Algorithms And Applications On Structural Sparsity High-Dimensional Data Reconstruction

With the rapid development of information technology,we can encounter all kinds of high-dimensional data which is large scale and structure-complex.The problem that how to effectively mine and process these high-dimensional data has been widely concerned by researchers.Compressed sensing is a novel and effective high-dimensional data processing theory,which can exactly reconstruct a signal with high probability by utilizing the sparsity of signal data.Based on the theory of compressed sensing,utilizing the sparsity and low-rank on high-dimensional data,this thesis makes a study on the different types of high-dimensional data processing.The main works of this thesis are as follows:Chapter one briefly introduces the research background,significance and latest research progress of compressed sensing,and summarizes the main work and the organizational structure of this thesis.Chapter two mainly elaborates the basic theory of two kinds of data reconstruction,including the research work of the current vector data reconstruction and low-rank matrix data reconstruction from the perspective of reconstruction model and algorithm.Chapter three proposes the two-dimensional generalized orthogonal matching pursuit algorithm(2D-gOMP)utilizing 2D separable sampling technique.The proposed 2D-gOMP algorithm is is superior to classical OMP algorithm on high-dimensional data,reducing the computation complexity significantly with guaranteed accuracy.Experimental results indicate that 2D-gOMP algorithm is superior to the existing 2D-gOMP algorithm in terms of reconstruction precision and computation time on synthetic data.The 2D-gOMP algorithm based on overlapping block processing is applied to real image data,which shows that it can achieve high PSNR and good visual effect.Chapter four investigates the low-rank tensor completion problem.The existing works are generally under the nuclear norm penalty framework to deal with the problem.However,the nuclear norm often over-penalizes large singular values of matrixes,and thus cannot avoid model bias.To overcome the drawback of the nuclear norm,we propose a non-convex minimization method based on a fraction penalty function and develop a non-convex tensor completion algorithm.We implement our algorithm on real image data,which exhibits that our proposed method is superior to the nuclear norm penalization method in terms of the visual effects,accuracy and robustness.Chapter five summaries the works of this thesis,and makes an analysis and prospect for High-dimensional data reconstruct.