Abstract
The problem of reconstructing a sparse signal vector from magnitude-only measurements (a.k.a. compressive phase retrieval) emerges in diverse applications, but it is NP-hard in general. Building on recent advances in nonconvex optimization, this paper puts forth a new algorithm that is termed compressive reweighted amplitude flow (CRAF) and abbreviated as CRAF, for compressive phase retrieval. Specifically, CRAF operates in two stages. The first stage seeks a sparse initial guess via a new spectral procedure. In the second stage, CRAF implements a few hard thresholding based iterations using reweighted gradients. When there are sufficient measurements, CRAF provably recovers the underlying signal vector exactly with high probability under suitable conditions. Moreover, its sample complexity coincides with that of state-of-the-art procedures. Finally, numerical tests showcase improved performance of the new spectral initialization, as well as improved exact recovery relative to competing alternatives. Empirically, the number of measurements required for exact recovery by CRAF is about 40% less than those of competing alternatives in our experiments using real images.
| Original language | English (US) |
|---|---|
| Article number | 8424911 |
| Pages (from-to) | 5029-5040 |
| Number of pages | 12 |
| Journal | IEEE Transactions on Signal Processing |
| Volume | 66 |
| Issue number | 19 |
| DOIs | |
| State | Published - Oct 1 2018 |
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Keywords
- Nonconvex optimization
- iteratively reweighting
- linear convergence to the global optimum
- model-based hard thresholding
Cite this
Compressive Phase Retrieval via Reweighted Amplitude Flow. / Zhang, Liang; Wang, Gang; Giannakis, Georgios B.; Chen, Jie.
In: IEEE Transactions on Signal Processing, Vol. 66, No. 19, 8424911, 01.10.2018, p. 5029-5040.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Compressive Phase Retrieval via Reweighted Amplitude Flow
AU - Zhang, Liang
AU - Wang, Gang
AU - Giannakis, Georgios B.
AU - Chen, Jie
PY - 2018/10/1
Y1 - 2018/10/1
N2 - The problem of reconstructing a sparse signal vector from magnitude-only measurements (a.k.a. compressive phase retrieval) emerges in diverse applications, but it is NP-hard in general. Building on recent advances in nonconvex optimization, this paper puts forth a new algorithm that is termed compressive reweighted amplitude flow (CRAF) and abbreviated as CRAF, for compressive phase retrieval. Specifically, CRAF operates in two stages. The first stage seeks a sparse initial guess via a new spectral procedure. In the second stage, CRAF implements a few hard thresholding based iterations using reweighted gradients. When there are sufficient measurements, CRAF provably recovers the underlying signal vector exactly with high probability under suitable conditions. Moreover, its sample complexity coincides with that of state-of-the-art procedures. Finally, numerical tests showcase improved performance of the new spectral initialization, as well as improved exact recovery relative to competing alternatives. Empirically, the number of measurements required for exact recovery by CRAF is about 40% less than those of competing alternatives in our experiments using real images.
AB - The problem of reconstructing a sparse signal vector from magnitude-only measurements (a.k.a. compressive phase retrieval) emerges in diverse applications, but it is NP-hard in general. Building on recent advances in nonconvex optimization, this paper puts forth a new algorithm that is termed compressive reweighted amplitude flow (CRAF) and abbreviated as CRAF, for compressive phase retrieval. Specifically, CRAF operates in two stages. The first stage seeks a sparse initial guess via a new spectral procedure. In the second stage, CRAF implements a few hard thresholding based iterations using reweighted gradients. When there are sufficient measurements, CRAF provably recovers the underlying signal vector exactly with high probability under suitable conditions. Moreover, its sample complexity coincides with that of state-of-the-art procedures. Finally, numerical tests showcase improved performance of the new spectral initialization, as well as improved exact recovery relative to competing alternatives. Empirically, the number of measurements required for exact recovery by CRAF is about 40% less than those of competing alternatives in our experiments using real images.
KW - Nonconvex optimization
KW - iteratively reweighting
KW - linear convergence to the global optimum
KW - model-based hard thresholding
UR - http://www.scopus.com/inward/record.url?scp=85051006150&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85051006150&partnerID=8YFLogxK
U2 - 10.1109/TSP.2018.2862395
DO - 10.1109/TSP.2018.2862395
M3 - Article
AN - SCOPUS:85051006150
VL - 66
SP - 5029
EP - 5040
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
SN - 1053-587X
IS - 19
M1 - 8424911
ER -