Analysis of Half-Quadratic Minimization Methods for Signal and Image Recovery

By Mila Nikolova, Michael Kwok-Po Ng. SIAM Journal on Scientific Computing, 2005

479 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/4c4cc51f38a2138f81c8c3984f6a89e9d7809af1

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. Wotao Yin
2. Yin Zhang
3. Junfeng Yang
4. Dacheng Tao
5. Ran He
6. Weishi Zheng
7. Liang Wang
8. Kaiye Wang

In Computer Vision and Pattern Recognition

1. Dacheng Tao
2. Liang Wang
3. Luc Van Gool
4. Xiaogang Wang
5. Wotao Yin
6. Yin Zhang
7. Ming-Hsuan Yang
8. Yi Yang

In Radiology, Nuclear Medicine and Imaging

1. Wotao Yin
2. Yin Zhang
3. Junfeng Yang
4. Liang Wang
5. Ran He
6. Dacheng Tao
7. Tien-Ping Tan
8. José Carlos Príncipe

Citations in the corpus

• Half-Quadratic-Based Iterative Minimization for Robust Sparse Representation (2014, methodology): “where ð:Þ is a potential loss function in HQ [33], [41] and vj is the jth entry of v.”
• Robust Principal Component Analysis Based on Maximum Correntropy Criterion (2011, methodology): “The rapid convergence of HQ-PCA may be due to the fact that maximization (or minimization) using HQ optimization can speed up computation [38].”
• Robust support vector machines based on the rescaled hinge loss function (2017, methodology): “utilizing the half-quadratic (HQ) optimization method [17].”
• Joint Feature Selection and Subspace Learning for Cross-Modal Retrieval (2016, methodology): “Then, we can optimize fð Þ in a half-quadratic way [53] according to the following Lemma 1 [9].”
• Proximal Algorithms in Statistics and Machine Learning (2015, methodology): “See Nikolova and Ng [2005] for convergence rates and comparisons of the different algorithms.”
• A New Alternating Minimization Algorithm for Total Variation Image Reconstruction (2008, methodology): “However, [34] does not include a convergence analysis or extensive numerical experiments on the half-quadratic model for this anisotropic TV approximation.”
• Maximum Correntropy Criterion for Robust Face Recognition (2011, methodology): “An estimator should satisfy some conditions as detailed in [57], and then can be optimized by the multiplicative form of the HQ.”
• Feature Selection Based on Structured Sparsity: A Comprehensive Study (2017, methodology): “The objective function can be optimized by additive form of half-quadratic or multiplicative form of half-quadratic [87].”
• Hyperspectral Image Denoising via Tensor Low-Rank Prior and Unsupervised Deep Spatial–Spectral Prior (2022, methodology): “In order to solve the proposed LRDS2, we resort to the half-quadratic splitting (HQS) [50], [51], [52] technique and transform the constrained problem (4) into following unconstrained problem : min where β 1 and β 2 are penalty parameters.”
• Learning Coupled Feature Spaces for Cross-Modal Matching (2013, methodology): “Then, we can optimize φ(·) in a half-quadratic way [16] according to the following Lemma 2 [8].”
• Perspective Functions: Properties, Constructions, and Examples (2016, background): “This function was introduced in [36] and it plays an important role in robust statistics and signal processing [37, 51], while its perspective function appears implicitly in robust regression problems [37, 39, 53].”