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Sparse Signal Recovery from a Mixture of Linear and Magnitude-Only Measurements
Mehmet Akçakaya1, Vahid Tarokh2
1Beth Israel Deaconess Medical Center, Harvard Medical School, Boston, MA, 02215.
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 ∈ ℂ is measured as r = Bx and y = |Cx|, where B ∈ ℂ and C ∈ ℂ 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.
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