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I am looking for references discussing the formal requirements for the dimension $m$ of the "measurement" mixing matrix in compressive sensing (as in ${\bf y} = M {\bf x}$ where ${\bf y} \in \mathbb{R}^ m$ and $ M \in \mathbb{R}^{ m \times n}$ with $m < n$. Here ${\bf x} \in \mathbb{R}^ n$ is the original sparse signal vector to be recovered from $\bf y$ data). Question: What is the "smallest" dimension $m$ to allow full recovery of $\bf x$, as related to the simple "sparsity measure" (i.e. 90% of entries are zero) of $\bf x$? Any references would be greatly helpful.

I am looking for references discussing the formal requirements for the dimension $m$ of the "measurement" mixing matrix in compressive sensing (as in ${\bf y} = M {\bf x}$ where ${\bf y} \in \mathbb{R}^ m$ and $ M \in \mathbb{R}^{ m \times n}$ with $m < n$. Here ${\bf x} \in \mathbb{R}^ n$ is the original sparse signal vector to be recovered from $\bf y$). Question: What is the "smallest" dimension $m$ to allow full recovery of $\bf x$, as related to the simple "sparsity measure" (i.e. 90% of entries are zero) of $\bf x$? Any references would be greatly helpful.

I am looking for references discussing the formal requirements for the dimension $m$ of the "measurement" mixing matrix in compressive sensing (as in ${\bf y} = M {\bf x}$ where ${\bf y} \in \mathbb{R}^ m$ and $ M \in \mathbb{R}^{ m \times n}$ with $m < n$. Here $\bf x$ is the original sparse signal vector to be recovered from $\bf y$ data). Question: What is the "smallest" dimension $m$ to allow full recovery of $\bf x$, as related to the simple "sparsity measure" (i.e. 90% of entries are zero) of $\bf x$? Any references would be greatly helpful.

I am looking for references discussing the formal requirements for the dimension $m$ of the "measurement" mixing matrix in compressive sensing (as in ${\bf y} = M {\bf x}$ where ${\bf y} \in \mathbb{R}^ m$ and $ M \in \mathbb{R}^{ m \times n}$ with $m < n$. Here ${\bf x} \in \mathbb{R}^ n$ is the original sparse signal vector to be recovered from $\bf y$ data). Question: What is the "smallest" dimension $m$ to allow full recovery of $\bf x$, as related to the simple "sparsity measure" (i.e. 90% of entries are zero) of $\bf x$? Any references would be greatly helpful.