Vector-valued, quaternion, and complex phase retrieval are characterized by the non-existence of decompositions f=u+v with orthogonal measurements, and graph vector fields are recoverable up to rotation when their associated simplex graph is connected.
Local and Global Phaseless Sampling in Real Spline Spaces
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abstract
We study the recovery of functions in real spline spaces from unsigned sampled values. We consider two types of recovery. The one is to recover functions locally from finitely many unsigned samples. And the other is to recover functions on the whole line from infinitely many unsigned samples. In both cases, we give characterizations for a sequence of distinct points to be a phaseless sampling sequence, at which any nonseparable function is determined up to a sign on an interval or on the whole line by its unsigned sampled values. Moreover, for the case of local recovery, we also study the almost phaseless sampling and give a necessary and sufficient condition for a sequence of points to admit local recovery for almost all functions.
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Phase retrieval of complex and vector-valued functions
Vector-valued, quaternion, and complex phase retrieval are characterized by the non-existence of decompositions f=u+v with orthogonal measurements, and graph vector fields are recoverable up to rotation when their associated simplex graph is connected.