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\title{Matlab code for BLO-OMP}
\author{Wenjing Liao and Albert Fannjiang}
\maketitle

\section{Spectral estimation}
The package contains the codes of Orthogonal Matching Pursuit (OMP) and Band-excluded and Locally Optimized OMP (BLO-OMP) for the spectral estimation problem:
\begin{align*}
 y_k  & = \sum_{j=1}^s x_j e^{-2\pi i k\omega_j} + e_k,
 \end{align*}
where $\omega_j \in [0,1), x_j \in \CC, k = -f_c,\ldots,f_c$ and $e \sim N(0,\sigma^2 I) + i N(0,\sigma^2 I)$.
\section{Functions}


\begin{enumerate}
\item {\bf Main:} the main function where frequencies and measurements are generated. 

\item {\bf OMP:} the code of realizing OMP \cite{OMP}. 

\item {\bf BLOOMP:} the code of realizing BLO-OMP \cite{FL}.

\item {\bf H\_dist:} the code of computing the Hausdorff distance between two frequency support set. For example, let $\supp = \{\omega_j\}$ and $\hat\supp = \{\hat\omega_j\}.$ The Hausdorff distance between $\supp$ and $\hat\supp$ is 
$$
d(\hat \supp,\supp) = \max\left\{ \max_{\hat\om\in\hat\supp }\min_{\om\in\supp}d(\hat\om,\om)\ ,\ \max_{\om\in\mathcal{S}}\min_{\hat\om\in\hat\supp }d(\hat\om,\om)\right\}.
$$
where $d(\om,\hat\om)$ is the distance between $\om$ and $\hat\om$ on Torus.


\end{enumerate}










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\bibitem{FL}
A. Fannjiang, and W. Liao, \lq\lq Coherence pattern-guided compressive sensing with unresolved grids,\rq\rq {\em SIAM Journal on Imaging Sciences} {\bf 5(1)} pp.179-202, 2012.

\bibitem{OMP}
Y. C. Pati, R. Rezaiifar and P. S. Krishnaprasad, \lq\lq Orthogonal matching pursuit: Recursive function approximation with applications to wavelet decomposition,\rq\rq {\em The Twenty-Seventh Asilomar Conference on Signals, Systems and Computers, IEEE,} 1993. 
 
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