Research Improved Of Measurement Matrix And Reconstructionalgorithm Based On Compressed Sensing

With the rapid development of information age, there is a growing number ofcontradictions between the traditional method of signal acquisition and the dataacquisition demand. Especially in the case of large numbers of high frequency, highaccuracy and high-speed signal, has been difficult to meet the reality demand basedon the traditional method of signal acquisition. The basic theory of Compressedsensing was born and developed in this context. The advantage of this theory is thatsignal compression can be achieved in the course of sampling, the samplingnumbers was reduced greatly. Then, according to the height of incompletemeasurement information, converted into a convex optimization or minimizationproblem. Finally, solving the convex optimization (minimization) problem by acertain reconstruction algorithm, to achieve high accuracy reconstruction of thesignal.This paper depth studies and detailed analyzes the basic theory andmathematical framework of CS, then studied the measurement matrix andreconstruction algorithm which are the two important aspects of CS, and the imagede-noising application based on compressed sen0sing. The main work andinnovation of this paper include:(1)Proposed an optimization method ofmeasurement matrix, for the shortcomings of existing stochastic or deterministicmeasurement matrix when measuring, the algorithm superimposed deterministicring measurement matrix to optimize the measurement process, which based on theexisting random measurement matrix, and extended the optimization method tostructure other random measurement matrix, the simulation and analysis results ofone-dimensional sparse signal and two-dimensional image signal showing, themethod can reduce the number of measurements, and improve the quality of thereconstructed signal.(2)Studies and analyzes several classical compressed sensingreconstruction algorithm, proposed an improved FR-CoSaMP reconstructionalgorithm, then analysis mathematical model and algorithm processes of the algorithm in detail, the algorithm improve the measurement matrix and iterativecalculate based on CoSaMP algorithm, the reconstruction quality of image signalcan be improved by using the CoSaMP algorithm.(3)For the CS applied in imagede-noising, by introducing some common noise model, in-depth comparison of theperformance of today’s several popular de-noising method based on CS. Provideobjective data analysis for the CS research in this direction.In the end of this paper, comprehensive summary the main contents of thispaper.And put forward the post-related research questions of this new CS theory.