| Sparse Bayesian learning (SBL) was first proposed in the machine learning literature and later applied to sparse signal recovery. It has been shown that SBL is easy to use and can recover sparse signals more accurately than the /1-norm based optimization approaches. In this dissertation, we present several Bayesian algorithms for sparse signal recovery in different applications.;Firstly, we propose a general sparse signal recovery algorithm. The computational complexities of the widely-used SBL approaches are quite high, which limit their use in large-scale problems. We propose herein an efficient Gibbs sampling approach, referred to as GS-SBL, for general sparse signal recovery problems. We show that GS-SBL provides better performance than Basis Pursuit (BP) and other SBL approaches for both small- and large-scale compressed sensing problems. For large-scale compressed sensing problems, GS-SBL can be faster than the so-called Fast Marginal Likelihood Maximization method, which is currently the fastest SBL approach among all existing SBL approaches.;Secondly, we propose a belief propagation (BP) sparse Bayesian learning algorithm, referred to as the BP-SBL, to recover sparse transform coefficients in large scale compressed sensing problems. BP-SBL is based on a widely-used hierarchical Bayesian model, which is turned into a sparse factor graph so that BP can be applied to achieve computational efficiency. The computational complexity of BP-SBL is proportional to the number of transform coefficients, allowing the algorithms to deal with large scale compressed sensing problems efficiently. Numerical examples are provided to demonstrate the effectiveness of BP-SBL.;Thirdly, we consider a radar/sonar range-Doppler imaging problem. We use the same hierarchical Bayesian model as before, but we show that this model can be turned into a hidden Markov model in range-Doppler imaging problems. To obtain the a posteriori distribution of the sparse signal vector, we can apply a modified forward-backward algorithm, which is computationally more stable and faster than the conventional forward-backward algorithm. We refer to this approach as the forward-backward sparse Bayesian learning (FB-SBL) algorithm. We show that FB-SBL performs similarly to the conventional SBL, but the former is computationally much more efficient than the latter.;Finally, we consider a multiple-input multiple-output (MIMO) radar imaging problem. MIMO radar can provide higher resolution, improved sensitivity, and increased parameter identifiability compared to more traditional phased-array radar schemes. Existing methods for target estimation, however, often fail to provide sufficiently sparse representations for MIMO angle-range-Doppler imaging. Sparse signal recovery algorithms can offer improved estimation when the scene of interest contains a limited number of targets. In this paper, we present a regularized approach to sparse signal recovery. Sparse Learning via Iterative Minimization, or SLIM, follows an /q-norm constraint (for 0 < q ≤ 1), and can thus be used to provide increased sparsity compared to existing approaches. We herein compare SLIM, through imaging examples and examination of computational complexity, to several well-known sparse methods, including the widely-used CoSaMP approach. Without significantly increasing computational cost, we show that SLIM provides superior performance for sparse MIMO radar imaging applications. (Full text of this dissertation may be available via the University of Florida Libraries web site. Please check http://www.uflib.ufl.edu/etd.html)... |
