Research On Signal Reconstruction Algorithm Based On LDPC-like Measurement And Its Application

Compressive Sensing (CS) is the rise of a new type of signal acquisition technology in recent years. The dimensions of the original sparse signal can be reduced by a small number of random linear projections by using the sparse characteristic of signals. The groundbreaking research in CS is for a variety of settings that the signal can be recovered in a computationally feasible manner from these random projections. Two key issues of the successful use of compressive sensing theory and related technologies in the actual application are reducing the complexity of the compressed sensing systems and overcoming the effects of noise signal to obtain an accurate reconstruction. The check matrix of Low-density parity check (LDPC) code is sparse and matrix elements are only two values 0 and 1, when it is used as compressive sensing measurement matrix, the system complexity will be reduced. Due to the breakthrough in Nyquist sampling theorem limit, the CS technology is promising for applications in the medical image imaging, remote sensing, communication channel estimation, spectrum detection, wireless sensor networks and other fields.Improving the practicability of the CS technology is crucial. So based on the LDPC-like matrix, this thesis carries out the researches on the signal reconstruction in noisy environments. Meanwhile as an attempt to the application of CS, this thesis carries out researches on the CS based data gathering schemes in wireless sensor networks (WSNs). For reducing the system complexity and prolonging network life, this thesis designs a data gathering scheme in WSNs based on the low complexity LDPC-like sparse measurement model.First, the Compressive Sensing Belief Propagation (CSBP) algorithm is studied, in the light of the precision problem existing in signal reconstruction, the improvements are made to increasing the reconstruction precision. Compression measurement process is modeled as a class of LDPC encoding process, based on bipartite graph belief propagation(BP) computes conditional marginal probability and the signal value of the MMSE (minimum mean square error) approximation. In the study, we find that the LDPC-like code is not strictly satisfied with the condition of the LDPC check matrix, the algorithm has certain divergence probability in the BP decoding, and the edge probability of the solution does not converge to the optimal value; In addition, the CSBP algorithm uses the results of BP decoding to directly estimate the approximate MMSE estimation of the signal, and the above two factors lead to the limitation of the reconstruction precision of the CSBP algorithm. In order to solve this problem, the following improvements are made to the CSBP algorithm:we add support set detection steps, the XMMSE(t) is only an initial value to obtain the signal support, establish a dynamic threshold selection mechanism, through the signal element value and threshold compares a detected signal of support set I(t); According to the obtained support set, the appropriate signal value estimation method is selected to estimate the nonzero value of the signal. Experimental results show that the improved method has higher reconstruction accuracy and faster convergence than the CSBP algorithm for two-dimensional image signals.Secondly, in order to improve the adaptability of the reconstruction algorithm, this thesis studies and improves the Bayesian Support Detection (BSD) algorithm in a noisy environment. BSD algorithm based on that the sparsity of the original signals subject to the assumption of one dimensional Gaussian distribution, using binary hypothesis test probability model determine the support set signal, so its performance advantages mainly reflected in the one-dimensional Gaussian distribution signal reconstruction accuracy.In order to reconstruct the sparse signal which can be adapted to both Gauss and non Gauss distribution, this paper improves the BSD algorithm, and proposes an algorithm based on backtracking and belief propagation:in the support set detection step, on the one hand, the initial value of the signal is obtained by the BP iteration, and the initial signal support is calculated by the nonlinear operator; The backtracking idea of similar subspace search is introduced, because a step backtracking is used, the detection of the support set is more optimized; And the estimation of the signal value is also used and different methods of BSD. In above improvements, support sets detection and non zero elements is estimated that do not need to limit signal sparse distribution as a Gaussian distribution, so the non Gaussian distribution of the sparse signal is also capable of high precision reconstruction. Respectively based on the one-dimensional Gaussian and two-dimensional image signals, simulation experiments show that, compared with BSD method, this thesis proposed using the backtracking and belief propagation method for non Gaussian and Gaussian distribution of signal reconstruction are able to obtain high reconstruction accuracy and faster convergence speed.Aimed at simplifying compressive measurements, we introduce the Kalman Filtering to BP reconstruction. The process of belief propagation decoding perform the support detection. And the signal values belonging to the support set is estimated by Kalman filtering. To reduce the computational complexity, the dynamical measurement matrix is introduced in Kalman filtering process, the measurement matrix ?T is dynamically selected according to the support detection results of BP iteration, the low dimensional matrix operations instead of the original high dimension. Our simulation results indicate that CS-BPKF can mitigate measurement noise effect and offer good reconstruction performance with a little sacrifice on computing complexity.At last, the thesis applies the compressed sensing model based on the LDPC-like sparse measurement to wireless sensor networks. For the most existing data gathering in WSNs transmitting data with single antenna and multi-hop strategy, it leads to large energy cost and poor transmission quality. The CS model based LDPC-like sparse measurement is applied to wireless sensor networks, a visual MIMO compressive data gathering scheme in WSNs is proposed. The key idea is a combination of CS based LDPC-like measurement and MIMO transmission technology. Firstly, energy consumption model of data gathering Etotal is proposed. Secondly, based on the energy minimum, number of cluster nc,number of nodes involved in the coordinated transmission Mt,sizes of modulation constellation b, density of measurement matrix ? and compression ratio ? are joint optimized and joint parameters(?,?,nc,Mt,b) can be obtained. According to these parameters, we configured the measurement matrix ? and design visual MIMO transmission scheme. Comparing to compressed data gathering with only single antenna, our scheme can make the data gathering more effective and prolongs lifetime of WSNs significantly.