Image denoising using scale mixtures of Gaussians in the wavelet domain

By Javier Portilla, Vasily Strela, Martin J. Wainwright, Eero P. Simoncelli. 2003

2,531 citations recorded by the source corpus.

Subfields: Biophysics, Computer Vision and Pattern Recognition, Media Technology

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Citations in the corpus

Density Modeling of Images using a Generalized Normalization Transformation (2015, methodology): “For comparison, we implemented two denoising methods that operate on orthogonal wavelet coef-ﬁcients, one assuming a marginal model (Figueiredo & Nowak, 2001), and the other an elliptically symmetric Gaussian scale mixture (GSM) model (Portilla et al., 2003).”
Lossy Image Compression with Compressive Autoencoders (2017, background): “GSMs are well established as useful building blocks for modelling ﬁlter responses of natural images (e.g., Portilla et al., 2003).”
Wavelets on Graphs via Spectral Graph Theory (2009, neutral): “Expression (9) is the analogue that we will use to later deﬁne the Spectral Graph Wavelet Transform.”
Solving Linear Inverse Problems Using the Prior Implicit in a Denoiser (2020, background): “While these models have led to steady advances in problems such as denoising (e.g., [1–7]), they are too simplistic to generate complex features that occur in our visual world, or to solve more demanding statistical inference problems.”
Exploiting compositionality to explore a large space of model structures (2012, background): “Many researchers have designed models to capture the dependencies between these scale variables, and such “Gaussian scale mixture” models represent the state-of-the art for low-level vision tasks such as denoising (Portilla et al., 2003) and texture synthesis (Portilla and Simoncelli, 2000).”
A Unified Energy-Based Framework for Unsupervised Learning (2007, background): “Energybased approaches produce suitable energy surfaces by minimizing other loss functionals than the negative log likelihood (see [1] for a general introduction to energy-based learning in the supervised case).”
Nonlinear Extraction of Independent Components of Natural Images Using Radial Gaussianization (2009, background): “…1999; Wainwright & Simoncelli, 2000; Huang & Mumford, 1999; Parra, Spence, & Sajda, 2001; Hyv¨arinen, Hoyer, & Inki, 2001; Srivastava, Liu, & Grenander, 2002; Sendur & Selesnick, 2002; Portilla, Strela, Wainwright, & Simoncelli, 2003; Teh, Welling, & Osindero, 2003; Gehler & Welling, 2006).”
FFDNet: Toward a Fast and Flexible Solution for CNN-Based Image Denoising (2017, background): “ing [10]–[13], in this paper we assume that the noise is”
Image Denoising by Sparse 3-D Transform-Domain Collaborative Filtering (2007, methodology): ““ ”: proposed BM3D; “ ”: FSP+TUP BLS-GSM [4]; “+”: BLS-GSM [3]; “ ”: exemplar-based [11]; “ ”: K-SVD [8]; “ ”: pointwise SA-DCT [9].”
A Nonlocal Bayesian Image Denoising Algorithm (2013, neutral): “[37] wavelet neighborhood denoising (BLS-GSM).”
Ieee Transactions on Pattern Analysis and Machine Intelligence Shape, Illumination, and Reflectance from Shading (neutral): “To construct these priors we build upon past work on natural image statistics, which has demonstrated that simple statistics govern local patches of natural images [2], [3], [37], and that these statistics can be used for denoising [38], inpainting [39], deblurring [40], etc.”
Why Simple Shrinkage Is Still Relevant for Redundant Representations? (2006, background): “A new trend of recent years is the use of overcomplete transforms, replacing the traditional unitary ones (see [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25] as representative works).”
Image Denoising and Inpainting with Deep Neural Networks (2012, background): “One approach is to transfer image signals to an alternative domain where they can be more easily separated from the noise [1] [2] [3].”
Medical Image Denoising Using Convolutional Denoising Autoencoders (2016, methodology): “Various methods exist, ranging from models based on partial differential equations (PDEs) [18], [20], [22], domain transformations such as wavelets [6], DCT [29], BLS-GSM [19] etc., non local techniques including NL-means [30], [3], combination of non local means and domain transformations such as…”
Stochastic Solutions for Linear Inverse Problems using the Prior Implicit in a Denoiser (2021, background): “While these models have led to steady advances in problems such as denoising (e.g., [1–7]), they are too simplistic to generate complex features that occur in our visual world, or to solve more demanding statistical inference problems.”
Fields of Experts (2009, methodology): “(2) On one of the noise levels, the FoE performed on par with the method of Portilla et al. (2003) (i. e., there was no significant performance difference).”
One Network to Solve Them All — Solving Linear Inverse Problems Using Deep Projection Models (2017, background): “The first approach regularizes the inverse problem with signal priors that identify the true solution from the infinite set of feasible solutions [9, 18, 19, 31, 39].”
Fast Image Deconvolution using Hyper-Laplacian Priors (2009, methodology): “With the exception of [ 14 ], these methods use CG and thus are slow.”