| Abstract: |
| We consider the sparse phase retrieval problem, that is, recovering an unknown $s$-sparse signal from the intensity-only measurements. Specically, we focus on the problem of recovering $x$ from the observations that are convoluted with some specfic kernel, it can also be considered as masked Fourier measurements. This model is motivated by real-world applications in optics and communications. If the convolutional kernel is generated by a random Gaussian vector and the number of subsampled measurements is on the order of $s\cdot polylog(n)$, one can recover $x$ up to a global phase. Here we discuss the behavior of sparse phase retrieval under more realistic measurements, as opposed to independent Gaussian measurements. |
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