Three-dimensional image reconstruction. II. Hamiltonian method for phase recovery

The problem of reconstructing a positive semidefinite three-dimensional (3D) image from the measurement of the magnitude of its 2D 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.