Study Of Structured Bayesian Compressed Sensing Technology And Its Application

The traditional approach of reconstructing signals or images from measured data follows the well-known Shannon-Nyquist sampling theorem, which states that the sampling rate must be twice the highest frequency. Similarly, the fundamental theorem of linear algebra suggests that the number of collected samples of a discrete finite-dimensional signal should be at least as large as its length (its dimension) in order to ensure reconstruction. This principle underlies most devices of current technology, such as analog to digital conversion, medical imaging or audio and video electronics. Now, we are in the era of information-explosion, billions of data that need to be sampled, transmitted and stored are produced in our daily life. However, the traditional signal acquisition mode makes the related hardware equipment need to meet the higher requirement year by year. For example, the massive video surveillance data sampled by the traditional method require huge storage space. The novel theory of Compressed Sensing (CS)—also known under the terminology of compressive sensing, provides a fundamentally new approach to data acquisition. It predicts that certain signals or images can be recovered from what was previously believed to be highly incomplete measurements. This new sampling method has broken the bondage of traditional Nyquist sampling theorem. The ability that can directly measure the information contained in signal leads CS to have a great potential in many application fields.With the rapid development of wireless communication technology and high demand for a wide range of wireless communication services, especially, the wireless spectrum resource will be scarce seriously. Thus, this makes the emergence of Cognitive Radio (CR). When we sample the signal of wide band, sometimes, the sampling rate needed to recover the original signal may reach as high as GHz, which leads to the premium cost of hardware device or the equipment hard to be realized. Due to the low utilization of spectrum in CR system, the wideband spectrum of interest typically possesses sparse feature in the frequency domain, which meets the prerequisite of compressed sensing. As a result, CS theory has been considered as an innovative framework for wideband spectrum sensing to relieve the high sampling rate pressure of front-end hardware in CR system. Since some of the two-dimensional image signals have sparsity feature, in addition, we can also use this new sampling technique for reducing the amount of samples so as to save storage space and relieve the pressure of data store.Actually, the spectrum of communications signals in CR system is usually not only with the sparse property but also with the feature of block structure. Because of this property, we propose a Double-Level Binary Tree Bayesian Compressed Sensing (DBT-BCS) algorithm to recover block sparse signals. Both sparse prior and block structure prior of block sparse signal are taken into account via a hierarchical Bayesian model and implement the Bayesian inference by MCMC sampling. With the Analog-to-Information Conversion (AIC), then, the proposed DBT-BCS is used to recover the spectrum of wideband signal. The experimental results show that the proposed DBT-BCS algorithm which takes into account additional structure information is outstanding some existing CS recovery algorithm without considering the structure information of signal interested. For two-dimensional image signals having block sparse property, the DBT-BCS algorithm can be also exploited for image reconstruction. Since DBT-BCS algorithm takes into account both the sparse property and the block structure feature of the signal, the recovery accuracy of DBT-BCS algorithm is higher than the recovery algorithms which dont consider the block structure property of the image.In fact, the spectrum of multi-users in cognitive radio is related with each other. Based on compressed sensing, as a result, we propose collaborative spectrum sensing in cognitive radio system. This proposed framework of multi-user cooperative wideband spectrum sensing is of particular relevance to Multi-Task BCS (MT-BCS). Owing to the fact that the sets of measurements sampled by CS at the same moment are relevant with each other, the spectrum of PUs can be reconstructed more accurately with fewer measurements sampled by each SU. At last, our simulation results confirm the validity of the proposed method.