Adapting to Unknown Smoothness via Wavelet Shrinkage

By David L. Donoho, Iain M. Johnstone. 1995

Subfields: Optimization & Training, Signal Processing

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Citations in the corpus

Optimization with Sparsity-Inducing Penalties (2011, background): “Applying the previous proposition and noting that the subdifferential ∂| · | is {+1} for w > 0, {−1} for w < 0 and [−1,1] for w = 0, it is easy to show that the unique solution admits a closed form called the softthresholding operator, following a terminology introduced in [42]; it can be written”
Learning with Submodular Functions: A Convex Optimization Perspective (2011, methodology): “If h is chosen to be the l1-norm, the proximal operator is simply the soft-thresholding operator applied elementwise [59].”
On Spatial Adaptive Estimation of Nonparametric Regression (2004, methodology): “2 Numerical results As the test signals, we used the functions Blocks, Bumps, HeaviSine and Doppler given in [1, 2] (see formulas therein1).”
Nonlinear estimation for linear inverse problems with error in the operator (2008, background): “, Donoho and Johnstone [10]) or the classical inverse problem case (Abramovich and Silverman [1]).”
INFERENCE FOR SEMIPARAMETRIC MODELS: SOME QUESTIONS AND AN ANSWER (2001, background): “This is, of course, widely discussed in the work of Donoho and Johnstone (1995), Birgé and Massart (1999), and others.”
Incorporating Information on Neighboring Coefficients Into Wavelet Estimation (2001, unknown): “Then the following inequalities hold: kxkp2 kxkp1 m 1 p1 1 p2 kxkp2 (14) Lemma 3 Let 0 < a < 1 andS = fx 2 IR : Pki=1 xi B; xi 0; i = 1; ; kg.”
Iterative Weighted Maximum Likelihood Denoising With Probabilistic Patch-Based Weights (2009, background): “Such approaches can be applied to additive Gaussian noise [6], [7] and have been extended to multiplicative speckle noise [8]–[13].”
Spatially Adaptive Regression Splines and Accurate Knot Selection Schemes (2001, methodology): “The work includes an adaptive regression spline method (e.g., Friedman 1991), an adaptive smoothing spline method by Luo and Wahba (1997), an adaptive kernel method by Fan and Gijbels (1995), and wavelet shrinkage methods by Donoho and Johnstone (1994, 1995).”
The optimal discovery procedure: a new approach to simultaneous significance testing (2007, unknown): “This result has been a motivation for work done in empirical Bayes methodology (Efron and Morris, 1972, 1973) and wavelet estimation ( Donoho and Johnstone, 1995 ).”
Correlation-Based Adaptive Localization With Applications to Ensemble-Based 4D-Seismic History Matching (2018, background): “ne is to reduce the size of seismic data by exploiting the sparse representation nature of wavelet basis functions, and the other is to exploit its capacity of noise estimation in the wavelet domain (Donoho and Johnstone, 1995). Based on the estimated standard deviation (STD) of the noise, one can c”