Stability Of Jointly Sparse Signal Recovery In Distributed Compressed Sensing

Compressed sensing is a hot area in recent years, Compressed sensing gradually become important concept in applied mathematics, computer science and electrical engineering. Compressed sensing theory is a new sampling based on signal sparse property. This new theory has been proven to use far less than the shannon sampling theorem and Nyquist sampling theorem of necessary sampling points to reconstruct the original signal. The compressed sensing theory has the absolute advantage.Distributed compressed sensing is based on the development of compression sensing theory. Distributed compressed sensing is the inoculation of sampling theory in the background of the rapid development of network and the reality of the increasing rate of the data. The multiple signals is the object of distributed compressed sensing theory.. The theory need to deal with a large number of complex multiple signals to reconstruction. The core idea of distributed compressed sensing for signal processing is make full use of the correlation between the inside signals and internal signal, further reduce the workload of signal processing, and improve the accuracy of signal reconstruction. Its emergence provides a new thought and method to the related fields of multi-sensor data fusion.The researchers have made a series of achievements in sparse signal reconstruction theory. But the results of the joint sparse signal reconstruction are very few; still exist many problems to be solved. In this regard, The stability of the previous conclusions are limited to a single signal reconstruction are discussed. There are only a few qualitative conclusions in the reconstruction of the joint signal stability. This article focuses on the stability in the reconstruction of distributed compressed sensing joint signal and thorough analysis of the twofold joint signal reconstruction. The concrete research content of the paper is as follows.First of all, this paper points out that the main research object of compressed sensing theory is sparse signal. The sparsity is special signal properties and widely exists in many fields. Secondly, the mathematical model is posed for signal reconstruction, and analyze the existence, uniqueness and certainty of solutions of the mathematical model under the sensing matrix satisfies the corresponding RIP condition. Presents two common algorithms to solve mathematical model. The applications of compression sense are discussed in image processing and face recognition. Then, further study the stability of joint signal reconstruction based on the stability of single signal reconstruction. Finally, compared and analyze the error between separated signal reconstitution and the joint signal reconstitution. The main contribution of this paper is to study quantitatively the error of reconstructing the two joint signals under distributed compressed sensing and show strictly that the reconstruction has a good stability under RIP condition.