Information recovery in missing angular data cases: an approach by the convex projections method in three dimensions

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Abstract
SUMMARY: We have studied the method of projections on to convex sets (POCS) for the restoration of three‐dimensional signals, especially applied for the degraded information obtained in three‐dimensional (3‐D) reconstructions by electron microscopy due to the limited tilting angular range of the sample that is obtainable in practice. A computer generated specimen has been used as a test object. Several noise levels were added to the specimen, obtaining signal‐to‐noise ratios (signal power/noise power) of between 12 and 0·5 dB. Different missing data angular regions of 30° and 10° zenithal angle have been considered. Our results illustrate the possibilities of POCS to restore incomplete 3‐D data in the absence and the presence of noise, and offer ways for further applications to improve the quality of 3‐D reconstructions based on real data.