2012/08/01 by Adam S. Charles, Christopher J. Rozell, Charles, Adam S. +1 · 2 citations
Computer Science · Engineering · Mathematics · #Applications (stat.AP) #Bayesian Methods and Mixture Models #Blind Source Separation Techniques #Control Systems and Identification #FOS: Computer and information sciences #FOS: Mathematics #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.AP #stat.TH
paper · pdf · doi:10.48550/arxiv.1208.0325
This paper has been withdrawn in lieu of a more complete paper containing additional results
openalex publication_date 2012/08/01 · arxiv created 2015/07/22 · arxiv updated 2015/07/23 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28
Signal estimation from incomplete observations improves as more signal structure can be exploited in the inference process. Classic algorithms (e.g., Kalman filtering) have exploited strong dynamic structure for time-varying signals while modern work has often focused on exploiting low-dimensional signal structure (e.g., sparsity in a basis) for static signals. Few algorithms attempt to merge both static and dynamic structure to improve estimation for time-varying sparse signals (e.g., video). In this work we present a re-weighted l1 dynamic filtering scheme for causal signal estimation that utilizes both sparsity assumptions and dynamic structure. Our algorithm leverages work on hierarchical Laplacian scale mixture models to create a dynamic probabilistic model. The resulting algorithm incorporates both dynamic and sparsity priors in the estimation procedure in a robust and efficient algorithm. We demonstrate the results in simulation using both synthetic and natural data.