restricted isometry property

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(k, δ)

$G$ has the $(k, δ)$ restricted isometry property (RIP) if for all $x \neq 0$ with $| | x | |_{0} \leq k$ we have

(1-\delta)\lvert \lvert x \rvert \rvert {#2} \leq \lvert \lvert Gx \rvert \rvert {#2} \leq (1+\delta) \lvert \lvert x \rvert \rvert {#2}

Remarks

Note

The RIP is more useful than the NSP for algorithms, especially when noise is added to $y = G x ⟹ y = G x + ε$ (see restricted isometry implies nullspace property)

File	Last Modified
dimension requirements for gaussian random matrix to be a restricted isometry with high probability	2025-09-10
Random Matrix Lecture 05	2025-09-11
restricted isometry implies nullspace property	2025-09-10

restricted isometry property

Remarks

References

See Also

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