Theories And Applications On Sparse Signal Reconstruction Via L₁-l₂ Minimization

As big data becomes more and more important in modern society,scholars and industrial researchers gradually focus on data processing in various fields.Because of the sparsity and compressibility of signals,compressed sensing theory stands out in signal data processing.It is widely studied and applied in the domains of image processing,wireless communication,bio-sensing,information theory and so on.In this paper,basing on a varietal elastic net model,we further study signal reconstruction via partial regularization method.The main content of this thesis is as follows:In chapter one,we briefly introduce the research background,research significance,study history and present situation of compressed sensing and l₁-l₂minimization in the first section.In the second section,we state the research status of l₁-l₂minimization model in the field of compressed sensing.In the last section,we give the full text structure of this thesis.In chapter two,we mainly present basic theoretical framework of compressed sensing which includes the sparse representation of signals,the design of measurement matrix and reconstruction algorithms in the first section.In the second section,we introduce certain basic properties of Lasso model and the elastic net.At last,we present the application of l₁-l₂minimization in compressed sensing field.In chapter three,we put forward the partial regularization form of minimization l₁-l₂.We derive the sufficient conditions which are the local null space property and restricted isometry property to make sure to obtain the solution of the partial regularization form of minimization l₁-l₂model.We find that a feasible solution which satisfies the sufficient condition is a strictly local minimizer of the model.We present the upper bound of error between a feasible solution and a strictly local minimizer.If a feasible solution is a k-sparse vector,the upper bound is only related to the noise energy and RIC.On the basis of iterative weight and approximative approaching,we give the corresponding algorithm?PREN1 and PREN2?.At last,the robustness of the new model and algorithm stability are indicated by simulation experiment.In chapter four,we provide some tentative suggestions for further study.