Research On Optimization Method Of Measurement Matrix Based On Compressive Sensing

Traditional analog signal sampling method will get a lot of samples,then the subsequent processing of hardware and storage will meet more difficult.The proposing of Compressive Sensing(CS)theory opens up new horizons in signal processing field.It can obtain the information samples from the original signal while compressing and use a small amount of observations instead of the most information in original signals.The original signals can be reconstructed from these observations.Compared with traditional methods of signal processing,the data rate of CS is not limited by the Nyquist sampling theorem.In the whole process of CS,measurement matrix and reconstruction algorithm are the critical content.In the CS processing,the obtain of observation vector is important,and the information of the observation vector is determined by measurement matrix.Measurement matrix with good performance can lead to obtain few observations which contain all the useful information from the compression process of original signal,and the original signal can be accurately reconstructed by a certain algorithm.If the same reconstruction algorithm was applied,the most important factor of the reconstruction is the measurement matrix.The better the performance of measurement matrix is,the smaller reconstruction error is.In summary,the research on optimization techniques to measurement matrix has important theoretical and practical significance.In recent years,many design and optimization methods of measurement matrix have been proposed,and various types of measurement matrix also have been applied to different occasions.It can be grouped into three categories.The first class is the random matrix,such as Gaussian random matrices,Bernoulli random matrix and so on.The second class is the orthogonal matrix,as partial Hadamard matrix,partial Fourier matrix,etc.The third class is the determined structured matrix,such as Toeplitz matrix,cyclic matrix,binary matrix,etc.Many problems exist in these matrices: such as the randomness of atoms in measurement matrix leading to a difficult implementation in storage hardware.Some determined measurement matrix need much more samples of original signal for getting a better reconstruction accuracy,although the hardware implementation is relatively simple.Because of the many restrictions of partial orthogonal measurement matrix,the application is limited in many aspects.The first part of this paper introduces the basic concept and principle of CS theory,selective analsis the main content of the CS theory: sparse representation,measurement matrix and recovery algorithm.The second part describes the classification of measurement matrix,analyze the characteristics and performance of frequently used measurement matrices,list the existing optimization and design method of measurement matrix,and summarize the shortcomings and advantages of the existing measurement matrix.The third part of the paper gives a detailed analysis of the nature which measurement matrix need to meet,and introduces the factors which design of the measurement matrix need to consider,propose an optimization method of measurement matrix,ASS-GDM.In this method,the step size is updated in the process of the gradient descent method and the adaptive changes of the step size can be further adjusted based on the simulated annealing coefficient,and the convergence rate of the algorithm is improved.The fourth part puts forward an approach to improve the performance of measurement matrix,RS code optimization method.The coherence of the measurement matrix opimized by this method would be asymptotically achieve to the Welch bound,and then the performance of the measurement matrix is asymptotically optimal.