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Below is the title and the abstract of my presentation.
Sparse Signal Recovery Exploiting Spatiotemporal Correlation
Sparse signal recovery algorithms have significant impact on many fields, including signal and image processing, information theory, statistics, data sampling and compression, and neuroimaging. The core of sparse signal recovery algorithms is to find a solution to an underdetermined inverse system of equations, where the solution is expected to be sparse or approximately sparse. Motivated by practical problems, numerous algorithms have been proposed. However, most algorithms ignore the correlation among nonzero entries of a solution, which is often encountered in a practical problem. Thus, it is unclear how this correlation affects an algorithm's performance and whether the correlation is harmful or beneficial.
This work aims to design algorithms which can exploit a variety of correlation structures in solutions and reveal the impact of these correlation structures on algorithms' recovery performance.
To achieve this, a block sparse Bayesian learning (BSBL) framework is proposed. Based on this framework, a number of sparse Bayesian learning (SBL) algorithms are derived to exploit intra-block correlation in a canonical block sparse model, temporal correlation in a canonical multiple measurement vector model, spatiotemporal correlation in a spatiotemporal sparse model, and local temporal correlation in a canonical time-varying sparse model. Several optimization approaches are employed in the algorithm development, including the expectation-maximization method, the bound-optimization method, and the fixed-point method. Experimental results show that these algorithms significantly outperform existing algorithms.
With these algorithms, we find that different correlation structures affect the quality of estimated solutions to different degrees. However, if these correlation structures are present and exploited, algorithms' performance can be largely improved. Inspired by this, we connect these algorithms to Group-Lasso type algorithms and iterative reweighted $\ell_1$ and $\ell_2$ algorithms, and suggest strategies to modify them to exploit the correlation structures for better performance.
The derived SBL algorithms have been used with considerable success in various challenging applications such as wireless telemonitoring of raw physiological signals and prediction of cognition levels of patients from their neuroimaging measures. In the former application, the derived SBL algorithms are the only algorithms so far that achieve satisfactory results. This is because raw physiological signals are neither sparse in the time domain nor sparse in any transformed domains, while the derived SBL algorithms can maintain robust performance for these signals. In the latter application, the derived SBL algorithms achieved the highest prediction accuracy on common datasets, compared to published results. This is because the BSBL framework provides flexibility to exploit both correlation structures and nonlinear relationship between response variables and predictor variables in regression models.