Before revision: The turnpike problem of recovering a set of points in \mathbb{R in R^d from intensity-only measurements in dimension d \geq 2. Phase retrieval can be equivalently formulated as the problem of recovering a signal from its autocorrelation, which is in turn directly } related to the phase retrieval problem of recovering a signal from magnitude-only measurements of its Fourier transform.
After revision: The turnpike problem of recovering a sparse signal \mathbf{x in R^d from intensity-only measurements in dimension d \geq 2. Phase retrieval can be equivalently formulated as the problem of recovering a signal from its autocorrelation, which is in turn directly } related to the phase retrieval problem of recovering a signal from magnitude-only measurements of its Fourier transform.