# A short note on non-convex compressed sensing

 Title A short note on non-convex compressed sensing Publication Type Conference Year of Publication 2009 Authors Rayan Saab, Ozgur Yilmaz Conference Name SAMPTA technical program Organization SAMPTA Keywords Presentation Abstract 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. URL https://slim.gatech.edu/Publications/Public/Conferences/SAMPTA/2009/saab09SAMPTAnccs/saab09SAMPTAnccs.pdf Citation Key saab2009SAMPTAnccs