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\title{Basis Pursuit for Signal Analysis}
\author{Shaobing Chen, David Donoho, Michael Saunders \\
Stanford University, USA}

\begin{document}
\date{}
\maketitle

Various methods exist for decomposiing a sinal y into a linear combination
of dictionary elements. Overcomplete dictionaries lead to large 
under-determined system $Fw = y$. 
\vskip 2truemm

To reduce the number of coefficients, Basis Pursuit minimizes the 1-norm
of $w$. Fore denoising, a residual is allowed ( $Fw + r = y$) and the 1-norm
of $w$ is balanced against the 2-norm of $r$. This leads to large least-
squares preoblems with bound constraints. 
\vskip 2truemm

We discuss the use of barrier methods for linear and quadratic programming.
Reasonable success has been achieved with structured dictionaries (wavelets,
chirplets, etc.), for which $F$ is dense but products $FW$ and $F'v$ may be
computed efficiently.
\end{document}
bob plemmon

