M. S. Gelfand and A. B. Goncharov, "Spatial rotational alignment of identical particles given their projections," in Mathematical Problems of Tomography, number 81 in Translations of Mathematical Monographs, pp. 97--122. Amer. Math. Soc., 1990.  Home/Search   Document Not in Database   Summary   Related Articles

....in which projections are acquired at random and unknown orientations in the plane of the object, and then the projections are postprocessed to extract the orientation information necessary to reconstruct the object. Previous work has addressed the determination of projection angles using moments [9, 10]. Although primarily focused on the 3D problem, both of these authors have addressed the 2D problem which we examine. However, neither author provides a theoretical justification for their claims and conjectures of unique recovery of the projection angles. Indeed, based on the results derived in ....

....for the angle recovery problem. Specific conditions, along with geometric interpretations of these conditions, are detailed in Section V. The case in which the projections are shifted by an unknown amount is treated in Section VI. The relationship between our results and the claims made in [9, 10] is examined in Section VII. Conclusions are discussed in Section VIII. II. Problem Formulation Background material on the tomographic problem can be found in many sources, including [1, 11] and the references therein. The image or object f we consider, is an element of the space L 2 (B 2 ) of ....

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M. S. Gelfand and A. B. Goncharov, "Spatial rotational alignment of identical particles given their projections," in Mathematical Problems of Tomography, number 81 in Translations of Mathematical Monographs, pp. 97--122. Amer. Math. Soc., 1990.

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