Signal Recovery Algorithm In Compressed Sensing

Compressed sensing theory breaks through the traditional Nyquist sampling rate,thus more and more scholars begin to study it. In reality, natural signal under some kind of transformation can have sparse characters, which makes the compressed sensing theory a very broad application in reality. Compressed sensing requires signals to be sparse, thus solving the minimum L0 norm model is a very intuitive way to handle compressed sensing problem. Due to the non-convex properties, L0 model needs complex calculation, therefore L1 model is commonly used instead of L0 model, and L1 model can be solved easily by using simple convex optimization method. However, compared with L0 model, L1 model has higher requirements of the measured quantities m of the measuring matrix A. So for L1 model, the log-sum model is a better choice to replace L0 model.In this thesis, we summarize the application prospect and the research status of compressed sensing theory, give a brief overview of compressed sensing theory, and utilizes various kinds of commonly used algorithms of compressed sensing to analyze the theory briefly. This paper mainly analyze the origin, transformation, and solution of the log-sum model.This thesis also presents the condition of the accurate reconstruction of log-sum model in the absence of noise. When the parameters of the log-sum model are small, it only requires the measurement matrix A to satisfy(31k? ?) to ensure accurate reconstruction, which demands much more loose condition for measurement matrix A than L1 model. Considering the influence of log-sum model parameters on the performance of reconstructing signal, a method of gradually reducing the values of parameters is proposed to replace fixed parameters in this thesis. Simulation shows that the performance of log-sum model is better than that of L1 model, and the simulation explores the influence of sparse level, number of measurements, iterations of algorithm, log-sum model parameters, fixed and changing parameters on the success rate of accurate reconstruction.In noisy cases, reconstructing signal error of log-sum model, is linearly limited by the level of noise. Log-sum model is verified to be better than L1 model by the simulation in the noisy environment. The influence of sparse level, number of measurements, iterations of algorithm, log-sum model parameters, fixed and changing parameters, and noise variance to the changes of reconstruction are also discussed in this thesis.