Abstract
We consider the problem of exact sparse signal recovery from a combination of linear and magnitude-only (phaseless) measurements. A k-sparse signal x in ∈ ℂn is measured as r = Bx and y = |Cx|, where B in ∈ ℂm1 × n and ∈ ℂm2 × n are measurement matrices and |·| is the element-wise absolute value. We show that if max(2m1,1) + m2 ≥ 4k - 1, then a set of generic measurements are sufficient to recover every k-sparse x exactly, establishing the trade-off between the number of linear and magnitude-only measurements.
Original language | English (US) |
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Article number | 7010925 |
Pages (from-to) | 1220-1223 |
Number of pages | 4 |
Journal | IEEE Signal Processing Letters |
Volume | 22 |
Issue number | 9 |
DOIs | |
State | Published - Sep 1 2015 |
Bibliographical note
Publisher Copyright:© 2015 IEEE.
Keywords
- Compressed sensing
- Phase retrieval
- Sparse phase retrieval
- Sparse signals