Double Sparsity: Learning Sparse Dictionaries for Sparse Signal Approximation

By Ron Rubinstein, Michael Zibulevsky, Michael Elad. 2010

644 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Computer Vision and Pattern Recognition, Representation & Self-Supervised Learning, Signal Processing

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. Guillermo Sapiro
3. Yaniv Romano
4. Vardan Papyan
5. Xiaolin Wu
6. Robert Calderbank
7. Qiang Qiu
8. Xiuyuan Cheng

In Computational Mechanics

1. Lei Zhang
2. Guangming Shi
3. Weisheng Dong
4. Michael Elad
5. Wangmeng Zuo
6. Guillermo Sapiro
7. Yaniv Romano
8. Julien Mairal

In Computer Vision and Pattern Recognition

1. Lei Zhang
2. Guangming Shi
3. Weisheng Dong
4. Wangmeng Zuo
5. Luc Van Gool
6. Ming-Hsuan Yang
7. Dacheng Tao
8. Guillermo Sapiro

In Representation & Self-Supervised Learning

1. Vardan Papyan
2. Yaniv Romano
3. Qiang Qiu
4. Guillermo Sapiro
5. Robert Calderbank
6. Xiuyuan Cheng
7. Guangming Shi
8. Michael Elad

In Signal Processing

1. Guillermo Sapiro
2. Lei Zhang
3. Qiang Qiu
4. Robert Calderbank
5. Guangming Shi
6. Weisheng Dong
7. Xiuyuan Cheng
8. Vardan Papyan

Citations in the corpus

• Predicting Parameters in Deep Learning (2013, neutral): “[23] studies approximating linear dictionaries with other dictionaries in a manner similar to how we approximate network features.”
• RotDCF: Decomposition of Convolutional Filters for Rotation-Equivariant Deep Networks (2018, methodology): “[26] interpreted CNN as an iterated convolutional sparse coding machine, and in this view, the factorized filters should correspond to a “dictionary of the dictionary” as in [30].”
• Data-driven discovery of coordinates and governing equations (2019, neutral): “Alternatively, one might attempt to learn the library functions using another neural network layer, a double sparse library (53), or kernel-based methods (54) for more flexible library representations.”
• Convolutional Neural Networks Analyzed via Convolutional Sparse Coding (2016, methodology): “Double sparsity – first proposed in (Rubinstein et al., 2010) and later employed in (Sulam et al.”
• Image Deblurring and Super-Resolution by Adaptive Sparse Domain Selection and Adaptive Regularization (2010, background): “Recently, there has been much effort in learning dictionaries from example image patches [13-15, 26-31, 55], leading to state-of-the-art”
• Deep Learning for Geophysics: Current and Future Trends (2021, background): “A double sparsity (DS) dictionary learning was proposed to explore deep decomposition (Rubinstein et al., 2010).”
• Sparse Representation Based Image Interpolation With Nonlocal Autoregressive Modeling (2013, background): “12 dictionaries learned from example images can lead to better image restoration results [23, 30, 39].”
• DCFNet: Deep Neural Network with Decomposed Convolutional Filters (2018, background): “…bases and learned coefficients has been studied in classical signal processing (Freeman et al., 1991; Mahalanobis et al., 1987), dictionary learning (Rubinstein et al., 2010) and computer vision (Henriques et al., 2013; Bertinetto et al., 2016), they were not designed with deep architectures in…”