Research On Key Techniques Of Signal Reconstruction Based On Compressed Sensing

Compressed sensing technology is a novel type of signal processing technology,which was introduced in 2006,and since then has already become a key theory in various areas of applied mathematics,computer science,and electrical engineering.It breaks through the requirements of the traditional Nyquist sampling theorem.By collecting a small number of signal values,the original signal can be reconstructed with high precision.This technology has opened up a new path to solve problems such as data redundancy and resource waste,greatly reducing the burden on hardware,and also providing a better opportunity for the development of related disciplines.In the theory of compressed sensing,the reconstruction algorithm is one of the most critical parts,and its performance directly determines whether the signal can be successfully reconstructed.Therefore,how to design a compressed sensing reconstruction algorithm with high reconstruction precision,high efficiency and low complexity has been the focus of scholars.With the development of compressed sensing theory,scholars have proposed a variety of reconstruction algorithms,such as convex optimization reconstruction algorithm,greedy iteration algorithm and combinatorial algorithm,etc.However,these algorithms are limited to the reconstruction of simple signals.For complex signals,there are problems such as low reconstruction accuracy,low efficiency and complex algorithm implementation.In general,optimization and improvement based on some original algorithms can alleviate these problems.In this thesis,the greedy iterative reconstruction algorithm is studied and improved for 1-D signal and 2-D signal.Based on the 2-D image reconstruction algorithm,a non-local similarity compressed sensing reconstruction algorithm is designed for the 3-D spatial signal.The main research contents are as follows:(1)Greedy iterative algorithms compute iteratively the support of the signal and the residual until reaching to the optimum solution.Greedy iterative algorithms easy to implement but don't have the strong reconstruction guarantees such as convex optimization.Most greedy iterative reconstruction algorithms require the sparsity of the known target signal as an input parameter,which directly determines the reconstruction accuracy of the algorithm.However,in practice,the data signals we are dealing with are complex and variable,and the sparsity is difficult to obtain directly.Later,a sparse adaptive algorithm was proposed.Although it does not need to know the signal sparsity in advance,the algorithm has high computational complexity and hardware implementation difficulties.In view of the above questions,an improved greedy iterative algorithm was proposed in this thesis,which does not require the sparsity of the target signal as a priori information,but a sparsity pre-estimate strategy is used to estimate the sparsity and the support set of the target signal before the signal reconstruction iteration,and then initialize the residual with the estimated value,the target signal can be reconstructed after a small number of iterations.The algorithm combines the advantages of greedy algorithms such as adaptive,backtracking and greedy selection to iteratively optimize,which ensures the accuracy of the reconstruction and improves the efficiency of the algorithm.This thesis demonstrates the advantages of the new algorithm through the reconstruction experiments of 1-D signals and 2-D signals.(2)In this era of big data,the information that people come into contact with is complex and diverse,and the original 1-D signal and 2-D signal processing technology can no longer meet people's living needs.Based on the inspiration of 1-D signal and 2-D signal reconstruction algorithm,the thesis further studies the compressed sensing reconstruction algorithm of 3-D image signal.Since the traditional compressive sensing reconstruction algorithm usually relies on convex optimization,its regularization constraints are often expressed by l0 or l1 norm.For the high-dimensional signal,it will lead to the problem of complex calculation and difficult implementation of the solution.In this thesis,a display filter non-parametric reconstruction scheme is proposed to replace the traditional regularized parameter model.A compressed sensing reconstruction algorithm based on spatial adaptive filtering for regularization is designed by applying the block-matching and 4-D filtering algorithm(BM4D)adaptive filter.In each iteration,the filtering operation excited by random noise,which makes the noise in the image gradually attenuate while the features and details of the unobservable part in the image are gradually revealed.After a lot of simulation experiments,the effectiveness of the 3-D compressed sensing reconstruction is proved.