An efficient augmented Lagrangian method with applications to total variation minimization

By Chengbo Li, Wotao Yin, Hong Jiang, Yin Zhang. Computational optimization and applications, 2013

646 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mathematical Physics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/9eab80f0c345cee51ca27f0b41a71a3f5e6b2c9b

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Zahra Kadkhodaie
2. Eero P. Simoncelli
3. Bernard Ghanem
4. Jian Zhang
5. Debin Zhao
6. Geoffrey Y. Li
7. Pavan K. Turaga
8. Ce Zhu

In Mathematical Physics

1. Zahra Kadkhodaie
2. Jian Zhang
3. Geoffrey Y. Li
4. Chao-Kai Wen
5. Shi Jin
6. Eero P. Simoncelli
7. Bernard Ghanem
8. Xin Yuan

In Numerical Analysis

1. Zahra Kadkhodaie
2. Jian Zhang
3. Eero P. Simoncelli
4. Yongdong Zhang
5. Bernard Ghanem

Citations in the corpus

• Group-Based Sparse Representation for Image Restoration (2014, methodology): “,wavelet method (DWT), total variation (TV) method [41], multi-hypothesis (MH) method [40], collaborative sparsity (CoS) method [42], which deal with image signals in the wavelet domain, the gradient domain, the random projection residual domain, and the hybrid space-transform domain, respectively.”
• ReconNet: Non-Iterative Reconstruction of Images from Compressively Sensed Measurements (2016, methodology): “At low measurement rates of 0.1, 0.04 and 0.01, our algorithm yields superior quality reconstructions than the traditional iterative CS reconstruction algorithms, TVAL3, NLR-CS, and D-AMP.”
• AMP-Net: Denoising-Based Deep Unfolding for Compressive Image Sensing (2020, methodology): “From Table II, it can be found that TVAL3 and D-AMP have worse performance at low CS ratios of 4% and 1%.”
• Convolutional Neural Network-Based Multiple-Rate Compressive Sensing for Massive MIMO CSI Feedback: Design, Simulation, and Analysis (2019, methodology): “12 ms while the LASSO [49], BM3D-AMP [50], and TVAL3 [51] need about 0.”
• ISTA-Net: Interpretable Optimization-Inspired Deep Network for Image Compressive Sensing (2017, methodology): “From Table 1, we observe that SDA and ReconNet work better at 1We use the source code made publicly available by the authors of TVAL3 [22], D-AMP [28], IRCNN [49], and ReconNet [21] and implement SDA [30] ourselves, since its source code is not available. extremely low CS ratios of 1% and 4%, while ”
• Solving Linear Inverse Problems Using the Prior Implicit in a Denoiser (2020, methodology): “TVAL3 [52] is an optimization-based algorithm with total variation regularization, ISTA-Net [53] is a CNN supervised method trained to reconstruct images from measurements obtained from one particular random matrix.”
• Stochastic Solutions for Linear Inverse Problems using the Prior Implicit in a Denoiser (2021, methodology): “Ratio TVAL3 [53] ISTA-Net [54] DIP [8] BNN [55] Ours±std Ours:avg 25% 26.”
• Generalized alternating projection based total variation minimization for compressive sensing (2015, background): “On the other hand, the total variation (TV) based algorithms have demonstrated high performance on variously CS problems [19–24].”
• DR2-Net: Deep Residual Reconstruction Network for Image Compressive Sensing (2017, methodology): “01 w/o BM3D w/ BM3D w/o BM3D w/ BM3D w/o BM3D w/ BM3D w/o BM3D w/ BM3D TVAL3 [20] 24.”