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

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. PACS numbers: 61.10.Eq, 42.30.Rx, 42.30.Wb, 81.07.Bc 1Work supported by the Department of Energy, contract DE–AC03–76SF00515. [email protected]