Tensor Matched Subspace Detection And Applications

Testing whether a signal lies within a given subspace,also named matched subspace detection,is an important problem in signal processing.Conventional methods is based on vectors,which represents a signal as an vector,and detects whether this signal belong to the given subspace or not according to the energy of this signal in the given subspace.With the development of Internet of Things(Io T)and big data,as well as the application of multisensor networks,the amount of data or multi-dimensional data increase,and the limits of conventional method based on vectors become more and more significant.Tensors,known as multi-dimensional arrays,have wide application in big data analysing and processing.Comparing with vectors,tensors have more dimensions to characterize signals,which can reserve more information of the signal.The data that have multi-attributes can be preserved better by tensors.Moreover,the data we obtained may be incomplete for the existence of noise and other uncontrollable factors.The study of matched subspace detection in this thesis also aims to incomplete signal,that is,the matched subspace detection with sampling data.In this thesis,based on the transform-based tensor model,we study the method for matched subspace detection to test whether an signal with missing data lies within a given tensor subspace,which contains the following three main aspects.First,the transform-based tensor model is studied.From the basic concepts and definitions,we study the fundamental theory of the transform-based tensor models and the definition of the tensor column subspace under the transform-based tensor model.In cases of discrete Fourier transform(DFT)and discrete cosine transform(DCT),we give the concrete definition of tensor product.We also study the tensor singular value decomposition and the relationship between tensor singular value decomposition and tensor column subspace.Then,we study the problem of tensor matched subspace detection.The problem of tensor matched subspace detection is formulated as a binary hypotheses test,and we construct the test statistics under two sampling model: tubal-sampling and elementwise-sampling.Moreover,two theorems are given,which prove that the test statistics we constructed are effective in theory.Finally,we study the detection problem under tubal-sampling and elementwise-sampling both for noiseless and noisy data,and give the decision expressions.We provide the computation of the thresholds under the constant false alarm rate(CFAR),and the performance of our detectors are analysed.In cases of DFT and DCT,some simulations of our detectors are given on the synthetic data.Furthermore,we apply tensor matched subspace to indoor localization and video target detection.Based on radio frequency data and KTH dataset,the experiments of indoor localization and video target detection are given with sampling data,and the simulations of the probability of correct localization and target detection probability are given.