# PCA Reduced Gaussian Mixture Models with Applications in Superresolution

arXiv: https://arxiv.org/abs/2009.07520 · HTML: https://mlsanity.com/paper/2009.07520/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Sep 2020.

## Built on by (most cited first, 12 of 12)

- [PatchNR: Learning from Very Few Images by Patch Normalizing Flow Regularization](https://mlsanity.com/paper/2205.12021/) (2022)
- [Wasserstein Patch Prior for Image Superresolution](https://mlsanity.com/paper/2109.12880/) (2021)
- [WPPNets and WPPFlows: The Power of Wasserstein Patch Priors for Superresolution](https://mlsanity.com/paper/2201.08157/) (2022)
- [Learning from small data sets: Patch-based regularizers in inverse problems for image reconstruction](https://mlsanity.com/paper/2312.16611/) (2023)
- [On unsupervised projections and second order signals](https://mlsanity.com/paper/2204.05139/) (2022)
- [Patch-based image Super Resolution using generalized Gaussian mixture model](https://mlsanity.com/paper/2206.03069/) (2022)
- [Hierarchical mixtures of Gaussians for combined dimensionality reduction and clustering](https://mlsanity.com/paper/2206.04841/) (2022)
- [Pluto's Surface Mapping using Unsupervised Learning from Near-Infrared Observations of LEISA/Ralph](https://mlsanity.com/paper/2301.06027/) (2023)
- [A Unified Theory of Exact Inference and Learning in Exponential Family Latent Variable Models](https://mlsanity.com/paper/2404.19501/) (2024)
- [Sublinear Variational Optimization of Gaussian Mixture Models with Millions to Billions of Parameters](https://mlsanity.com/paper/2501.12299/) (2025)
- [GRIT: Graph-Regularized Logit Refinement for Zero-shot Cell Type Annotation](https://mlsanity.com/paper/2508.04747/) (2025)
- [Classification EM-PCA for clustering and embedding](https://mlsanity.com/paper/2511.18992/) (2025)

## Abstract (arXiv)

Despite the rapid development of computational hardware, the treatment of large and high dimensional data sets is still a challenging problem. This paper provides a twofold contribution to the topic. First, we propose a Gaussian Mixture Model in conjunction with a reduction of the dimensionality of the data in each component of the model by principal component analysis, called PCA-GMM. To learn the (low dimensional) parameters of the mixture model we propose an EM algorithm whose M-step requires the solution of constrained optimization problems. Fortunately, these constrained problems do not depend on the usually large number of samples and can be solved efficiently by an (inertial) proximal alternating linearized minimization algorithm. Second, we apply our PCA-GMM for the superresolution of 2D and 3D material images based on the approach of Sandeep and Jacob. Numerical results confirm the moderate influence of the dimensionality reduction on the overall superresolution result.