Research On Compressed Sensing Reconstruction Algorithms With Prior Information

With the rapid development of mobile communications, mobile Internet,Internet of Things and other emerging communication technologies, the "Inter-net of Everything" is coming. It is a significant problem for processing hundreds of millions of data. Especially for future 5G communication, the traditional Nyquist sampling theorem will not only significantly increase the hardware cost of the communication device but also produce a lot of data redundancy.It is clear that how to securely and efficiently obtain and process as much use-ful information as possible from the sparse signal is an important research is-sue for compressed sensing evolution. Compressed Sensing theory is proposed by Donoho, Candes and Tao et al. By Combining the compression step and sampling step into one step, compressed sensing can project high-dimensional sparse signals by compressed sampling method into low-dimensional spaces and reduce the sampling rate of communication devices, achieve the goal of re-ducing the cost of hardware and reducing the pressure of data sampling. Com-pressed sensing proposes a new sampling idea and breaks the confinement of the traditional sampling theorem. Then, compressed sensing has gradually be-come a new signal processing technology.Although compressed sensing has great advantage in terms of sampling rate and data dimensionality, there are still many problems to be solved ur-gently. Over the past ten years, the compressed sensing theory is improved perfectly and mainly divided into three parts that including the sparse repre-sentation of signals, compressed sampling and signal reconstruction. For the procedure of compressed sensing, how to effectively use the sparse structure of the signal itself (such as block sparse structure, sparse tree structure, etc.) or other kind prior information (such as the non-zero probability vector of support set, measurement matrix disturbance and partially known correct support set information, etc.) to enhance the reconstruction performance is an important topic. In addition, the research on the theoretical performance of compressed sensing reconstruction algorithms (such as reconstruction error, mathematical requirements of measurement matrix, number of measured values, etc.) is also a very meaningful research direction. Therefore, in this paper, we focus on two aspects: one is to study the quantifiable prior information on the performance of compressed sensing reconstruction algorithms to provide theoretical support for the follow-up algorithms; the other is to study the combination of the prior information of sparse signals and compressed sensing. By designing a reason-able optimization model to maximize the use of signal a prior information, the designed efficient and robust compressed sensing reconstruction algorithms can achieve the goal of improving the performance and reconstruction speed of the reconstruction.In this paper, we enjoy the merit of the special sparse structure and prior information of the signal itself. Then, we incorporate it into the reconstruction process of the recovery algorithm to establish a new optimization model and propose efficient and robust compressed sensing algorithms. Finally, we ana-lyze the reconstruction performance of the related algorithm. The innovation of this paper is mainly listed as the following points:· First of all, we derived the reconstruction performance of compressed sensing reconstruction algorithms of point-to-point link and multi-point link and obtain the RIP constant performance bound based on the sup-port set non-zero probability vector as prior information in the point-to-point link scene and RIP constants performance bound based on known measurements and measurement matrices perturbation in the multi-point links scene. Firstly, the non-zero probability of the sparse signal support is quantified as prior information for orthogonal matching tracing algorithm in point-to point link scene. Then, The impact for the performance of the restricted isometry property for measurement matrix with this condition is studied. Secondly, we study the problem of signal reconstruction based on multi-point link scenarios. When the measurements and the measure-ment matrix are perturbed, based on RIP, we analyze the performance of the measurements matrix of simultaneous orthogonal matching pursuit al-gorithm. For the sparse signals where each signal has the same position of the K largest amplitude term and different amplitude, we analyze the restricted isometry property condition that the support of these signals can be accurately reconstructed.· Then, we propose the compressed sensing reconstruction algorithm based on certain prior information in point-to-point link scenarios. The signal it-self may has certain sparse structures, such as the segmented smooth signal and the image signal under the wavelet transform domain, the important coefficients are organized as tree structure. This kind of prior information is used to derived a reasonable optimization model for the reconstruction process. By exploiting the tree structure to select the parent nodes and the ancestor nodes to expand the candidate support set selected for each iter-ation process, the reconstruction process of the reconstruction algorithm is achieved the purpose of accelerating the reconstruction of the algorithm and improving the robustness of the algorithm. The simulation results show that the use of prior information can effectively reduce the times of iteration and improve the performance of reconstruction algorithm.· Finally, we propose the reconstruction algorithm based on the non-zero probability vector of the support set in multi-point link scenario. The non-zero probability vector of support set is a common prior information, such as sparse positions of block sparse signal are block with a larger prob-ability. By using the nonzero probability vector of the support set, we derived of a correction factor to increase the correlation coefficients of the support position with large non-zero probability in the reconstruction process. This step can avoid the wrong selection of support set in the iter-ative process and achieve the purpose of improving the robustness of the reconstruction algorithm. The simulation results show that the using of the non-zero probability vector of the support set can effectively improve the robustness of the reconstruction algorithm.