Research On Compressed Sensing Reconstruction Algorithm

Compressed sensing(CS)theory breaks through the limitations of the traditional Nyquist sampling theorem,which is a sampling theory that uses more useful means to sample the signal.Since the theory of compressed sensing can achieve better results in practical applications,it has gained more researchers' attention.For sparse or compressible signals,a non-linear reconstruction algorithm based on a small number of measurements is used to accurately reconstruct the original signal,saving storage space and time.The reconstruction algorithm,an important component of the theory of compressed sensing,plays a decisive role in the theory of compressed sensing,and it can solve the problem of reconstructing the original signal from a small number of measurement signals.In this paper,some problems in compressed sensing reconstruction algorithms,especially the greedy reconstruction algorithms,are studied.Based on the traditional compressed sensing algorithms,some improved reconstruction algorithms are proposed to improve the existing algorithms.The improved algorithms are compared with existing mainstream algorithms to verify that the improved algorithms hare better reconstruction performances.The specific research work has the following aspects:(1)OMP algorithm,ROMP algorithm,SP algorithm and other algorithms are classical algorithms in compressed sensing and are widely used in practical applications.However,these algorithms need to be reconstructed when the sparsity is known,and all of these algorithms have long time to reconstructed signals.These problems make the algorithm unable to be applied to more practical situations.In order to accurately reconstruct unknown sparse signals,special signals,and noisy signals,an improved compressed sensing reconstruction algorithm is proposed.The improved algorithm predicts and selects the required atoms based on the total number of atoms in the selected support set,the energy difference between signals,and the residuals in the case of unknown sparsity,and it can accurately reconstructs block sparse signals,noise signals,and picture signals.Through simulation analysis,the optimized algorithm improves the reconstruction quality and reduces the running time.(2)The St OMP algorithm and the SWOMP algorithm improve the OMP algorithm by setting the threshold.However,both of these two reconstruction algorithm do not include the backtracking mechanism.Once the "error atom" is selected,the algorithm will reduce the reconstruction effect.Choice of parameters will also have some effect on the algorithm.In response to the above problems,this paper proposes an improved algorithm.The backtracking idea is added to the algorithm of threshold selection.The selected atoms are filtered twice to filter the wrongly selected atoms during the first screening.It can guarantee signal reconstruction with higher quality.Through experimental verification,the two threshold filters effectively reconstruct one-dimensional and two-dimensional signals.It can make sure that the reconstruction accuracy in a high quality and the operation speed fast.Reflecting the superiority of the two screenings.(3)When the sparseness is known,the reconstruction quality is greatly improved.The sparsity estimated by the existing sparsity estimation method is smaller than the real value.So the new sparseness estimation method needs to be proposed.In order to solve the above problems,a new sparsity estimation method which applied to the improved algorithm-a stepwise improved compression sensing algorithm is proposed.It solves the choice of the initial step size which exiting in SAMP algorithm ant uses the energy difference between the reconstructed signals as a method to change the step size,and dynamically adjusts the step size during the execution of the algorithm.Experimental results indicate that the improved algorithm has certain advantages.(4)The complementary matching pursuit algorithm is a complementary form of the matching pursuit algorithm.The algorithm removes N-1 mismatched atoms and retains the remaining closest matching atoms,thereby achieving the purpose of selecting atoms.The matching algorithm in the complementary space has only one atom per iteration,which increases the execution time of the algorithm.At present,there is less research on the compressive sensing algorithm for the complementary space.In this paper,a method combining with the framework of complementary and non-complement is proposed.The step-by-step method,backtracking the mind and setting the mark idea are added in the improved algorithm.A large number of experimental studies have shown that the performance of the improved algorithm is better than the similar algorithms.