Dictionary Learning Algorithms for Sparse Representation

By Kenneth Kreutz-Delgado, Joseph F. Murray, Bhaskar D. Rao, Kjersti Engan, Te-Won Lee, Terrence J. Sejnowski. Neural Computation, 2003

932 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/306de9c553695822ae9e6de044b6856baf0cce7d

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Citations in the corpus

Image Denoising and Inpainting with Deep Neural Networks (2012, methodology): “Following this strategy, A family of models exploiting the (linear) sparse coding technique have drawn increasing attention recently [4] [5] [6] [7] [8] [9].”
Underdetermined blind source separation based on sparse representation (2006, methodology): “FOCUSS-based algorithms were designed to solve underdetermined linear inverse problems in cases where both the dictionary and the sources were unknown (e.g., [ 4 ]).”
Sparse Coding via Thresholding and Local Competition in Neural Circuits (2008, methodology): “While FOCUSS can implement both ℓ 1 global optimization and ℓ 0 local optimization (Rao and Kreutz-Delgado, 1999) in a dynamical system (Kreutz-Delgado et al., 2003) that uses parallel computation to implement a competition strategy among the nodes (strong nodes are encouraged to grow while weak…”
Seismic data restoration via data-driven tight frame (2014, methodology): “Research of the data-driven TF is focused on adopting the machine-learning methodology (Olshausen and Field, 1997; Lewicki and Sejnowski, 2000; Kreutz-Delgado et al., 2003; Aharon et al., 2006; Elad and Aharon, 2006; Mairal et al., 2008, 2009) to construct a set of shift-invariant framelets.”
New Algorithms for Learning Incoherent and Overcomplete Dictionaries (2013, background): “(We will later discuss why current algorithms in [39], [22], [4], [36], [38] do not come with such guarantees.)”
Image Denoising Via Learned Dictionaries and Sparse representation (2006, background): “This idea of learning a dictionary that yields sparse representations for a set of training image-patches, has been studied in a sequence of works [22, 23, 24, 25, 26].”
Machine learning in acoustics: Theory and applications. (2019, methodology): “24,25,28,52 Neural network models, called autoencoders, are also used for learning latent models.”
Machines that learn to segment images: a crucial technology for connectomics. (2010, background): “Features are learned from images by optimizing an objective function that does not depend on the desired output of the ultimate task to be learned [68 – 71].”
On the Identifiability of Overcomplete Dictionaries via the Minimisation Principle Underlying K-SVD (2013, background): “…the research focus in dictionary learning has been on algorithmic development, meaning that by now there are several dictionary learning algorithms, which are efﬁcient in practice and therefore popular in applications, see [13], [19], [1], [22], [34], [20], [29] or [26] for a more complete survey.”
Compressed Sensing for Wireless Communications: Useful Tips and Tricks (2015, background): “This task, kn own asdictionary learning[76], [77], is to learn an overcomplete dictionary D ∈ Cn×m (n < m) from a set of signalsxi such that xi can be approximated as xi ≈ Dsi, wheresi ∈ Cm×1 and ‖si‖0 ≪ m.”
A Conditional Gradient-based Method for Simple Bilevel Optimization with Convex Lower-level Problem (2022, methodology): “A common approach is to formulate this as the following non-convex optimization problem (Kreutz-Delgado et al., 2003; Yaghoobi et al., 2009; Rakotomamonjy, 2013; Bao et al., 2016): min D∈Rm×p min X∈Rp×n 1 2n ∑ i∈N ‖ai −Dxi‖22 s.t. ‖dj‖2 ≤ 1, j = 1, . . . , p; ‖xi‖1 ≤ δ, i ∈ N .”
Blind Source Separation and Independent Component Analysis : A Review (2004, methodology): “Wide classes of extrapolation, reconstruction, estimation, approximation, interpolation and inverse problems can be converted to minimum norm problems of solving underdetermined systems of linear equations (2) for m < n [88, 40].”