Iteratively reweighted algorithms for compressive sensing

By Rick Chartrand, Wotao Yin. IEEE International Conference on Acoustics, Speech, and Signal Processing, 2008

1,367 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/eae546e4f801607300ac833efcab230f9652c5eb

How researchers see this paper

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

In Biomedical Engineering

1. Lei Zhang
2. Gitta Kutyniok
3. Wotao Yin
4. Maryam Fazel
5. Yin Zhang
6. Bhaskar D. Rao
7. Wangmeng Zuo
8. Deyu Meng

In Computational Mechanics

1. Lei Zhang
2. Wotao Yin
3. Wangmeng Zuo
4. E.J. Candes
5. Yin Zhang
6. Stephen P. Boyd
7. Guangming Shi
8. Weisheng Dong

In Electrical and Electronic Engineering

1. René Vidal
2. Wotao Yin
3. Bhaskar D. Rao
4. Gitta Kutyniok
5. Lei Zhang
6. Yin Zhang
7. E.J. Candes
8. Maryam Fazel

Citations in the corpus

• Toward Real-World Single Image Super-Resolution: A New Benchmark and a New Model (2019, methodology): “τ , and this objective function can be solved by an iteratively reweighted least square problem (IRLS) as follows [9]:”
• ACNe: Attentive Context Normalization for Robust Permutation-Equivariant Learning (2020, methodology): “To address this issue, we take inspiration1 from a classical technique used in robust optimization: Iteratively Reweighted Least Squares (IRLS) [8].”
• Compressive sensing: From theory to applications, a survey (2013, methodology): “There are many algorithms proposed in literature that use this technique like focal underdetermined system solution (FOCUSS) [48], iterative re-weighted least squares [49], sparse bayesian learning algorithms [50], Monte-Carlo based algorithms [51], etc.”
• Modern WLAN Fingerprinting Indoor Positioning Methods and Deployment Challenges (2016, methodology): “Several algorithms have been proposed to solve this problem, e.g. greedy algorithms [164], iteratively re-weighted linear least-squares (IRLS) [165], and basis pursuit [166].”
• A Globally Convergent Algorithm for Nonconvex Optimization Based on Block Coordinate Update (2014, background): “For example, KSVD [1] only has nonincreasing monotonicity of its objective sequence, and iterative reweighted algorithms for sparse and low-rank recovery in [15, 28, 35] only has subsequence convergence.”
• Sparse Representation Based Image Interpolation With Nonlocal Autoregressive Modeling (2013, methodology): “In the iteratively re-weighted lp-norm minimization [41, 21], it is suggested that the weight assigned to coding coefficient α should be set as”
• Fast Global Image Smoothing Based on Weighted Least Squares (2014, methodology): “The proposed global smoother can also be used to optimize an objective function defined on the Lγ norm with the iterative re-weighted least squares (IRLS) algorithm [35].”
• Minimization of ℓ1-2 for Compressed Sensing (2015, methodology): “• An improved IRLS-ℓp algorithm [38] that solves the unconstrained ℓp problem with 0 p 1: (5.1) min x∈Rn 1 2 ∥Ax− b∥22 + λ∥x∥pp. • Reweighted ℓ1 [10] which is at heart a non-convex CS solver based on IRL1 algorithm attempting to solve min x∈Rn n∑ i=1 log(|xi|+ ε) subject to Ax = b. • Half thresh”
• Enhancing Sparsity by Reweighted ℓ1 Minimization (2007, background): “It must be noted, however, that since the initial submission of our manuscript, we have learned of ongoing work in developing reweighting strategies for FOCUSS as well [56, 57]; in some situations the performance can be competitive with reweighted 1 minimization, and a more comprehensive study is wa”
• Fast and Robust Iterative Closest Point (2020, methodology): “Our approach has a similar structure as the iteratively reweighted least squares (IRLS) method that minimizes the p -norm ( p 1 ) for compressive sensing [59].”
• L1−2 minimization for exact and stable seismic attenuation compensation (2018, background): “The aforementioned non-convex penalties can be solved by iteratively reweighted least squares (Sacchi 1997; Gorodnitsky & Rao 2002; Chartrand & Yin 2008; Lai et al. 2013) or multistage convex relaxation (Zhang 2010b).”
• Fast algorithms for nonconvex compressive sensing: MRI reconstruction from very few data (2009, background): “The results take advantage of the sparsity inherent in realworld images: the ubiquity of image compression points to the existence of transforms converting a digital image into one having relatively few values significantly different from zero.”
• Lower Bound Theory of Nonzero Entries in Solutions of ℓ2-ℓp Minimization (2010, background): “1) attracted great attention in variable selection and sparse reconstruction [5, 7, 8, 9, 28].”
• Compressed Sensing (2014, positive): “Los experimentos numéricos realizados en [22], donde se considera un problema CS aleatorio de tamaño n = 256 y m = 100, con medidas sin ruido y valores no nulos xi ∼ N (0, σ = 2), indican que esta regularización logra una mejora considerable en el desempeño del algoritmo RW`2.”
• A Generalized Iterated Shrinkage Algorithm for Non-convex Sparse Coding (2013, methodology): “Several typical algorithms include iteratively reweighted least squares (IRLS) [12, 14, 23, 24, 28], iteratively reweighted 1 -minimization (IRL1) [8], iteratively thresholding method (ITM-(cid:2) p ) [33, 34], and look-up table (LUT) [25].”