Reliable Function Approximation and Estimation
Abstract
Exploiting the latent structure in many real-world signals can dramatically increase algorithmic robustness to both noise and missing data. The theory of compressed sensing shows that if a signal of interest is sparse --- well-approximated by some small subset of a dictionary of basis elements --- then the signal can be acquired from a reduced number of measurements and reconstructed using efficient convex programming techniques. However, the standard compressed sensing theory is valid only for a restrictive set of dictionaries, limiting the scope of applications. In this award, the PI developed a range of reliable and structure-aware sampling theorems based on the weighted sparsity model for real-world systems which are governed mostly by low-order interactions. The weighted sparsity model allows for more freedom than linear regression butprovides sufficient structure to extend compressed sensing results to a wide class of infinite-dimensional problems. We discuss four key application domains for the methods developed in this project arising from this project: uncertainty quantification, image processing, matrix completion, and stochastic optimization.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 16, 2016
- Accession Number
- AD1013972
Entities
People
- Rachel A. Ward
Organizations
- University of Texas at Austin