Study On New Joint Sparse Recovery Algorithms And Their Applications

Compressed sensing(CS) is a revolutionary theory in the mathematical sciences and signal processing fields. It goes against the famous Shannon-Nyquist sampling theory,and integrates the signal sampling and compression steps into a single process. Then CS can significantly reduce the sparse(or compressible) signal acquisition and storage cost. These advantages make CS attract much attention and be rapidly developed since it was proposed ten years ago. The sparse recovery problem is of central importance in CS. The joint sparse recovery(also called multiple measurement vectors, MMV) problem belongs to one important class of structured sparse recovery problems, and it has extensive applications and attracted considerable attention in recent years. This dissertation focuses on the model, algorithm design and analysis, applications of the MMV problem. The main work and innovation are embodied as follows.1. Based on simulated annealing, particle swarm optimization, and genetic algorithm, three new MMV algorithms are proposed.The MMV problem is modeled as a combinatorial optimization problem, and based on the aforementioned three computational intelligence algorithms and some existing sparse recovery algorithms, three novel algorithms are proposed. Theoretical analysis and simulation results show that the proposed algorithms has several advantages: 1? They have strong global search ability, and even can achieve the sparse recovery upper bound under certain conditions; 2? In the rank-defective case, they still perform well; 3? When the sparsity level is relatively small, they perform relatively fast; 4? They are robust to the sparsity level. These works firstly connect the computational intelligence with CS, and not only enrich the MMV algorithms but also extend the application fields of computational intelligence.2. In order to improve the ReMBo method, a novel reduced l2- l1 minimization model and a new algorithm based on ADMM are proposed.ReMBo(Reduce MMV and Boost) is an important MMV algorithm, and reduces the problem to a series of the single measurement vector problems to recover the support. It attracts much attention due to its unique idea and easy implementation. However, ReMBo performs unsatisfactorily in the noisy case and has relatively high complexity. In order to overcome these shortcomings, the ReMBo model is transformed into a reduced l2- l1 minimization model, and then a fast algorithm based on ADMM(Alternating Direction Method of Multipliers) is proposed to solve the modeled problem. Theoretical analysis validates the rationality of the model and the global convergence property of the algorithm.The simulation results on both random data and DOA(Direction-of-Arrival) estimation illustrate the efficiency of the proposed method.3. Inspired by MUSIC and some existing sparse recovery algorithms, two novel MUSIC-based algorithms which have very good balance between accuracy and speed are proposed.MUSIC(MUltiple SIgnal Classification) is an efficient MMV algorithms, and RAORMP(Rank Aware Order Recursive Matching Pursuit) is one of the MMV algorithms which have best recovery performances. However, MUSIC performs unsatisfactorily in the rank-defective case, and RA-ORMP has too high complexity. Based on a specifical analysis for MUSIC, and combine the ideas of the subspace pursuit algorithm, the compressive sampling matching pursuit algorithm, the orthogonal matching pursuit algorithm for MMV and RA-ORMP, two novel MUSIC-based algorithms are proposed. Theoretical analysis and simulation results illustrate that the two proposed algorithms perform very well while maintaining relatively low complexity. That is, these two MUSIC-based algorithms have very good balance between accuracy and speed.4. The properties of three stochastic measurement schemes in the MMV method for DOA estimation are studied.In the current MMV methods for DOA estimation, the RGS(Random Gaussian Sampling) and URS(Uniform Random Sampling) schemes are popularly used as the measurement schemes. The other two measurement schemes, UJS(Uniform Jittered Sampling)and PDS(Poisson Disk Sampling), are firstly considered in the MMV method for DOA estimation. In the perspectives of incoherence and average aperture, the properties of URS, UJS and PDS are mathematically studied. Theoretical analysis shows that UJS and PDS schemes have better properties than RGS and URS. The simulation results on DOA estimation validate the theoretical analysis and illustrate the efficiencies of UJS and PDS.