Research On Compressive Signal Detection And Multitask Recovery Algorithms

The platforms of signal reconnaissance and receive, such as the satellite, have limited resource in data storage, imformation transmission and signal processing. It is important for us to find the solution to slove these problems. Meanwhile, compressive sensing can compress the spasity signals and then robustly recover them, which can help solve the above problems. So it is meaningful that we deeply reseach on the sparse reconstruction algorithms. In the paper, we focuse on the techniques of the compressive detection, the multitask recovery, the multitask classification and recovery, and synthesized compressive sensing. The main content of the dissertation are detailed as follows:In chapter 2, we discuss the detection problem of the stochastic signal based on the Neyman-Pearson theorem. First, we discuss the detection problem when the stochastic signal has a Gaussian distribution with variance having a diagonal form and provide the explicit expressions about the detection probability, the false probability and the detection threshold. Then the detection problem is generalized to the cases where the signal has a Gaussian distribution with variance having any form and the signal has a non-Gaussian distribution. When the number of compressive measurement is too small to recover original signals, the performance of the compressive detection may be well.In chapter 3, for the case where original signals belong to the same group, we propose the Laplace prior based multitask compressive sensing algorithm, which is the extension of Laplace prior based compressive sensing. We analyze the difference between the Laplace prior sharing mechanism and the MCS sharing mechanism. The former has another layer of hyper-prior information, which makes it easy to estimate the sharing parameters. We find that MCS is the special case of LMCS. The reconstruction model of multitask, which has less parameters, is developed by integrating a nuisance parameter out. From the reconstruction model, a fast and robust inference algorithm is developed. Experimental results demonstrate that LMCS has the superior performance to MCS. Then we consider the problem of jointly reconstructing multiple block-sparse signals with block partition unknown. Based on the framework of block sparse Bayesian learning(BSBL), we develop a new multitask recovery algorithm, called the extension algorithm of multitask block sparse Bayesian learning(EMBSBL). In contrast to existing methods, EMBSBL exploits not only the statistical interrelationships of signals, but also signals’ intra-block correlation, and does not need a priori information on block partition.In chapter 4, for the case where original signals belong to different groups, from the framework of MCS and LMCS, we propose the new sparse reconstruction and classification algorithms based on the minimum description length(MDL) principle, i.e., MDL-MCS and MDL-LMCS, which can classify tasks into different groups and then jointly reconstruct signals in every cluster. Experimental results demonstrate that the proposed algorithms have the superior performance to the state-of-art algorithms. Then, for the block-sparse signals, we propose the use of the state evolution(SE) property to enhance existing Turbo-GAMP-MMV techniques, and obtain new multitask classification and reconstruction algorithms. The newly developed methods, i.e., GCEM-Turbo-GAMP-MMV, first achieve task classification via dividing the CS tasks into groups and then reconstruct the original signals in each group jointly. Experiments demonstrate that for the block-sparse signals, the GCEM-Turbo-GAMP-MMV algorithms developed in this paper have better signal reconstruction performance MDL-MCS and MDL-LMCS.In chapter 5, for the block-sparse singlas, we propose the synthesized multitask recovery framework. We first propose a multitask synthesis method, by which we can synthesize some tasks from the original task. All tasks are the same vectors, but they are products of different measurement matrices and original signals, which are obtained by translating columns of the original measurement matrix and elements of the original signal in turn. Then, we utilize MCS to reconstruct the original signal and adopt the minimum description length(MDL) principle to determine the proper number of synthesized tasks. Based on the synthesized multitask framework, we develop SMCS and SEMBSBL. SMCS has less computational cost than SEMBSBL, but the latter has better recovery performance than the former. The advantages of SMCS and SEMBSBL are that the algorithms can achieve good reconstruction performance without the prior information of the block-sparse signal.