cs_solvers.tex

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\lstset{language=Python}

\title[CS Solvers in Python]{Compressed Sensing Solvers in Python}
\author{Jaidev Deshpande}
\institute{Enthought, Inc}
\date{December 15, 2013}

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  \titlepage
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\section{Introduction}

\begin{frame}{Introduction - What is Compressed Sensing?}
\begin{itemize}
  \item The very fact that data can be compressed means that too many measurements were taken.
  \item Problem: Compressing White Noise
  \item What would be the sampling rate?
  \item No compression possible when $F_{s} \to \infty$
  \item Most real signals are not white noise!
\end{itemize}

\vskip 1cm
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\section{Sampling Theorem}


\begin{frame}{Nyquist Sampling Theorem}
\begin{quotation}
In order to accurately reconstruct an analog signal having a finite bandwidth $W$, it must have been sampled with atleast twice that bandwidth.
\end{quotation}
$$F_{s} >= 2W$$
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\begin{frame}{Nyquist Sampling Theorem}
\includegraphics[trim=2in 0 0 0,clip=True,scale=0.25,width=5in]{nyquist}
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\subsection{Magic Reconstruction}

\begin{frame}{The Magic Reconstruction Problem}
\begin{itemize}
\item Appeared in Cleve Moler's blog\footnote{\url{http://www.mathworks.in/company/newsletters/articles/clevescorner-compressed-sensing.html}} in 2010
\item Sequel to "The World's Simplest Impossible Problem"\footnote{\url{http://www.mathworks.in/company/newsletters/articles/the-worlds-simplest-impossible-problem.html}} from 20 years ago.
\end{itemize}
$$
\left[\begin{smallmatrix} m & n \end{smallmatrix}\right]
\left[\begin{smallmatrix} \frac{1}{2} \\ \frac{1}{2}\end{smallmatrix}\right]
 = 3
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$$
Ax = b
$$
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\begin{frame}{Underdetermined system of equations}
\lstinputlisting[language=Python, frame=single]{pinv_demo.py}
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\begin{frame}{Underdetermined system of equations}
\lstinputlisting[language=Python, frame=single]{pinv_demo2.py}
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\begin{frame}{Sparsity and the $L_{1} norm$}
\begin{itemize}
\item Why is the $L_{2}$ norm not sufficient?\footnote{\url{http://scikit-learn.org/stable/auto_examples/applications/plot_tomography_l1_reconstruction.html}}
\item LASSO = Least Absolute Shrinkage and Selection Operator
\item Also known as $L_{1}$ magic.
\item Implementations in Python:
\begin{itemize}
\item \href{http://cvxopt.org}{cvxopt} - many experimental implementations
\item \href{https://bitbucket.org/liubenyuan/pybsbl}{PyBSBL} - Amazing use of the scipy.sparse module
\item \href{http://code.soundsoftware.ac.uk/projects/pycsalgos}{PyCSAlgos} - WIP, simple adaptations of experimental MATLAB code.
\item \href{http://aspics.krzakala.org/}{ASPICS} - Badly documented, very unreadable.
\item \href{https://sites.google.com/site/stephanegchretien/twostage}{Two Stage $L_{1}$ approach} - Stephane Chreitin
\item \href{https://sites.google.com/site/stephanegchretien/twostage}{SPAMS} (SParse Modeling Software) - Alexandre Gramfort - Best of the lot, sparsely documented, seems short-lived.
\end{itemize}
\end{itemize}
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\begin{frame}{Summary}
\begin{itemize}
\item Compressed sensing software remains largely inaccessible to Pythonistas
\item Too much bad code
\item Very hot topic in signal processing / data compression
\item Perfect opportunity to dive in!
\item How?
\end{itemize}
\end{frame}

\begin{frame}{Come, contribute to scikit-signal}
\begin{itemize}
\item \url{http://github.com/scikit-signal}
\item Started by David Cournapeau and yours truly in mid 2012
\item Most work focuses on time-frequency analysis, need to diversify
\item Looking for developers!
\end{itemize}
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\begin{frame}
Slides hosted at \url{https://gist.github.com/jaidevd/7967600}
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