De-noising by soft-thresholding

By David L. Donoho. 1995

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Citations in the corpus

Solving Linear Inverse Problems Using the Prior Implicit in a Denoiser (2020, methodology): “ting some additional noise: yt= yt 1 +htf(yt 1)+ tzt; (5) where f(y) = ^x(y) yis the residual of the denoising function, which is proportional to the gradient of p(y), from Eq. (4). The parameter ht 2[0;1] controls the fraction of the denoising correction that is taken, and zt˘N(0;I) is a sample of ”
Deep Decoder: Concise Image Representations from Untrained Non-convolutional Networks (2018, background): “For example, imposing the assumption that an image can be represented with few non-zero wavelet coeﬃcients enables modern (lossy) image compression [Ant+92] and eﬃcient de-noising [Don95].”
Optimal selection of wavelet basis function applied to ECG signal denoising (2006, background): “The universal threshold selection by Donoho and Johnstone [19–22] explicitly proposes a threshold value σ √ 2 logM proportional to the amount of noise σ (assumed to be known or estimated from data) and M the number of samples.”
Iterative Thresholding for Sparse Approximations (2008, background): “For example, a wide range of signal processing applications such as source coding [1], [2], denoising [3], source separation [4] and pattern analysis [5] have benefited from progress made in this area.”
Orthogonal AMP (2016, methodology): “7 shows the OAMP SE accuracy with the following soft-thresholding function [31]:”
Block Compressed Sensing of Images Using Directional Transforms (2010, methodology): “To set a proper τ for hard thresholding, we employ the universal threshold method of [17].”
Recovering edges in ill-posed inverse problems: optimality of curvelet frames (2002, background): “This acts as proxy for the mean-squared error of estimation of a threshold estimator; in studies [25, 19] it has been shown that its behavior mimics, to within logarithmic factors, the true mean-squared error of estimation.”
Coupled minimum-cost flow cell tracking for high-throughput quantitative analysis (2011, methodology): “To approximate the signal term, we threshold the image stack with an Amplitude-scale-invariant Bayes Estimator (ABE) using Jeffreys’ non-informative prior [70, 71, 72] as an estimate of the significance of wavelet coefficient W I i (x,y) at a given scale i and position (x,y) W I i (x,y)≈ δ ABE (Wi(x”
Sparsity Constrained Nonlinear Optimization: Optimality Conditions and Algorithms (2012, background): “uction Sparsity has long been exploited in signal processing, applied mathematics, statistics and computer science for tasks such as compression, denoising, model selection, image processing and more [7, 8, 14, 17, 19, 21, 22]. Recent years have witnessed a growing interest in sparsitybased processi”
Forecasting East Asian Indices Futures via a Novel Hybrid of Wavelet-PCA Denoising and Artificial Neural Network Models (2016, methodology): “Denoising algorithms based onWavelet Transform have become a widespread technique for single-dimensional signal filtering and data mining [28, 32, 33].”
Application of Iterative Soft Thresholding for Fast Reconstruction of NMR Data Non-uniformly Sampled with Multidimensional Poisson Gap Scheduling (2012, methodology): “The use of iterative thresholding has been proposed previously for extracting unknown functions from noisy data (Donoho 1995).”
A New TwIST: Two-Step Iterative Shrinkage/Thresholding Algorithms for Image Restoration (2007, background): “Examples of such choices are total-variation (TV) regularization [11], [15], [42] and wavelet-based regularization [13], [22], [23], [39].”
An introduction to continuous optimization for imaging (2016, methodology): “D. L. Donoho (1995), ‘De-noising by soft-thresholding’, IEEE Trans.”
Automated breast cancer detection and classification using ultrasound images: A survey (2015, background): “Most filters are traditional techniques in spatial domain and can be categorized as linear and nonlinear filters.”
Improving the Gaussian Mechanism for Differential Privacy: Analytical Calibration and Optimal Denoising (2018, background): “Quite remarkably, Donoho [1995] shows that choosing λ = σ √ 2 log d in the soft-thresholding estimator”
Wavelets, Ridgelets, and Curvelets for Poisson Noise Removal (2008, methodology): “Once we are brought to the Gaussian denoising problem, standard approaches such as wavelet thresholding [5][6] are used before the VST is inverted to get the final estimate.”