Low Rank Matrix Factorization Denoising Model Based On Mixture Distribution

The development of technology has brought about a diversity of data types,among which image data is widely used in modern life.However,in the process of image formation,the image is influenced by various factors,resulting in different types of complex noise,which can lead to challenges in subsequent research.Therefore,it is necessary to establish a model to remove complex noise.Most of the traditional denoising models assume noise to be Gaussian distribution,Poisson distribution and Gaussian mixture distribution,and these distributions deteriorates when dealing with heavy-tailed noise.In this paper,we combine low-rank matrix factorization theory with the heavy-tailed nature of t-distribution to assume the noise to be a mixture of t distribution,and propose a low-rank matrix factorization model based on penalized mixture t distribution to solve the complexity and heavy-tailed noise.The main research contents include:(1)Based on the low-rank matrix factorization theory,we derive the likelihood function assuming noise to be a Gaussian mixture distribution or a mixture of t-distribution,propose two models of penalized mixture distribution,and give the update formulas of the model parameters.By comparing six indicators on simulated datasets with different noises,we verify the effectiveness and robustness of the proposed model when assuming noise to be a mixture of t-distribution.(2)For real image data contaminated by lighting and shading,we use the proposed models to denoise and compare them with traditional models.Experimental results show that the model based on penalized mixture distribution is more stable in dealing with lighting pollution in different directions,and the mixture of t-distribution model is more robust among the two penalized mixture distribution models.(3)For the restoration of missing real image data,we use the proposed models to restore the missing images and compare them with traditional models using structural similarity and peak signal-to-noise ratio.Experimental results show that as the missing ratio increases,the traditional noise model performs poorly,while the proposed mixture of tdistribution model is more robust and stable in restoration,outperforming the model based on Gaussian mixture distribution.This paper conducts research on image denoising and restoration from the perspective of noise modeling,combining the mixture of t-distribution with the low-rank matrix decomposition model,providing new ideas and methods for handling heavy-tailed noise in images.