Research On Greedy Reconstruction Algorithm Based On Compressed Sensing

Compressed sensing theory is an emerging signal sampling and processing theory,which is widely used in many fields such as data communication,medical imaging,biosensing,radar detection,etc.It breaks the traditional signal sampling mode,and accurately reconstructs the original signal from lower sampling rate by utilizing the sparsity or compressibility of signals and combining the two steps of sampling and compressing.The reconstruction algorithm is the core part of compressed sensing theory,which directly determines the application of compressed sensing theory.Therefore,how to design an algorithm with low computational complexity,high accuracy and strong anti-interference ability has been the research focus of compressed sensing theory.At present,common reconstruction algorithms include convex relaxation method and greedy algorithm.The greedy reconstruction algorithms mainly reconstruct the signal by iteration and are widely used in practical problems because of the advantages of easy implementation and excellent reconstruction performance.Therefore,this graduation thesis will focus on the greedy reconstruction algorithms based on compressed sensing theory.The main work is as follows:In chapter 1,we first introduce the background and significance of the compressed sensing theory.And then the research status of greedy reconstruction algorithms at home and abroad is summarized.Finally,we organize the main research content and chapter arrangement of this graduation thesis.In chapter 2,we describe the basic theory of compressed sensing,including the three important parts of the signal sparse representation,the measurement matrix design and the reconstruction algorithms.And we focus on the four classic greedy reconstruction algorithms and their basic principles and algorithms flow.In chapter 3,we provide a nearly optimal number of iterations for generalized orthogonal matching pursuit(gOMP)that stably reconstructs signals from the noisy measurements.In the noise scenario,based on restricted isometry property(RIP),we discuss the lower bound of the number of iterations required to make g OMP perform stable reconstruction of signal when the number of iterations is more than the signal sparsity .And the theoretical basis is also provided.Finally,the experiment result by MATLAB has shown that gOMP has better reconstruction performance.In Chapter 4,we present a sufficient condition for multiple orthogonal least squares(MOLS)that can accurately reconstruct signals from the noise-free measurements.In the noise-free scenario,using RIP,we give sufficient condition to ensure that MOLS accurately reconstructs signals with K in iterations,and also analyze the upper bound of this sufficient condition.The better reconstruction performance of MOLS is illustrated by experimental results.