2015/11/12 by Xiaoyi Gu, Gu, Xiaoyi, Deanna Needell +3
Engineering · #41A46 #68Q25 #68W20 #Algorithm #Compressed sensing #Computer science #Context (archaeology) #FOS: Computer and information sciences #FOS: Mathematics #Indoor and Outdoor Localization Technologies #Information Theory (cs.IT) #Microwave Imaging and Scattering Analysis #Numerical Analysis (math.NA) #Orthonormal basis #Physics #Projection (relational algebra) #SIGNAL (programming language) #Signal processing #Signal reconstruction #Signal recovery #Space (punctuation) #Sparse and Compressive Sensing Techniques #Telecommunications #Theoretical computer science
paper · pdf · doi:10.48550/arxiv.1511.03763
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2015/11/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/01
Compressive sensing (CS) is a new technology which allows the acquisition of signals directly in compressed form, using far fewer measurements than traditional theory dictates. Recently, many so-called signal space methods have been developed to extend this body of work to signals sparse in arbitrary dictionaries rather than orthonormal bases. In doing so, CS can be utilized in a much broader array of practical settings. Often, such approaches often rely on the ability to optimally project a signal onto a small number of dictionary atoms. Such optimal, or even approximate, projections have been difficult to derive theoretically. Nonetheless, it has been observed experimentally that conventional CS approaches can be used for such projections, and still provide accurate signal recovery. In this letter, we summarize the empirical evidence and clearly demonstrate for what signal types certain CS methods may be used as approximate projections. In addition, we provide theoretical guarantees for such methods for certain sparse signal structures. Our theoretical results match those observed in experimental studies, and we thus establish both experimentally and theoretically that these CS methods can be used in this context. \endabstract