deletions | additions       diff --git a/FigreffigSamplingVsS.tex b/FigreffigSamplingVsS.tex  deleted file mode 100644  index 07fcc27..0000000  --- a/FigreffigSamplingVsS.tex  +++ /dev/null 
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Fig.~\ref{fig:SamplingVsSparsity} depicts this relationship more explicitly, showing how the minimum number of sampled entries (\(M^*\)) required for exact recovery (relative error \( < 10^{-7}\)) scales with the sparsity of the matrix to be recovered. For comparison, the graph also compares two limiting cases: the worst-case scenario of ``no prior knowledge,'' where \emph{all} entries of the matrix must be measured, and the best-case scenario of a ``perfect oracle'' who reveals where the non-zero entries of the matrix are located, so that only those entries need to be measured. Not surprisingly, compressed sensing falls between these two limits: knowing the matrix is sparse provides a clear advantage, but there is a price to pay for not knowing \emph{a priori} where the non-zeros are located. As the graph shows, when the matrix to be recovered is very sparse (less than 10\% non-zero entries), the required sampling scales linearly with the sparsity, in accordance with the relationship \(M^* \propto \mu^2 S \log N^2\). This is the case of interest in the physical applications covered in the next section: we can make a number of measurements that scales linearly with the number of non-zero elements to be recovered, rather than a number of measurements that scales with the full size of the matrix.  diff --git a/layout.md b/layout.md  index 271856d..952e388 100644  --- a/layout.md  +++ b/layout.md 
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In_this_section_we.tex  figures/RelErrorVsSampling/ErrorVsSampling.png  figures/SamplingVsSparsity/SamplingVsSparsity.png  FigreffigSamplingVsS.tex  sectionCompressibili.tex  sectionApplication_m.tex  figures/Hessian/Hessian.png