TY - GEN

T1 - Computing the 3-D structure of viruses from unoriented cryo electron microscope images

T2 - 28th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS'06

AU - Lee, Junghoon

AU - Zheng, Yili

AU - Doerschuk, Peter C.

PY - 2006

Y1 - 2006

N2 - In a cryo electron microscopy experiment, the data is noisy 2-D projection images of the 3-D electron scattering intensity where the orientation of the projections is not known. In previous work we have developed a solution for this problem based on a maximum likelihood estimator that is computed by an expectation maximization algorithm. In the expectation maximization algorithm the expensive step is the expectation which requires numerical evaluation of 3- or 5-dimensional integrations of a square matrix of dimension equal to the number of Fourier series coefficients used to describe the 3-D reconstruction. By taking advantage of the rotational properties of spherical harmonics, we can reduce the integrations of a matrix to integrations of a scalar. The key property is that a rotated spherical harmonic can be expressed as a linear combination of the other harmonics of the same order and the weights in the linear combination factor so that each of the three factors is a function of only one of the Euler angles describing the orientation of the projection. Numerical example of the reconstructions is provided based on Nudaurelia Omega Capensis Virus.

AB - In a cryo electron microscopy experiment, the data is noisy 2-D projection images of the 3-D electron scattering intensity where the orientation of the projections is not known. In previous work we have developed a solution for this problem based on a maximum likelihood estimator that is computed by an expectation maximization algorithm. In the expectation maximization algorithm the expensive step is the expectation which requires numerical evaluation of 3- or 5-dimensional integrations of a square matrix of dimension equal to the number of Fourier series coefficients used to describe the 3-D reconstruction. By taking advantage of the rotational properties of spherical harmonics, we can reduce the integrations of a matrix to integrations of a scalar. The key property is that a rotated spherical harmonic can be expressed as a linear combination of the other harmonics of the same order and the weights in the linear combination factor so that each of the three factors is a function of only one of the Euler angles describing the orientation of the projection. Numerical example of the reconstructions is provided based on Nudaurelia Omega Capensis Virus.

UR - http://www.scopus.com/inward/record.url?scp=34047127577&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34047127577&partnerID=8YFLogxK

U2 - 10.1109/IEMBS.2006.260210

DO - 10.1109/IEMBS.2006.260210

M3 - Conference contribution

C2 - 17945721

AN - SCOPUS:34047127577

SN - 1424400325

SN - 9781424400324

T3 - Annual International Conference of the IEEE Engineering in Medicine and Biology - Proceedings

SP - 2538

EP - 2541

BT - 28th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, EMBS'06

Y2 - 30 August 2006 through 3 September 2006

ER -