Research On Tensor Decomposition Algorithm For Images

Tensor is a form of data organization,its essence is high-dimensional array.A lot of data can be organized into the form of tensor.There are many kinds of calculations for tensor,in which tensor decomposition has been widely used in many fields.Human face images can be organized to the form of tensor,and the video itself is composed of a series of frame images,and therefore it can also be regarded as a form of tensor.After modeling these data objects,they can be used in face recognition and video processing,respectively.For face recognition,the most important part is feature extraction.The study of tensor decomposition algorithm is very extensive,we can consider the use of tensor decomposition for the face image processing,without affecting the recognition accuracy,and speed up the process of feature extraction.For video processing,consider the decomposition of the tensor before the partial reduction of parts,and then get different compression ratio under the reduction of video.The main work of this thesis includes:(1)Through the theoretical analysis and research on the characteristics of tensor and tensor decomposition algorithms,the purpose and significance of the image-oriented tensor decomposition algorithm research are clarified.At the same time,tensor singular value decomposition is a kind of tensor decomposition algorithm,from the principle it is the expansion of matrix singular value decomposition in the tensor field.(2)Through the constructed face database of the test case,the face tensor modeling is conducted,and by the organization of the facial images in the database of in a certain can be organized into different tensor forms.The processing of the tensor decomposition algorithm can realize the extraction and recognition of face features.This thesis shows that the HOSVD(high order singular value decomposition)algorithm based on TTr1 SVD can achieve more efficient face feature extraction method than the Tensor Toolbox based implementation under certain conditions and data sets.It is verified that the decomposition algorithm of this paper is effective in extracting facial features.The experiment results show that the algorithm achieves a certain degree of acceleration ratio under the premise of ensuring the accuracy of the recognition result.Moreover,based on the flexible nature of the tensor itself,it is possible to make the processing of the face tensor data more efficient by changing the organization form of the face tensor.(3)For the video data,with its own natural high-dimensional features,tensor can be very good on the video data modeling.Through the tensor modeling for the tested video sample,a numerical simulation experiment was carried out.Based on the tensor decomposition algorithm,the video tensor can be processed to obtain reduction video with different resolution.And,the accuracy of the reduction video tensor can be flexibly controlled to achieve a certain degree of video compression effect.And the accuracy and efficiency of the tensor decomposition algorithm are verified when characterizing the video data.The video compression is explored and studied from the perspective of tensor decomposition.