Research On The Reconstruction Algorithms Of Bayesian Compressive Sensing

Compressive sensing (CS) theory overcomes the disadvantage of Nyquist sampling theorem so that the sampling frequency will never be subject to the signal bandwidth but the intrinsic of that signal. CS theory has not only a much lower sampling frequency than the Nyquist sampling theorem, but also much higher recovery accuracy. The core theory of CS can be divided into three parts:signal sparse representation, selection of the measurement matrix and reconstruction algorithm. This study is about Bayesian compressive sensing (BCS), which using Bayesian inference to solve CS problem, focusing on the reconstruction algorithm and the selection of measurement matrix.To handle noisy compressive sensing (NCS) problem, BCS is proved successful, which can be classified into two types:one is the sparse reconstruction algorithm using sparse matrix, and its popularization and spread application mainly profits from LDPC (Low-density parity-check) code; another is the sparse Bayesian learning algorithm, which combines SVM (Support Vector Machine) mechanism with the sparse linear regression to revert the original signal.The study of BCS in this thesis can be summarized as follows:Firstly, greedy matching pursuit algorithm is introduced as an example to understand the process of traditional CS reconstruction as well as its insufficiency; via combining the Bias probability theory, the basic model and theory of BCS is introduced then.What comes second, a novel method to work out NCS problem based on Bayesian inference and iterative support detection is introduced, which is named BCS_ISD (Bayesian Compressive Sensing via Iterative Support Detection). BCS_ISD uses LDPC to optimize the measurement matrix in CS, according to the spread application of LDPC in CS successfully. In terms of Bayesian inference, a reverted support detection of the original signal can be used to reconstruct the original signal through MMSE, finally the results of related simulations are listed as well as some analysis.At last, FBMP is the classic method in sparse Bayesian learning area, which can quickly estimate the average and minimum mean square error of the Bayesian model and obtain a set of high posterior probability. Assuming the sparse coefficients obey the mixed Gaussian distribution, a list of experiments is carried to analyze the differences between this algorithm and the traditional greedy algorithm. During this study, sparse measurement matrix is introduced into the original FBMP, and also there are series of simulations to analyze the performance.