2015/07/17 by Ritwik Giri, Bhaskar D. Rao
Computer Science · Engineering · Mathematics · #Algorithm #Artificial intelligence #Bayesian probability #Blind Source Separation Techniques #Compressed sensing #Computer science #Digital signal processing #Gaussian Processes and Bayesian Inference #Mathematics #Pattern recognition (psychology) #Physics #SIGNAL (programming language) #Scale (ratio) #Signal processing #Signal reconstruction #Signal recovery #Sparse and Compressive Sensing Techniques #Type (biology) #cs.LG #stat.ML
paper · pdf · doi:10.1109/tsp.2016.2546231
Under Review
arxiv created 2015/07/17 · openalex publication_date 2016/03/23 · arxiv updated 2016/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
In this paper, we propose a generalized scale mixture family of distributions, namely the Power Exponential Scale Mixture (PESM) family, to model the sparsity inducing priors currently in use for sparse signal recovery (SSR). We show that the successful and popular methods such as LASSO, Reweighted ℓ1and Reweighted ℓ2methods can be formulated in an unified manner in a maximum a posteriori (MAP) or Type I Bayesian framework using an appropriate member of the PESM family as the sparsity inducing prior. In addition, exploiting the natural hierarchical framework induced by the PESM family, we utilize these priors in a Type II framework and develop the corresponding EM based estimation algorithms. Some insight into the differences between Type I and Type II methods is provided and of particular interest in the algorithmic development is the Type II variant of the popular and successful reweighted ℓ1method. Extensive empirical results are provided, and they show that the Type II methods exhibit better support recovery than the corresponding Type I methods.