Recovery Conditions in Weighted Sparse Phase Retrieval via Weighted ℓq(0
Autor:
Huo, Haiye, Xiao, Li
Předmět:
Zdroj:
Circuits, Systems & Signal Processing; Sep2024, Vol. 43 Issue 9, p5878-5896, 19p
Abstrakt:
In this paper, we generalize the conditions for the exact or stable recovery of weighted k-sparse signals in weighted sparse phase retrieval in our previous work [11] from the weighted ℓ 1 minimization to the weighted ℓ q (0 < q ≤ 1) minimization in a broad sense. Specifically, we first present that the weighted null space property (WNSP) is a sufficient and necessary condition to guarantee the exact recovery of a weighted k-sparse signal from its noiseless phaseless measurements via the weighted ℓ q (0 < q ≤ 1) minimization in both the real and complex cases. In addition, we establish a general strong weighted restricted isometry property (SWRIP) condition for the stable recovery of a weighted k-sparse signal from its noisy phaseless measurements via the weighted ℓ q (0 < q ≤ 1) minimization in the real case. [ABSTRACT FROM AUTHOR]
Databáze:
Complementary Index
Externí odkaz:
| Autor: | Huo, Haiye, Xiao, Li |
|---|---|
| Předmět: | |
| Zdroj: | Circuits, Systems & Signal Processing; Sep2024, Vol. 43 Issue 9, p5878-5896, 19p |
| Abstrakt: | In this paper, we generalize the conditions for the exact or stable recovery of weighted k-sparse signals in weighted sparse phase retrieval in our previous work [11] from the weighted ℓ 1 minimization to the weighted ℓ q (0 < q ≤ 1) minimization in a broad sense. Specifically, we first present that the weighted null space property (WNSP) is a sufficient and necessary condition to guarantee the exact recovery of a weighted k-sparse signal from its noiseless phaseless measurements via the weighted ℓ q (0 < q ≤ 1) minimization in both the real and complex cases. In addition, we establish a general strong weighted restricted isometry property (SWRIP) condition for the stable recovery of a weighted k-sparse signal from its noisy phaseless measurements via the weighted ℓ q (0 < q ≤ 1) minimization in the real case. [ABSTRACT FROM AUTHOR] |
| Databáze: | Complementary Index |
| Externí odkaz: |
|
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