Multiband Signal Reconstruction Base On Discrete Prolate Spheroidal Sequences

Multi-band signals are widely used in daily life.In traditional signal processing methods,if you want to sample the target signal completely,the sampling frequency of the signal must be greater than twice the target frequency.However,technology is developing rapidly at this stage,and the demand for information and the bandwidth of signals are constantly increasing.Because multi-band signals have multiple frequency bands,the increasing bandwidth makes traditional signal processing methods are difficult to deal these signals.The Compressed Sensing(CS)has proposed in 2006,which provides a new way to solve this problem.According to CS theory,in the process of signal sampling,the signal can be compressed and then sampled,and in this way can reduce the sampling frequency.Then use reconstruction algorithm to reconstruct it completely or with high quality.Since the multi-band signal is continuous in the time domain,according to the compressed sensing theory,this paper uses the Discrete Prolate Spheroidal Sequences(DPSS)to sparse the multi-band signal,and then brings it into the signal reconstruction algorithm and reconstructs the signal.In this paper,starting from improving the accuracy and speed of the reconstruction algorithm,the research and improvement of the multi-band signal reconstruction algorithm are mainly analyzed.The main contributions of the paper are as follows:(1)In the regularization matching pursuit algorithm,if use the regularization strategy,it will select some atoms that do not contain signal information are selected,which makes the estimated signal compared with the original signal have a larger deviation and affects the signal reconstruct.This subject proposes a method of dual screening using fuzzy thresholds and regularization strategies,using two strategies to select atoms and taking intersections.In this way can make atomic selection more accurate.At the same time,the backtracking strategy is introduced,and the selected atoms are re-screened again to improve the reconstruction accuracy of the algorithm.(2)In the Stage-wise weak matching pursuit algorithm,the geometric mean is used to calculate the atomic correlation using the inner product method,which cannot keep the original state of the atom well,so it will affect the discrimination of similar atoms,then it will a?Oeect the result;The fixed weak selection threshold is too large or too small will affect the reconstruction results of the algorithm.This subject proposes an improved method of generalized Jaccard sparse substitution of the inner product matching criterion,which uses the arithmetic mean instead of the geometric mean,and at the same time subtracts the same part of two atoms to enlarge the difference.Makes calculations more accurate when calculating atomic similarity.At the same time,in the aspect of atomie selection,this subject proposes an adaptive weak selection threshold method.The size of the residual is used to control the change of the weak selection threshold.Reduce the possibility of redundancy of the augmented set,and at the same time use the backtracking method to improve the accuracy of atom selection,so that the accuracy of the algorithm is improved.(3)In the sparsity adaptive matching pursuit algorithm,the algorithm relies on a fixed step size.If the step size is too large,the estimated signal sparsity will be inaccurate and the accuracy will decrease.This topic proposes a method to improve the step size,which makes the step size larger at the beginning,speeds up the convergence speed of the algorithm,and then gradually reduces the step size to make the estimated sparsity close to or eqxual to the true sparsity.At the same time,in terms of atom selection,a larger fixed value i5 used to replace the selection value changed in each round of iteration,which reduces the calculation amount of the algorithm and accommodates more atoms in each round of iteration.Improve the convergence speed and reconstruction quality of the algorithm.