Xavier Andrade edited Compressed_sensing.tex  over 9 years ago

Commit id: cba7bfb14dfba0f956ddc6d139a1bfd3379ff087

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%  \begin{equation}  \label{eq:bp}  \min_{\vec{\tau}} |\vec{\tau}|_1 \min_{\vec{\sigma}} |\vec{\sigma}|_1  \quad \textrm{subject to}\quad \mat{F}\vec{f}=\ \mat{\mathcal{F}}\vec{\sigma}=\  vec{\tau}\ ,  \end{equation}  %  where \(|\tau|_1=\sum_k|\tau_k|\) \(|\sigma|_1=\sum_k|\sigma|\)  is the standard 1-norm). 1-norm. \(\tau\) is the discretized time series and \(\sigma\) is the frequency resolved function, the spectrum, that we want to calculate. \(\mathcal{F}\) is a matrix of Fourier coefficients.