Why Simple Shrinkage Is Still Relevant for Redundant Representations?

By Michael Elad. IEEE Transactions on Information Theory, 2006

304 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition, Geophysics

View Paper: https://www.semanticscholar.org/paper/4a8074734bd55ff386c64d56689b524ae7809480

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Citations in the corpus

Sparse Coding via Thresholding and Local Competition in Neural Circuits (2008, background): “The connection between soft-thresholding and BPDN is well-known in the case of orthonormal dictionaries (Chen et al., 2001), and recent results (Elad, 2006) have given some justiﬁcation for using soft-thresholding in overcomplete dictionaries.”
Alternating Direction Algorithms for 1-Problems in Compressive Sensing (2009, methodology): “To date, the most widely studied ﬁrst-order method for solving (1.5) is the iterative shrinkage/thresholding (IST) method, which is ﬁrst proposed in [21, 37, 14] for wavelet-based image deconvolution and then independently discovered and analyzed by many others [19, 43, 44, 13].”
Morphological Component Analysis: An Adaptive Thresholding Strategy (2007, background): “In [ 24 ], the author shows that thresholding is still relevant for overcomplete representations for sparse minimization.”
Fixed-Point Continuation for l1-Minimization: Methodology and Convergence (2008, methodology): “These contributions include [29] by Figueiredo and Nowak, [15] by De Mol and Defrise, [13] by Daubechies, Defrise, and De Mol, [2] by Aubert, Bect, Blanc-Feraud, and Chambolle, [25, 26, 27] by Elad et al.”
From Sparse Solutions of Systems of Equations to Sparse Modeling of Signals and Images (2009, methodology): “Handling of the general case is somewhat more involved, as can be seen in [76, 75, 32, 62, 5, 67, 59].”
On the Role of Sparse and Redundant Representations in Image Processing (2010, background): “In recent years, iterative shrinkage/thresholding (IST) algorithms, tailored for objective functions of the form (6), were independently proposed by several authors [46], [29], [17], [30], [4], [23], [25], [52], [53].”
FISTA-Net: Learning a Fast Iterative Shrinkage Thresholding Network for Inverse Problems in Imaging (2020, unknown): “proximal operator) [31], [32]:”
Handbook of Blind Source Separation: Independent Component Analysis and Applications (2010, methodology): “Efficient iterative numerical methods were proposed [28, 36, 42] for calculating the optimum c x , for the P = 1 single-channel case.”
Augmented Lagrangian alternating direction method for matrix separation based on low-rank factorization (2014, methodology): “One type of algorithm is based on a scheme called iterative shrinkage, which has been successfully applied to 1 minimization [13,17,20,26] and to matrix completion [3,36].”
From Local Kernel to Nonlocal Multiple-Model Image Denoising (2009, background): “A number of threshold operators ρ derived from (13) for different penalty functions are studied by Elad [ 25 ].”
Sparse Reconstruction by Separable Approximation (2008, background): “…known in the literature by different names, such as iterative denoising, thresholded Landweber, forward-backward splitting, and fixed-point iteration algorithms (see Combettes and Wajs [17], Daubechies, Defriese, and De Mol [21], Elad [32], Figueiredo and Nowak [36], and Hale, Yin, and Zhang [51]).”