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.

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This paper proposes a general method for dealing with the problem of recovering the low-rank structure, in which the data can be deformed by some unknown transformations and corrupted by sparse or nonsparse noises. Nonconvex penalization method is used to remedy the drawbacks of existing convex penalization method and a quadratic penalty is further used to better tackle the nonsparse noises in the data. We exploits the local linear approximation (LLA) method for turning the resulting nonconvex penalization problem into a series of weighted convex penalization problems and these subproblems are efficiently solved via the augmented Lagrange multiplier (ALM). Besides comparing with the method of robust alignment by sparse and low-rank decomposition for linearly correlated images (RASL), we also propose a nonconvex penalized lowrank and sparse decomposition (NLSD) model as comparison. Numerical experiments are conducted on both controlled and uncontrolled data to demonstrate the outperformance of the proposed method over RASL and NLSD.Keywords low-rank decomposition, nonconvex relaxation, quadratic penalized, batch image alignment, sparse or nonsparse noise CitationChen X A, Han Z, Wang Y, et al. Nonconvex plus quadratic penalized low-rank and sparse decomposition for noisy image alignment.

Falling snow not only blocks human vision, but also significantly degrades the effectiveness of computer vision systems in outdoor environment. In this paper, we aim to remove snowflakes in videos by using the global and local low-rank property of snowflake-removed scenes. The stationary background and the mixture of moving foreground as well as falling snowflake are extracted via the global low-rank matrix decomposition. Some snowflake features, such as its color and size, are used to separate out the snowflakes from other moving objects. Then, the mean absolute difference based patch matching is applied to align every same moving object over frames to grab its low-rank structure. As such, the falling snowflake in front of moving objects can be removed via the local low-rank decomposition. Finally, the snowflake removed videos are generated by pasting moving foreground to stationary backgrounds. Experiments show that our method can remove snowflakes effectively and outperforms the comparison methods. Index Terms-Snowflake removal, desnowing, low-rank decomposition. I. INTRODUCTION S NOWFLAKES cause complex visual effects of spatial or temporal domains in images and videos. Such effects may cause serious degradation of outdoor vision and monitoring tasks such as tracking, detecting critical events, and manual video analysis. Therefore, the removal of rain or snowflakes in a video will promote the performance of vision and monitoring systems in bad weather. So far, the research works on eliminating dynamic weather conditions in the literature have been mainly focused on rain removal and few papers discuss the snowflake removal. A method for rain removal usually is not directly suitable for snow re-Manuscript

The low-rank tensor factorization (LRTF) technique has received increasing attention in many computer vision applications. Compared with the traditional matrix factorization technique, it can better preserve the intrinsic structure information and thus has a better low-dimensional subspace recovery performance. Basically, the desired low-rank tensor is recovered by minimizing the least square loss between the input data and its factorized representation. Since the least square loss is most optimal when the noise follows a Gaussian distribution, -norm-based methods are designed to deal with outliers. Unfortunately, they may lose their effectiveness when dealing with real data, which are often contaminated by complex noise. In this paper, we consider integrating the noise modeling technique into a generalized weighted LRTF (GWLRTF) procedure. This procedure treats the original issue as an LRTF problem and models the noise using a mixture of Gaussians (MoG), a procedure called MoG GWLRTF. To extend the applicability of the model, two typical tensor factorization operations, i.e., CANDECOMP/PARAFAC factorization and Tucker factorization, are incorporated into the LRTF procedure. Its parameters are updated under the expectation-maximization framework. Extensive experiments indicate the respective advantages of these two versions of MoG GWLRTF in various applications and also demonstrate their effectiveness compared with other competing methods.