A short note on non-convex compressed sensing

TitleA short note on non-convex compressed sensing
Publication TypeConference
Year of Publication2009
AuthorsRayan Saab, Ozgur Yilmaz
Conference NameSAMPTA technical program

In this note, we summarize the results we recently proved in\cite{SY08} on the theoretical performance guarantees of the decoders $Δ_p$. These decoders rely on $\ell^p$ minimization with $p ın (0,1)$ to recover estimates of sparse and compressible signals from incomplete and inaccurate measurements. Our guarantees generalize the results of \cite{CRT05} and \cite{Wojtaszczyk08} about decoding by $\ell_p$ minimization with $p = 1$, to the setting where $p ın (0,1)$ and are obtained under weaker sufficient conditions. We also present novel extensions of our results in \cite{SY08} that follow from the recent work of DeVore et al. in \cite{DPW08}. Finally, we show some insightful numerical experiments displaying the trade-off in the choice of $p ın (0,1]$ depending on certain properties of the input signal.

Citation Keysaab2009SAMPTAnccs