Nonlinear Wavelet Image Processing: Variational Problems, Compression, and Noise Removal through Wavelet Shrinkage *

By Antonin Chambolle, Ronald A. DeVore, N. Lee, B. Lucier. 1996

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Citations in the corpus

Interpretable Recurrent Neural Networks Using Sequential Sparse Recovery (2016, methodology): “Here we will focus on ISTA [19, 18], which is a proximal gradient method that consists of K iterations of soft-thresholding.”
Split Bregman Methods and Frame Based Image Restoration (2009, background): “This is essentially the approach in [31, 40]; see also [24, 35, 46, 49].”
A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems (2009, unknown): “For such computation and other separable regularizers, see, for instance, the general formulas derived in [25, 7, 9].”
Vector Approximate Message Passing (2019, methodology): “Relation of AMP to IST The AMP Algorithm 1 is closely related to the well-known iterative soft thresholding (IST) algorithm [26], [27] that can be used2 to solve (2) with convex f (·).”
Sparse regression using mixed norms (2009, result): “Remark 5 This proposition generalises the result given in the wavelet and Besov spaces framework in [4].”
Hierarchical Convolutional Deep Learning in Computer Vision (2013, methodology): “Fast iterative shrinkage-thresholding algorithm (FISTA) [4] is the most immediate extension to the ISTA algorithm and changes the convergence properties to be O(1/t2) rather than the O(1/t) convergence rate of ISTA, where t is there number of iterations.”
Parameter-Efficient Fine-Tuning for Large Models: A Comprehensive Survey (2024, methodology): “The gate g is updated using a variation of proximal gradient iteration for l 1 loss [7], [13], which has a clear mathematical meaning and do not need the heuristic premise.”
Differential Privacy via Wavelet Transforms (2009, background): “, [13], [14], [15], [16], [17]) for choosing an appropriate based only on the noisy wavelet coefficients.”
An efficient algorithm for compressed MR imaging using total variation and wavelets (2008, background): “First, it has been well known (see [4], for example) that the unique solution of (15) is soft-thresholding or shrinkage:”
Probing the Pareto Frontier for Basis Pursuit Solutions (2008, background): “’s [13] derivation of the soft-thresholding operation (4.”
A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration (2007, background): “The adopted regularizer is then the corresponding Besov norm ‖·‖Ba p(Lp(I)), which has an equivalent weighted l sequence norm of wavelet coefficients on an orthogonal wavelet basis (see [12] for details).”
Besov priors for Bayesian inverse problems (2011, methodology): “ on wavelet bases for recovering ﬁnite dimensional estimates of the unknown function are extensively studied in the approximation theory, signal processsing and statistics literature; see for example [1, 6, 13, 14]. The paper [2] introduced a nonparametric Bayesian approach to the problem of signal ”
Color demosaicking by local directional interpolation and nonlocal adaptive thresholding (2011, methodology): “Actually soft-thresholding is widely used to solve the l1-norm minimization problems [30-31, 40].”
An iterative thresholding algorithm for linear inverse problems with a sparsity constraint (2003, unknown): “Of particular importance for the background of this paper is the article by Chambolle et al. [6], which provides a variational formulation for denoising, through the use of penalties on a Besov-norm of the signal; this is the perspective adopted in the present paper.”
Deep learning for visual understanding (2017, unknown): “A popular algorithm for sparse coding inference is the Iterative Shrinkage-Thresholding Algorithm (ISTA) [131], which takes a gradient step to optimize the reconstruction term, followed by a sparsity term which has a closed form shrinkage operation.”
Discriminative Recurrent Sparse Auto-Encoders (2013, unknown): “By breaking complex calculations into many steps, deep networks can gradually build up complicated decision boundaries or input transformations, facilitate the reuse of common substructure, and explicitly compare alternative interpretations of ambiguous input (Lee, Ekanadham, & Ng, 2008; Zeiler,…”