Scale Mixtures of Gaussians and the Statistics of Natural Images

By Martin J. Wainwright, Eero P. Simoncelli. 1999

Subfields: Computer Vision and Pattern Recognition

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Citations in the corpus

On the Quantitative Analysis of Decoder-Based Generative Models (2016, background): “3In particular, heavy-tailed radially symmetric distributions can be viewed as Gaussian scale mixtures (Wainwright & Simoncelli, 1999).”
Density Modeling of Images using a Generalized Normalization Transformation (2015, methodology): “Normalization has also been derived as an inference method for a Gaussian scale mixture (GSM) model for wavelet coefﬁcients of natural images (Wainwright & Simoncelli, 2000).”
Mixtures of Conditional Gaussian Scale Mixtures Applied to Multiscale Image Representations (2011, positive): “A family of distributions which has repeatedly been shown to contain suitable building blocks for modeling the statistics of natural images is given by Gaussian scale mixtures (GSMs) [8,9],”
Learning to Relate Images (2011, methodology): “Like an auto-encoder, this model can be trained with gradient based optimization.”
Pros and Cons of GAN Evaluation Measures (2018, background): “Another important property of natural image statistics is the non-Gaussianity [76, 106, 85].”
Learning a No-Reference Quality Metric for Single-Image Super-Resolution (2016, methodology): “We sort to the Gaussian scale mixture (GSM) model, which shows effective in describing the marginal and joint statistics of natural images [36, 21] using a set of neighboring wavelet bands.”
Learning Energy-Based Models in High-Dimensional Spaces with Multiscale Denoising-Score Matching (2019, methodology): “While also providing density information, our model learns an order of magnitude faster than the models based on maximum likelihood and sampling.”
Generating more realistic images using gated MRF's (2010, background): “These models are useful for extracting representations [2, 3, 4] that can be used for discriminative tasks and they can also provide adaptive priors [5, 6, 7] that can be used in applications like denoising and inpainting.”
Blind Image Quality Assessment: From Natural Scene Statistics to Perceptual Quality (2011, methodology): “We anticipate that the approach taken here could be eventually extended to video to achieve good results.”
Fast Image Deconvolution using Hyper-Laplacian Priors (2009, background): “Other types of sparse image prior include: Gaussian Scale Mixtures (GSM) [ 21 ], which have been used for image deblurring [3] and denoising [14] and student-T distributions for denoising [25, 16].”
Machine learning for detection and diagnosis of disease. (2006, background): “For example, the marginal statistics of many natural signals (or filtered versions of the signals) are highly non-Gaussian (27, 28).”
Modeling pixel means and covariances using factorized third-order boltzmann machines (2010, background): “This is the simplest example of a Gaussian Scale Mixture [33] that more generally combines an infinite number of zero mean Gaussian distributions with different variances.”
Image denoising using scale mixtures of Gaussians in the wavelet domain (2003, background): “In the context of denoising, if one assumes the noise is additive and independent of the signal, and is also a Gaussian sample, then the optimal estimator is linear.”
Fine-Grained Similarity Measurement between Educational Videos and Exercises (2020, background): “Theis et al. [31] used the conditional distribution of a mixture of GSMs (gaussian scale mixtures) [34, 37] to model the distribution of a pixel given its causal neighborhood.”
Video Quality Assessment by Reduced Reference Spatio-Temporal Entropic Differencing (2013, unknown): “We conclude this paper in Section VII.”
The Hamiltonian Brain: Efficient Probabilistic Inference with Excitatory-Inhibitory Neural Circuit Dynamics (2014, background): “The Gaussian scale mixture (GSM) model is relatively simple, yet captures some fundamental higher-order statistical properties of natural image patches by introducing latent variables, u, coordinating the linear superposition of simple edge features and an additional latent variable, z, determining ”