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3-D image reconstruction from averaged Fourier transform magnitude by parameter estimation

An object model and estimation procedure for three-dimensional (3-D) reconstruction of objects from measurements of the spherically averaged Fourier transform magnitudes is described. The motivating application is the 3-D reconstruction of viruses based on solution X-ray scattering data. The object model includes symmetry, positivity and support constraints and has the form of a truncated orthonormal expansion and the parameters are estimated by maximum likelihood methods. Successful 3-D reconstructions based on synthetic and experimental measurements from Cowpea mosaic virus are described.