Reconstructing symmetric images from their undersampled Fourier intensities

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Abstract
An algorithm is described for reconstructing a symmetric three-dimensional image from its Fourier intensity that is sampled below the Nyquist rate. The study is motivated by an image reconstruction problem in macromolecular x-ray crystallography. Application of the algorithm to simulated crystallographic problems shows that it converges to the correct solution, with no initial phase information, where algorithms currently used in crystallography fail. The algorithm is potentially useful in a variety of situations in macromolecular crystallography. The results presented also lend support to the possibility of ab initio phase retrieval in macromolecular crystallography when sufficient a priori information is available. Other applications in image reconstruction are possible.

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