Abstract
This paper proposes an exact recovery analysis of greedy algorithms for non-negative sparse representations. Orthogonal greedy algorithms such as Orthogonal Matching Pursuit (OMP) and Orthogonal Least Squares (OLS) consist of gradually increasing the solution support and updating the nonzero coefficients in the least squares sense. From a theoretical viewpoint, greedy algorithms have been extensively studied in terms of exact support recovery. In contrast, the exact recovery analysis of their non-negative extensions (NNOMP, NNOLS) remains an open problem. We show that when the mutual coherence μ is lower than 12K−1, the iterates of NNOMP / NNOLS coincide with those of OMP / OLS, respectively, the latter being known to reach K-step exact recovery. Our analysis heavily relies on a sign preservation property satisfied by OMP and OLS. This property is of stand-alone interest and constitutes our second important contribution. Finally, we provide an extended discussion of the main challenges of deriving improved analyses for correlated dictionaries.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
