Phase retrieval and phase-space tomography from incomplete data sets

The problem of signal recovery from incomplete data is investigated in the context of phase-space tomography. Particular emphasis is given to the case where only a limited number intensity measurements can be performed, which corresponds to partial coverage of the ambiguity function of the signal. Based on numerical simulations the impact of incomplete knowledge of the ambiguity function on the performance of phase-space tomography is illustrated. Several schemes to address the limited data problem are evaluated. This includes the use of prior information about the phase retrieval problem. In addition, the redundancy of phase-space representations is investigated as the means to recover the signal from partial knowledge of phase space. A generalization of deterministic phase retrieval is introduced which allows one to obtain a model based phase estimate for bandlimited functions. This allows one to use prior information for improving the phase estimate in the presence of noise.

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