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.
Bibliographical notePublisher Copyright:
© 2015 IEEE.
Copyright 2015 Elsevier B.V., All rights reserved.
- Compressed sensing
- Phase retrieval
- Sparse phase retrieval
- Sparse signals