Research On Compressed Sensing Algorithms And Applications

As a new signal sampling theory,Compressed Sensing breakthrough the limitation of traditional Nyquist sampling theory,its core ideas is to merge the compressed and sampling process. It puts forward that if the signal is sparse or compressible in a transform domain,a irrelevant measure matrix can be used to transform the high-dimensional signal to the low dimensional vector,and then reconstruct the original signal with relevant optimiza tion reconstruction algorithm.The new type of sampling method not only overcome the faults of the traditional Nyquist first sampling and then compressed, but also reduce the sampling rates,alleviate the pressure on the sampling, and save the imformation acquisition time and storage space.At present,the Compressed Sensing theory was widespread attention in the academic field,and get the application in pratice.In this paper,the main works as follows:(1)Introduced the research status of the image de-noising and Compressed Sensing at home and abroad.Deeply researched on the main content of the Compressed Sensing Theroy and detailed analysis its three importants parts:the signal sparse representation,the design of the observation matrix and the signal reconstruction algorithm.(2)Research is mainly focused on greed reconstruction algorithm of the Compressed Sensing.Through the analysis and comparison,we summarizes the advantages and disadvantages of the greed reconstruction algorithm. According to the shortcomings of the SAMP algorithm,an improved SAMP algorithm is proposed.The experimental results show that the improved SAMP algorithm can not only guarantee the performance of the reconstruction algorithm but also greatly shorten the running time.(3)The Compressed Sensing is used in image de-noising. At first,we introduced the traditional image denoising algorithm,analyzed its advantages and disadvantages. Then,on the basis of the Compressed Sensing theoretical framework,we researched the Total Variational image denoising method,and improved the traditional TV model.Finally,the paper put forword a improved TV image denoising based on the Compressed Sensing, simulation experiments show that the improved algorithm is effective.