Robust Tensor Factorization with Unknown Noise

Abstract

Because of the limitations of matrix factorization, such as losing spatial structure information, the concept of low-rank tensor factorization (LRTF) has been applied for the recovery of a low dimensional subspace from high dimensional visual data. The low-rank tensor recovery is generally achieved by minimizing the loss function between the observed data and the factorization representation. The loss function is designed in various forms under different noise distribution assumptions, like L1 norm for Laplacian distribution and L2 norm for Gaussian distribution. However, they often fail to tackle the real data which are corrupted by the noise with unknown distribution. In this paper, we propose a generalized weighted low-rank tensor factorization method (GWLRTF) integrated with the idea of noise modelling. This procedure treats the target data as high-order tensor directly and models the noise by a Mixture of Gaussians, which is called MoG GWLRTF. The parameters in the model are estimated under the EM framework and through a new developed algorithm of weighted low-rank tensor factorization. We provide two versions of the algorithm with different tensor factorization operations, i.e., CP factorization and Tucker factorization. Extensive experiments indicate the respective advantages of this two versions in different applications and also demonstrate the effectiveness of MoG GWLRTF compared with other competing methods.

Robust Kronecker-Decomposable Component Analysis for Low-Rank Modeling

“…Out of all methods, KDRSDL provided the best reconstruction quality: it is the only algorithm that removed all the noise and for which all the aforementioned details are distinguishable in the reconstruction. At the 60% noise level, our method scored markedly higher than its competitors on image quality metrics, as seen both in Figure 6 and in Color image denoising Our benchmark is the Facade image [10]: the rich details and lighting makes it interesting to assess fine reconstruction. The geometric nature of the building's front wall, and the strong correlation between the RGB bands indicate the data can be modeled by a low-rank 3-way tensor where each frontal slice is a color channel.…”

Hyperspectral Image Restoration Via Total Variation Regularized Low-Rank Tensor Decomposition

“…In the future, we are interested in conducting the following studies. Firstly, incorporate the noise modeling idea of [47] (a) into our SSTV regularized low rank tensor decomposition framework to further enhance its capability for removing more complex noise in some real-word scenarios. Secondly, extend the deep learning ideas of [48], [49] to design a deep tensor architecture to learn the multilinear structure of clean HSI and identify the noise structures of observered HSI.…”

Generalized Convolutional Sparse Coding With Unknown Noise

“…The alpha-stable noise we considered is Cauchy distribution, which is one representative symmetric alpha-stable distribution apart from Gaussian and should be modeled well by αCSC and GCSC. 1) Quantitative Evaluation: Following [39], [40], performance is evaluated by the mean absolute error (MAE) and root mean squared error (RMSE):…”