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Results tagged with compressed-sensing
Search options questions only
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user 41123
4
votes
2
answers
277
views
Can one always find sparse solutions to an $\ell^1$-minimization problem?
Consider $A\in\mathbb{R}^{m \times N}$ and $b \in \mathbb{R}^m$, with $m<N$. Is it true that the optimization problem
$$\min \|x\|_1 \quad \text{s.t.} \quad A x = b,$$
admits an $m$-sparse solution in …
- 837
4
votes
1
answer
629
views
Can sparse matrices satisfy the Null Space Property?
Definition A matrix $A \in \mathbb{C}^{m \times N}$ with $m < N$ satisfies the Null Space Property (NSP) of order $s$ if
$$\|x_S\|_1 < \|x_{\bar{S}}\|_1, \quad \forall x \in \ker A \setminus \{0\}, \ …
- 837