Sparse Signal Recovery and Acquisition with Graphical Models

A Tutorial on Sparse Signal Acquisition and Recovery with Graphical Models

Sparse signal recovery with unknown signal sparsity

In this paper, we proposed a detection-based orthogonal match pursuit (DOMP) algorithm for compressive sensing. Unlike the conventional greedy algorithm, our proposed algorithm does not rely on the priori knowledge of the signal sparsity, which may not be known for some application, e.g., sparse multipath channel estimation. The DOMP runs binary hypothesis on the residual vector of OMP at each ...

Sparse Nonparametric Graphical Models

We present some nonparametric methods for graphical modeling. In the discrete case, where the data are binary or drawn from a finite alphabet, Markov random fields are already essentially nonparametric, since the cliques can take only a finite number of values. Continuous data are different. The Gaussian graphical model is the standard parametric model for continuous data, but it makes distribu...

Sparse Matrix Graphical Models

Matrix-variate observations are frequently encountered in many contemporary statistical problems due to a rising need to organize and analyze data with structured information. In this paper, we propose a novel sparse matrix graphical model for this type of statistical problems. By penalizing respectively two precision matrices corresponding to the rows and columns, our method yields a sparse ma...

Greedy Sparse Signal Recovery with Tree Pruning

Recently, greedy algorithm has received much attention as a cost-effective means to reconstruct the sparse signals from compressed measurements. Much of previous work has focused on the investigation of a single candidate to identify the support (index set of nonzero elements) of the sparse signals. Wellknown drawback of the greedy approach is that the chosen candidate is often not the optimal ...