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.