Reconstrucion Method On Compressen Sensing

With the rapid development of information science and technology, the amount of information is huge.The demand of technology on information processing will be high and the original traditional information precessing methods can not fully meet the requirements of people. So the study of compression perception theory is very important.In compressed sensing framework,a detailed carding and research on the sparse representation,measurement matrix design, reconstruction algorithm is discussed. The main content of this thesis is reconstruction algorithm,which has played an important role in the theory of the compressed sensing.A few typical algorithms such as OMP and StOMP algorithm for solving the l1, optimization problem and BP algorithm for solving the l0optimization problem are firstly analyzed.Through reconstruct Barbara512image,we contrast complexity and reconstruction results of these algorithms.For nonsmooth in l1, norm, smooth function is constructed, discrete optimal solution sequences are used to approximating the global optimal solution. The property of smooth approximation function and the convergence of optimal solution sequences guarantee the algorithm is feasible.The numerical results show that smooth approximation is an effective technique.The original l0norm problem is NP-hard problem,and based on the minimum l1, norm problem of reconstruction algorithm has high time complexity.So,in this paper, using the pseudo||X||(0≤p≤1) norm instead of||X||norm.In order to overcome the nonsmooth problem in lp norm,this paper proposes a new Maximum Entropy Function Method (MEFM) to solve the lp optimization problem via smoothing the objective function with maximum entropy function.The numerical results show that smooth approximation is an effective technique and signal reconstruction effect of MEFM algorithm is better than OMP algorithm.