Research On Image Processing Algorithm Based On Tensor Decomposition

With the rapid development of computer science, large amounts of high-dimensional massive data, such as video data and remote sensing imagery, have been produced in our daily life. Traditional matrix-based data analysis technologies have been relatively backward due to the requirement of huge storage as well as high computational cost. Multidimensional signal processing based on tensor decomposition has received much attention due to its significant advantages over traditional matrix-based signal processing methods.The main contributions of this thesis can be summarized as follows:1. A hierarchical splitting binary decision tree is established by using the nonnegative second order tensor decomposition of rank-two for the spectral unmixing of hyperspectral image. Under the abundance nonnegative constraint and abundance sum one constraint, hyperspectral image can be regarded as a linearly mixed model. Under this linear hypothesis, this thesis analyzes the spectral unmixing principle based on the convex geometry theory, namely, the pixel spectral vectors constitute a simplex in multidimensional linear space and the vertexes of the simplex correspond to spectral vector of endmembers, whereas the spectral vectors of mixed pixel are located in the interior of the simplex. Here, the outstanding endmember extraction algorithm, namely, successive projections algorithm, is adopted to determine what type of spectral vectors are located at the vertex position. In doing so, the endmembers are just the vertexes of the simplex. Then, a nonnegative second order tensor decomposition of rank-two is adopted to solve the abundance matrix. Note that, splitting the cluster hierarchically is a basis framework of the work, which is eventually used to perform the spectral unmixing.2. This thesis proposes a denoised algorithm based on the normalized noise energy ratio and Tucker decomposition Firstly, the correlation among different pixels in spatial dimension and correlation between different bands in spectral dimension are analyzed. Then, we use the multiple regression theory to estimate the normalized noise power in different modes of the hyperspectral dataset to estimate the Tucker rank. Based on the experiments under different signal to noise ratio(SNR) of the input dataset, conclusion is made that the proposed method presents an obvious peak signal to noise ratio(PSNR) improvement, especially under low signal–to-noise ratio environment. Motivated also by the advantages of principal component analysis(PCA) in signal separation, the proposed method is combined with the PCA to denoise the hyperspectral images, which yields better denoising performance than the existing methods.3. An improved algorithm for edge extraction of multidimensional remote sensing images based on weighted structure tensor is proposed in this thesis. Standard initial matrix field is just the average of all the initial matrix fields corresponding to different two-dimensional images at the same pixel respectively which means that all images contribute the same amount of local structure information. However, this is impossible in actual remote sensing images. The differenc between the two eigen values of a structure tensor provides the local structure information. Inspired by this fact, a texture coherence equation to measure the spatial continuity is defined. And then the initial matrx field is amended by multiplying this coherence as a weighter. In doing so, the smoothed structure tensor is used to extract the edge of multiway images.