Compressed Sensing and its Applications by Holger Boche Robert Calderbank Gitta Kutyniok & Jan Vybíral

Author:Holger Boche, Robert Calderbank, Gitta Kutyniok & Jan Vybíral
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(7.54)

Denote by P ℓ the ℓ × m matrix that maps a vector to its first ℓ components. Moreover, denote by the set of k-sparse signals x whose support can be recovered from with the decoder as in Proposition 3. The following theorem describes the reconstruction performance.

Theorem 6 ([37]).

Let be a matrix such that for a fixed ℓ ≤ m, the ℓ × n matrix has restricted isometry constant δ k ≤δ. Then the following holds uniformly for all .

If x has support T, q is the r-th order ΣΔ quantization of Ax, and , then

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