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Open AccessReport10.2172/812989

3D Image Reconstruction: Hamiltonian Method for Phase Recovery

R. Blankenbecler-2003-03-13
2

TL;DRAbstract

The problem of reconstructing a positive semi-definite 3-D image from the measurement of the magnitude of its 2-D fourier transform at a series of orientations is explored. The phase of the fourier transform is not measured. The algorithm developed here utilizes a Hamiltonian, or cost function, that at its minimum provides the solution to the stated problem. The energy function includes both data and physical constraints on the charge distribution or image.

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The problem of reconstructing a positive semi-definite 3-D image from the measurement of the magnitude of its 2-D fourier transform at a series of orientations is explored. The phase of the fourier transform is not measured. The algorithm developed here utilizes a Hamiltonian, or cost function, that at its minimum provides the solution to the stated problem. The energy function includes both data and physical constraints on the charge distribution or image.

Keywords

Fourier transformHamiltonian (control theory)Fourier seriesImage (mathematics)Phase correlationMathematicsPhase functionAlgorithm

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