Image denoising with heterogeneous low rank matrix factorization

Abstract

Low rank matrix factorization (LRMF) is an important research direction in computer vision. It can learn low dimensional subspace from high dimensional data. LRMF is mostly constructed by L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> loss function and L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> loss function in optimization problems. And whether LRMF is constructed by L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf> loss function or L <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</inf> loss function, it is important to describe the noise in the dataset. In order to describe the noise in the dataset well, this paper describes the noise from a pixel-level perspective to construct LRMF. Considering that there maybe uneven light intensity and differences in light reflection intensity between different parts of each picture in the dataset, this paper assumes that all noise in the image dataset is heterogeneous. Based on this assumption, this paper describes the noise in the dataset by the Student-t distributions with different parameters, and constructs two hierarchical Bayesian models, and deduces all the parameters of the models design through variational Bayesian inference. It not only improves the calculation accuracy of the LRMF, but also improves the calculation speed of the model to a certain extent. A large number of experiments on face reconstruction and medical image denoising prove the superiority of the methods.