Problems
• Bregman Iterative Algorithms for $\ell_1$-Minimization with Applications to Compressed Sensing
• Signal Recovery by Proximal Forward-Backward Splitting
• Proximité et dualité dans un espace hilbertien
• Weak convergence of the sequence of successive approximations for nonexpansive mappings
• Compressed sensing

This page was built for publication: Weighted-average alternating minimization method for magnetic resonance image reconstruction based on compressive sensing