| Compressive sensing is a new branch of mathematics,electrical engineering and computer science.In recent years,it has played an important role in many practical scientific and technological problems.Compressive sensing focuses on two issues:one is which matrix is suitable for observation matrix design,and the other is which algorithm can effectively reconstruct signal approximation.This thesis mainly studies the hard threshold iterative algorithm,and the main contents are summarized as follows:（1）In order to better understand the design of observation matrix in signal,the definition and connection of symbols krank,spark,coherence and restricted isometry constant（RIC）are systematically combed,and the three reconstruction algorithms are described as a whole.In addition,according to the classical algorithm and recovery conclusion in the reconstruction iteration of hard threshold,different representations of the forms of recovery conditions are sorted out by time line,so as to facilitate readers to have a clear understanding of the hard threshold algorithm.（2）This thesis further discusses the properties of spark and better understands the sparse representation and uniqueness recovery theorem from the matrix structure itself by analogy with the definition of matrix rank.（3）Based on the classical IHT algorithm and the NIHT algorithm with onestep improvement in the hard threshold iterative algorithm,inspired by the twostep constant iteration process,this thesis proposes a new two-step iterative hard thresholding algorithm 2s-IHT and adds β(xn-xn-1))to the original iteration step.Increases the chance of quickly finding the original vector support set.Results the reconstruction condition is relaxed theoretically,and the value range of β is given when the new algorithm converges,and the performance of the algorithm is confirmed by numerical experiments.The expcrimental results show that the new algorithm has higher recovery accuracy and faster running speed than IHT and NIHT when β=0.1,0.2,0.3 are selected. |
