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Xavier Andrade edited Compressed_sensing.tex
over 9 years ago
Commit id: cba7bfb14dfba0f956ddc6d139a1bfd3379ff087
deletions | additions
diff --git a/Compressed_sensing.tex b/Compressed_sensing.tex
index fa2d707..642623c 100644
--- a/Compressed_sensing.tex
+++ b/Compressed_sensing.tex
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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}
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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.