Robust Signal Analysis Based On Tensor Completion

With the rapid development and widespread application of modern sensors,multimedia,computer communication and network technologies in fields of society,people often need to store,transmit,analyze and process various complicated large-scale data such as face image data,video surveillance data and biological information data.Large amounts of data can not only provide us with sufficient information but also pose challenges to the computer's data storage,transmission,computing,and processing capabilities.Tensor completion aims at recovering the original information from the observation matrix or tensor data that is contaminated by strong noises,singular points and/or even partially disappears.It has become a core issue in computer vision,image processing,video surveillance,robust subspace recovery,data mining,machine learning and many other research fields in recent years.The thesis analyses advantages and disadvantages of state-of-the-art tensor completion algorithms form domestic and overseas.Combined with non-convex optimization theory,two tensor completion algorithms based on lp-PARAFAC are proposed as follows:Firstly,the thesis proposes a tensor completion method based on the smooth block iteratively reweighted(SBIR)algorithm.This method devises an enhanced lp-metric by constructing a local quadratic approximation around the non-smooth region of the original lp function,outside which the cost function retains its original form to restrain outliers.The optimal solution is obtained by minimizing a simple quadratic reweighted surrogate function in a block update fashion.The convergence of the proposed methods to a stationary point is also proved and has the remarkable advantage in complexity and robustness.Secondly,the thesis proposes a new tensor completion algorithm based on the augmented Lagrangian multiplier(ALM).By employing the theory of ALM,we can rewrite the lost function and divide it into three subproblems which can be solved by alternating direction method(ADM).The superiority of the proposed algorithm over several state-of-the-art schemes in terms of convergence speed and outlier robustness is demonstrated by extensive numerical examples.This thesis compares the above two algorithms using common evaluation criteria on the two datasets.Compared with the existing methods,the low-rank tensor completion optimization algorithm based on SBIR can achieve better performance when recovering data,especially synthetic data.At the same time,the proposed low-rank tensor completion optimization algorithm based on ALM can achieve faster convergence speed and more robust data recovery.