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Jacob Sanders edited Numerical Foundation 2.tex
over 9 years ago
Commit id: 2a2d62e78d32ed522eed20eb98fbb84a74acf815
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It can be proven~\cite{Candes2006,Donoho2006,Candes2008} that the number of entries of \(B\) which must be measured in order to fully recover \(A\) by solving the BP problem in eq.~\ref{eq:bpdn} scales as
\begin{align}
\label{eq:csscaling}
M^* M \propto \mu^2 S \log N^2\ .
\end{align}
This scaling equation encapsulates the important aspects of compressed sensing applied to sparse matrices: if a proper basis is chosen, the number of entries which must be measured scales linearly with the the matrix.