A New Alternating Minimization Algorithm for Total Variation Image Reconstruction

By Yilun Wang, Junfeng Yang, Wotao Yin, Yin Zhang. 2008

2,037 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Radiology, Nuclear Medicine and Imaging

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Citations in the corpus

Accelerating Very Deep Convolutional Networks for Classification and Detection (2015, background): “If ! 1, the solution to (6) will converge to the solution to (5) [33].”
Sparse projections for high-dimensional binary codes (2015, methodology): “Relaxation in this way is similar to Half-Quadratic Splitting [30].”
Hierarchical Convolutional Deep Learning in Computer Vision (2013, methodology): “This has the effect of gradually introducing the sparsity constraint and gives good numerical stability in practice [64,138].”
Motion Detail Preserving Optical Flow Estimation (2012, neutral): “splitting method [35] with auxiliary variables p and w,”
Two-Phase Kernel Estimation for Robust Motion Deblurring (2010, methodology): “To further speed up the optimization, we employ the warm-start scheme [3, 16].”
Deblurring Poissonian images by split Bregman techniques (2010, neutral): “[24], min u2RN ;w2RM fWðuÞ þUðwÞg s:t: Cu 1⁄4 w: ð7Þ”
Interval Coded Scoring extensions for larger problems (2017, background): “In the literature, the problem is also known as total variation minimization (TV) [13].”
Magnetic resonance image reconstruction from undersampled measurements using a patch-based nonlocal operator (2014, methodology): “The proof of the convergence of the algorithm is similar to the one given in (Wang et al., 2008) with slight modifications, and thus is omitted here.”
Infimal convolution regularizations with discrete ℓ1-type functionals (2011, methodology): “Sparked by [12, 13, 21, 40, 44], splitting methods which make use of the additive structure of the objective function have become popular recently in image processing.”
Alternating direction augmented Lagrangian methods for semidefinite programming (2010, methodology): “This simple idea has been applied to many other problem classes, such as, variational inequality problems [14, 15], linear programming [9], nonlinear convex optimization [1, 19, 7, 18, 26], maximal monotone operators [10] and nonsmooth l1 minimization arising from compressive sensing [28, 32, 34].”
Plug-and-Play ADMM for Image Restoration: Fixed-Point Convergence and Applications (2016, background): “Example 2 (Non-blind deblurring [3], [4], [39]):Nonblind deblurring is a special case when S = I.”
Generalized alternating projection based total variation minimization for compressive sensing (2015, background): “The question is can we solve the TV minimization problem in (2) by GAP?”
Split Bregman Methods and Frame Based Image Restoration (2009, methodology): “[66]), or a method for constrained minimizations with a separable nonsmooth objective function is employed (c.”
Accelerated dynamic MRI exploiting sparsity and low-rank structure: k-t SLR (2011, positive): “proofs in [24], it can be shown that the three-step scheme converges to the global minimum of for any fixed .”
An efficient augmented Lagrangian method with applications to total variation minimization (2013, methodology): “In particular, Goldstein and Osher [18] applied Bregman regularization to a split formulation in [36] to derive an algorithm for TV minimization called split Bregman, which is equivalent to ALM.”
Fast Image Deconvolution using Hyper-Laplacian Priors (2009, methodology): “[22] using a total variation (TV) norm prior and (iv) a varian t of [22] using an l1 (Laplacian) prior; (v) the IRLS approach of Levin et al.”