Do Generalized=Gamma Scale Mixtures of Normals Fit Large Image Data-Sets?

2025-12-18

AI Summary

This work investigates the universality and practical efficacy of the Generalized Gamma Scale Mixture of Normals (GGSN) as a sparse prior for image transform-domain coefficients. We systematically evaluate its modeling capability on Fourier coefficients, Haar/Gabor wavelet coefficients, and first-layer AlexNet convolutional features across remote sensing, medical, and natural image datasets. For the first time, large-scale empirical validation confirms GGSN’s broad applicability across diverse real-world image transforms, revealing an effective parameter space substantially larger than previously reported. To enhance fitting robustness, we introduce exchangeable coefficient identification and data augmentation strategies. Across all test scenarios, GGSN consistently outperforms conventional priors—including Gaussian, Laplacian, ℓₚ-norm, and Student’s t-distributions—in terms of goodness-of-fit. Furthermore, we characterize the specific structural image patterns under which GGSN modeling degrades, thereby delineating its practical limits.

Technology Category

• Computer Vision: Generative Adversarial Networks (GANs) for Vision
• Machine Learning: Probabilistic Circuits and Graphical Models
• Reasoning under Uncertainty: Graphical Models

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

Abstract

A scale mixture of normals is a distribution formed by mixing a collection of normal distributions with fixed mean but different variances. A generalized gamma scale mixture draws the variances from a generalized gamma distribution. Generalized gamma scale mixtures of normals have been proposed as an attractive class of parametric priors for Bayesian inference in inverse imaging problems. Generalized gamma scale mixtures have two shape parameters, one that controls the behavior of the distribution about its mode, and the other that controls its tail decay. In this paper, we provide the first demonstration that the prior model is realistic for multiple large imaging data sets. We draw data from remote sensing, medical imaging, and image classification applications. We study the realism of the prior when applied to Fourier and wavelet (Haar and Gabor) transformations of the images, as well as to the coefficients produced by convolving the images against the filters used in the first layer of AlexNet, a popular convolutional neural network trained for image classification. We discuss data augmentation procedures that improve the fit of the model, procedures for identifying approximately exchangeable coefficients, and characterize the parameter regions that best describe the observed data sets. These regions are significantly broader than the region of primary focus in computational work. We show that this prior family provides a substantially better fit to each data set than any of the standard priors it contains. These include Gaussian, Laplace, $ell_p$, and Student's $t$ priors. Finally, we identify cases where the prior is unrealistic and highlight characteristic features of images that suggest the model will fit poorly.

Problem

• Evaluates generalized gamma scale mixtures for large image datasets
• Assesses model realism across diverse imaging applications and transformations
• Compares performance against standard priors and identifies limitations

Innovation

• Generalized gamma scale mixtures model image data priors
• Fits multiple large imaging datasets across transformations
• Outperforms standard priors like Gaussian and Laplace