# Low-rank Matrix Factorization under General Mixture Noise Distributions

arXiv: https://arxiv.org/abs/1601.01060 · HTML: https://mlsanity.com/paper/1601.01060/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Jan 2016.

## Built on by (most cited first, 11 of 11)

- [Efficient Diffusion Model for Image Restoration by Residual Shifting](https://mlsanity.com/paper/2403.07319/) (2024)
- [HIR-Diff: Unsupervised Hyperspectral Image Restoration Via Improved Diffusion Models](https://mlsanity.com/paper/2402.15865/) (2024)
- [Unsupervised Hyperspectral Pansharpening via Low-rank Diffusion Model](https://mlsanity.com/paper/2305.10925/) (2023)
- [Fast Noise Removal in Hyperspectral Images via Representative Coefficient Total Variation](https://mlsanity.com/paper/2211.01825/) (2022)
- [Pan-denoising: Guided Hyperspectral Image Denoising via Weighted Represent Coefficient Total Variation](https://mlsanity.com/paper/2407.06064/) (2024)
- [No-Clean-Reference Image Super-Resolution: Application to Electron Microscopy](https://mlsanity.com/paper/2401.08115/) (2024)
- [Diffusion-Denoised Hyperspectral Gaussian Splatting](https://mlsanity.com/paper/2505.21890/) (2025)
- [Beyond Motion Cues and Structural Sparsity: Revisiting Small Moving Target Detection](https://mlsanity.com/paper/2509.07654/) (2025)
- [Auto robust relative radiometric normalization via latent change noise modelling](https://mlsanity.com/paper/2111.12406/) (2021)
- [Rank-Enhanced Low-Dimensional Convolution Set for Hyperspectral Image Denoising](https://mlsanity.com/paper/2207.04266/) (2022)
- [HIDFlowNet: A Flow-Based Deep Network for Hyperspectral Image Denoising](https://mlsanity.com/paper/2306.17797/) (2023)

## Abstract (arXiv)

Many computer vision problems can be posed as learning a low-dimensional subspace from high dimensional data. The low rank matrix factorization (LRMF) represents a commonly utilized subspace learning strategy. Most of the current LRMF techniques are constructed on the optimization problems using L1-norm and L2-norm losses, which mainly deal with Laplacian and Gaussian noises, respectively. To make LRMF capable of adapting more complex noise, this paper proposes a new LRMF model by assuming noise as Mixture of Exponential Power (MoEP) distributions and proposes a penalized MoEP (PMoEP) model by combining the penalized likelihood method with MoEP distributions. Such setting facilitates the learned LRMF model capable of automatically fitting the real noise through MoEP distributions. Each component in this mixture is adapted from a series of preliminary super- or sub-Gaussian candidates. Moreover, by facilitating the local continuity of noise components, we embed Markov random field into the PMoEP model and further propose the advanced PMoEP-MRF model. An Expectation Maximization (EM) algorithm and a variational EM (VEM) algorithm are also designed to infer the parameters involved in the proposed PMoEP and the PMoEP-MRF model, respectively. The superseniority of our methods is demonstrated by extensive experiments on synthetic data, face modeling, hyperspectral image restoration and background subtraction.