Research Of Image Denoising And Recognition Based On Tensor Decomposition

High-dimensional image processing is a very important research topic in the field of computer vision.However,compared with classical one-dimensional and two-dimensional data,high-dimensional data processing has many difficulties,such as curse of dimensionality.In the past few decades,researchers have proposed many theories and methods to process high-dimensional data,but these theories and methods are far from adapting to high-dimensional data processing in the era of large data.In this dissertation,according to the characteristics that the math-ematical representation of high-dimensional image data in the digital information age is tensor,high-dimensional image processing method is further studied by us-ing tensor algebra theory and method.Specifically,based on the problems existing in the data acquisition and recognition phase,combined with the characteristics of the data itself,the tensor decomposition theory and methods are used to achieve high-dimensional image denoising and recognition,and enhance image processing capabilities.The main content is as follows.For Gaussian noise and sparse noise in high-dimensional images generated by data acquisition,a high-dimensional image denoising model,Kronecker basis repre-sentation based mixture denoise model(KBRMDM),is proposed.In the model we also consider Gaussian noise and sparse noise,which is more in line with the actual situation.A algorithm termed KBRMDM to solve the KBRMDM model is pro-posed.Under the NSS and GCS priori,by using ?-means++algorithm,KBRMDM converts three-dimensional image into several four-dimensional image blocks,which has better denoising effect.Since the low rank degree of each module of the fourth-order tensor corresponding to four-dimensional image blocks is different,KBRMDM adopts an improved KBR low rank metric to further improve the image denoising performance.Experimental results of multi-spectral image denoising show that the KBRMDM algorithm is effective.For the face recognition problem,a tensor patch alignment framework(TPAF)is established.A new tensor subspace learning based feature extraction model,tensor rank preserving discriminant.analysis(TRPDA),is proposed.TRPDA can be transformed into a generalized Rayleigh quotient problem,and solved by TRPDA algorithm.Furthermore,TRPDA preserves the spatial structure of input tensor data in the modeling process,and at the same time,under the TPAF,a distance penalty function is introduced to preserve the ranking information of the within class samples on local patch.Experiments on several datasets show the effectiveness of the algorithm.Compared with other existing tensor subspace learning based algorithms,TRPDA can shorten the computing time in the training stage.For the human action recognition problem,by introducing a new within-class distance metric,a new tensor subspace learning based model,tensor manifold dis-criminant projection(TMDP),is established.TMDP can also be transformed to a generalized Rayleigh quotient problem,the TMDP model extract discriminant in-formation through maximizing each sample and mean value of its interclass sample,and the TMDP algorithm is used to solve the TMDP problem.Experiments on NMHA 2.0 dataset show the effectiveness of the algorithm.