The Improvement of Smoothed LO Norm Algorithm Based on Compressive Sensing
|Course||Communication and Information System|
|Keywords||Compressed Sensing Sparse representation Signal reconstruction Smoothed l0norm Conjugate gradient method|
Compressed Sensing theory received extensive attention of people when it just put forward. In this theoretical framework, sampling rate is no longer the same as the Nyquist rate depends on the bandwidth of the signal, it reduces the enormous pressure which sampling procedure brings to signal processing and hardware systems; and the theory combined the sampling and compression process of traditional signal processing, finally use a small amount of sample values to reconstruct the original signal. It avoids the disadvantages of traditional sampling theorem which generated a lot of redundant data, relieves the pressure on storage space. In recent years, a lot of theories and practical application have been developed.The thesis first introduces the research background and research status of the theory of Compressed Sensing, and illustrates the advantages of Compressed Sensing theory. Describes the basic framework of the theory of Compressed Sensing, then highlights the main elements of the theory of Compressed Sensing which including signal Sparse representation,the design of observation matrix,Signal reconstruction and the applications of Compressed Sensing theory in real life. Signal reconstruction is focused on the theory of Compressed Sensing research, the thesis describes three types of reconstruction algorithm, introduces the core idea and the advantages and disadvantages of these typical Compressed Sensing reconstruction algorithms. Then use these reconstruction algorithms simulate the one-dimensional time-domain pulse signal and two-dimensional image, through simulation analysis, verify the simulation reconstruction results of these algorithms.Smoothed l0norm (SLO) algorithm uses gradient projection and the principles of the steepest descent method to gradually approach the optimal solution. The core is to find a continuous function used to approximate the l0norm. However, because the result of the reconstruction algorithm exists sawtooth effect, can’t guarantee the accuracy of approximation, and this algorithm has the disadvantage of slow convergence. For these problems, make some improvements to the original Smoothed l0norm (SLO) algorithm, take use of numerical better performance conjugate gradient method to replace the steepest descent method of the original Smoothed l0norm (SLO) algorithm.Computer simulations confirm the effectiveness of the introduced algorithm comparisons with the existing methods in terms of run time, reconstructive probability and accuracy. The simulation results obtained by the improved Smoothed l0norm (SLO)algorithm shows better reconstruction results.