A Fast Alternating Direction Method for TVL1-L2 Signal Reconstruction From Partial Fourier Data

By Junfeng Yang, Yin Zhang, Wotao Yin. IEEE Journal on Selected Topics in Signal Processing, 2010

585 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7dfce7cd85255d25b7dbf9e41d3321a3b5f817e0

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Citations in the corpus

Exact Recoverability From Dense Corrupted Observations via $\ell _{1}$-Minimization (2011, methodology): “To optimize (49), we employ the classic alternating direction method (ADM) as presented in [32].”
Magnetic resonance image reconstruction from undersampled measurements using a patch-based nonlocal operator (2014, methodology): “These methods include Lustig’s method (Lustig et al., 2007), Yang’s method (Yang et al., 2010), Chen’s method (Chen and Huang, 2012), Huang’s method (Huang and Yang, 2012) and Egiazarian’s method (Egiazarian et al., 2007), repectively.”
An Augmented Lagrangian Approach to the Constrained Optimization Formulation of Imaging Inverse Problems (2009, methodology): “…the reconstruction from partial Fourier (RecPF) algorithm was designed for signal reconstruction from partial Fourier observations and also uses ADMM; the optimization problem addressed by RecPF also has the form (4), but with a regularizer that is the sum of two terms: a TV norm and an norm [56].”
Plug-and-Play Methods Provably Converge with Properly Trained Denoisers (2019, methodology): “We compare PnP frameworks with zero-ﬁlling, total-variation (TV) (Lustig et al., 2005), RecRF (Yang et al., 2010), and BM3D-MRI (Eksioglu, 2016) 4 .”
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?”
DAGAN: Deep De-Aliasing Generative Adversarial Networks for Fast Compressed Sensing MRI Reconstruction (2018, methodology): “Finally, nonlinear optimisation algorithms ensure the achievement of efﬁcient, stable and accurate reconstruction [16], [18], [29], [30].”
Multiscale X-ray tomography of cementitious materials: A review (2020, methodology): “Classical techniques include total variation minimization [59, 91, 92], `0 sparse regularization [93] and wavelet/curvelet expansions [94, 95].”
Deep ADMM-Net for Compressive Sensing MRI (2016, methodology): “These methods include Zero-filling [22], TV [2], RecPF [4], SIDWT 3, and also the state-of-the-art methods such as PBDW [6], PANO [10], FDLCP [8] and BM3D-MRI [11].”
NESTA: A Fast and Accurate First-Order Method for Sparse Recovery (2009, methodology): “Known methods include interior point methods ( 1-magic) [10], proximalsubgradient methods [5, 19], split Bregman [35], and the very recently introduced RecPF9 [59], which operates in the special case of partial Fourier measurements.”
ADMM-CSNet: A Deep Learning Approach for Image Compressive Sensing (2020, methodology): “The average PSNR curves of RecPF method [29], BasicADMM-CSNet and Generic-ADMM-CSNet are shown in”
An efficient augmented Lagrangian method with applications to total variation minimization (2013, methodology): “From then on, TV minimizing models have become one of the most popular and successful methodologies for image denoising [8, 33], deconvolution [9, 36] and restoration [5, 34, 37, 39], to cite just a few.”
Alternating Direction Algorithms for 1-Problems in Compressive Sensing (2009, methodology): “Recently, the ADM has also been applied to total variation based image reconstruction in [20, 52, 34] and to semi-deﬁnite programming in [49].”