Theory And Applications Of The Fast Block Sparse Bayesian Learning Algorithm

Block sparsity is a typical structure in nature and information space, which widely exists in applications such as Radar, image processing and biomedical engineering. Compared with the traditional spike sparse structure, the block sparse structure can model the physical information and the spatial distribution of signals, which may improve the quality of signal recoveries. Currently, Block Sparse Bayesian Learning(BSBL) has become an active direction in the theory of Compressive Sensing(CS). Most of the BSBL algorithms developed so far focus on extending the models of the block structure. But these algorithms are complex and have high computational requirements, which limit its use in real-time, large-scale sparse reconstruction problems.This thesis studied the optimization of the BSBL method and extended the signal models for more applications. We proposed novel algorithms based on the block sparse structure of single measurement vector(SMV) model, the time-varying structure of multiple measurement vector(MMV) model, the spatiotemporal MMV model and the quantized CS model respectively. We applied the proposed algorithms on source localization and single/multi-channel physiological data compression. We also used quantized CS as a low-energy data compressor for wireless telemonitoring and analyzed its low-resource,low-energy properties in FPGA. The major contributions of the thesis are:1. We proposed a fast block sparse Bayesian learning algorithm(BSBL-FM) for the single measurement vector model. The BSBL-FM method adopts the Fast Marginalized Likelihood Maximization(FMLM) method to optimize the BSBL framework. It is extensible and can incorporate different types of correlation models. Experiment results showed that BSBL-FM had nearly the same reconstruction performance as traditional BSBL methods but was about 6 times faster. We also extended the BSBL-FM algorithm to recover complex-valued block sparse signals. The BSBL-FM algorithm can use the correlated structure of complex-valued signals to improve the quality and efficiency. In the experiment on complex-valued signals, BSBL-FM outperformed BSBL-BO and was nearly 110 times faster.2. We developed fast temporal-smooth Bayesian learning algorithm(TSBL-FM)and spatiotemporal fast Bayesian learning algorithm(STSBL-FM) for the multiple measurement vector model. The proposed algorithms can use the correlated structure in the temporal domain and the block sparse structure in the spatial domain to improve the quality and efficiency of sparse reconstructions. In the experiments on source localization and multiple channels physiological data compression, TSBL-FM and STSBL-FM had nearly the same recoveries as traditional BSBL algorithms but were about 27 times and24 times faster respectively. Meanwhile, TSBL-FM and STSBL-FM algorithms can be implemented in parallel. These algorithms do not need to calculate the inverse of large matrices and have high efficiency and low storage requirements, which are especially suited for real-time hardware implementations.3. We developed a Bayesian De-quantization(BDQ) algorithm for the quantized CS model and applied quantized CS as a low-energy data compressor for wireless telemonitoring. For the quantized CS model, we developed a recovery algorithm that can exploit both the correlated structures of physiological signals and the model of quantization errors. We also applied quantized CS as a low-energy data compressor for wireless telemonitoring. In the experiments, the BDQ algorithm can fidelity recover physiological signals from compressed measurements with only 2 bits quantization. Its Reconstruction Signal-to-Noise Ratio(RSNR) was approximately 3d B better than state-of-the-art. For the application on remote heart rate monitoring, we may transmit N bits instead of N samples by suitable tuning the parameters of quantized CS and using the BDQ algorithm,which greatly reduced the power consumption and the transmission bit-budget.4. We systematically evaluated data compression via Compressive Sensing using real-life physiological signals, we also implemented CS in FPGA and proved its lowenergy property. In the experiments, different sensing matrices, different compression ratios and different recovery algorithms were used to evaluate the quality of signal recoveries and task orientated metrics. We implemented the CS-based data compressor and a traditional DWT-based data compressor in FPGA and proved that, the CS-based compressor was low-energy, low-resource consuming and supported on-line compression.