Tomographic reconstruction from projections with unknown view angles exploiting moment-based relationships

In this paper we describe a straightforward, yet effective method of recovering angles from a set of tomographic projections when the view-angles are completely unknown. Existing works on this problem have consistently assumed availability of projections from a large number of angles as well as made assumptions on the underlying distribution of angles to aid reconstruction. We make no such assumptions, and yet show a principled technique which is empirically validated, and quite robust to noise.

[1]  Thomas W. Parks,et al.  Adaptive principal components and image denoising , 2003, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).

[2]  Karthik Ramani,et al.  sLLE: Spherical locally linear embedding with applications to tomography , 2011, CVPR 2011.

[3]  Stephen P. Boyd,et al.  An Interior-Point Method for Large-Scale $\ell_1$-Regularized Least Squares , 2007, IEEE Journal of Selected Topics in Signal Processing.

[4]  J. Frank Three-Dimensional Electron Microscopy of Macromolecular Assemblies , 2006 .

[5]  M. L. Wood,et al.  Planar‐motion correction with use of k‐space data acquired in fourier MR imaging , 1995, Journal of magnetic resonance imaging : JMRI.

[6]  Yoram Bresler,et al.  Uniqueness of tomography with unknown view angles , 2000, IEEE Trans. Image Process..

[7]  T. W. Sze,et al.  The image moment method for the limited range CT image reconstruction and pattern recognition , 2001, Pattern Recognit..

[8]  F. Natterer The Mathematics of Computerized Tomography , 1986 .

[9]  Karthik Ramani,et al.  Estimating view parameters from random projections for Tomography using spherical MDS , 2010, BMC Medical Imaging.

[10]  Ronald R. Coifman,et al.  Graph Laplacian Tomography From Unknown Random Projections , 2008, IEEE Transactions on Image Processing.

[11]  E. Dubois,et al.  Digital picture processing , 1985, Proceedings of the IEEE.

[12]  Yoram Bresler,et al.  Feasibility of tomography with unknown view angles , 1998, Proceedings 1998 International Conference on Image Processing. ICIP98 (Cat. No.98CB36269).

[13]  H. Krapp,et al.  In Vivo Time-Resolved Microtomography Reveals the Mechanics of the Blowfly Flight Motor , 2014, PLoS biology.

[14]  Amit Singer,et al.  Two-Dimensional Tomography from Noisy Projections Taken at Unknown Random Directions , 2013, SIAM J. Imaging Sci..