Wick–Wigner Functions and Tomographic Methods

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Abstract
The ambiguity function, occurring in radar problems, is the total Fourier transform of the Wigner function, the latter being linked with Weyl quantization of pseudodifferential operators. This remark leads to a microlocal approach for tomographic problems. First, an exact inversion formula for a distribution of objects is proved, using the symplectic invariance of the Weyl quantization. Second, asymptotic methods of microlocal analysis give an approximate inversion formula, involving fewer oscillatory integrals than in the first case.

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