Normalized Iterative Hard Thresholding: Guaranteed Stability and Performance

By Thomas Blumensath, M. Davies. IEEE Journal on Selected Topics in Signal Processing, 2010

503 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Signal Processing

View Paper: https://www.semanticscholar.org/paper/563746d4d9e08752effafec88362482196ebba5b

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. Yonina C. Eldar
2. Amir Beck
3. Simon Foucart
4. Oluwasanmi Koyejo
5. Sanjay B. Dhok
6. Jacky Y. Zhang
7. Meenu Rani
8. Raghavendra B. Deshmukh

In Computer Vision and Pattern Recognition

1. Yonina C. Eldar
2. Amir Beck
3. Oluwasanmi Koyejo
4. Sanjay B. Dhok
5. Simon Foucart
6. Meenu Rani
7. Raghavendra B. Deshmukh
8. Anastasios Kyrillidis

In Signal Processing

1. Yonina C. Eldar
2. Oluwasanmi Koyejo
3. Sanjay B. Dhok
4. Jacky Y. Zhang
5. Simon Foucart
6. Meenu Rani
7. Raghavendra B. Deshmukh
8. Anastasios Kyrillidis

Citations in the corpus

• A Systematic Review of Compressive Sensing: Concepts, Implementations and Applications (2018, background): “On the other hand, if the step size is adaptive, then algorithm becomes more complicated [43].”
• Sparsity Constrained Nonlinear Optimization: Optimality Conditions and Algorithms (2012, methodology): “m. This result is consistent with Theorem 3.2 since when kAk 2 < 1, the Lipschitz constant satisfies L(f) < 1, and we can therefore assure convergence by Theorem 3.2 with stepsize equal to 1. In [5] the authors note that the IHT method with stepsize 1 might diverge when kAk 2 > 1. To overcom”
• Bayesian Coresets: Revisiting the Nonconvex Optimization Perspective (2021, background): “Moreover, the authors in (Blumensath & Davies, 2010) present toy examples by carefully selecting Φ so that the vanilla IHT algorithm diverges without appropriate step size selection.”
• Event-Triggered State Observers for Sparse Sensor Noise/Attacks (2013, unknown): “These two ingredients, multiple gradient steps and eventtriggering, result in weaker conditions for convergence: δ2s > (4/9)λmax{QQ} for the ETPG algorithm vs δ2s > (8/9) λmax{QQ} for the NIHT algorithm (Theorem 4 in [25]).”
• Hard Thresholding Pursuit: An Algorithm for Compressive Sensing (2011, methodology): “The original terminology of Normalized Iterative Hard Thresholding used in [4] corresponds to the specific choice (where the notation zT ∈ C stands for a vector equal to a vector z ∈ C on a set T and to zero outside of T )”