Research Of Signal Reconstruct Algorithm Based On Compressive Sensing

Compressed sensing (CS) is a theory which has developed in recent years, it can using far less than the required sampling frequency of the Nyquist sampling theorem to sample the signal while there's no loss of information, and t the same time, it could be able to accurately reconstruct the signal. Compared with the traditional method of signal processing based on the Nyquist sampling theorem, Compressed sensing has obvious advantages. it is based on space transformation and use a random measurement matrix as a means, and then, to solve the optimization problem as a signal processing method. The theory requires only a few points can be simultaneously sampling data acquisition and compression, so it can significantly reduce the cost of data storage and transmission, to further reduce signal processing time cost and device cost.Compressed sensing theory has three core elements: (1) Signal sparse transformation: for a non-sparse natural signals, we need to find a suitable transform domain which the signal has a sparse representation; (2) Design of observation matrix: we need to design a smooth random matrix which is irrelevant with the transformation base; (3) signal reconstruction: we use a mathematical algorithm to ensure the accuracy and simultaneously finish the signal reconstruction, the whole reconstruction process can be treat as the solve to a optimization problem.The main content of this paper is signal reconstruction. As the core link of compressed sensing theoretical framework, the choice of algorithm directly determines the reconstructed signal quality, reconstructed speed and the results of application. For now, Signal reconstruction algorithm can be attributed to three main categories the greedy algorithm, convex relaxation algorithm and the combination algorithm. Three methods have their own characteristic. In this paper we choose representative algorithm such as gradient projection algorithm and orthogonal matching pursuit algorithm as the key research. They are the basal algorithm, and therefore they have important guiding significance to new algorithms and improved algorithms. Then, we give a general summary of various existing algorithms.Gradient projection algorithm is a reconstruction algorithm based on l1 -norm minimization. The general idea is to start from the feasible point, research feasibility along the direction of the drop, and then, we have a new feasible point calculated the target function decreases. According to the simulation analysis of the experimental results, the effect of the algorithm is very good. It could maintain a good quality at a high sampling frequency and has a good performance in the reconstruct time. But the quality of the reconstructed image has a sharp decline while the sampling frequency is declining.Orthogonal matching pursuit algorithm is an iterative greedy algorithm. In every iterative step, the algorithm selects a atom from a complete dictionary which could be the best matching of the target signal and uses Schmidt orthogonal method, the algorithm could be constringency after a finite number of iterations, and eventually, we could accurately reconstruct the signal. In this paper, we make a simulation by using the two-dimensional images and one-dimensional signals. The results show that the orthogonal matching pursuit image processing results will be ideal, but also has some shortcomings: the quality of reconstructed image can't be guaranteed when the sampling frequency is low; reconstruction process is relatively slow and time-consuming is large. In addition, the algorithm has more stringent requirements on the observation matrix and need to set the number of iterations that it need more samples to achieve the purpose of accurate reconstruction, and so, the application is greatly limited.According to the above issues and constraints in the context, we propose an optimized orthogonal matching pursuit algorithm. The algorithm uses the best matching atom selection criteria of the optimal orthogonal matching pursuit orthogonal. It minimizes the modulus value of the Redundancy errors in every iterative step. At the same time, let the sparse degree of the original signal to be the standards of the number of iterations. Then we add the idea of the back projection, backward selection to remove redundant wrong atoms, so that the residual vectors could be reduced quickly and accurately reconstruct the original signal. Finally, we make a simulation on MATLAB. The results show that the optimization algorithm can guarantee the quality of the reconstructed image while reducing the samples, and also increasing the processing speed.