1980Kam AutoCorrelation: Difference between revisions
Jump to navigation
Jump to search
Amit Singer (talk | contribs) |
Amit Singer (talk | contribs) |
||
| (One intermediate revision by the same user not shown) | |||
| Line 5: | Line 5: | ||
== Abstract == | == Abstract == | ||
If the viewing directions of the projection images are uniformly distributed, then the Fourier projection slice theorem implies that the 3D autocorrelation of the 3D reciprocal space representation of the volume with itself can be estimated from the 2D sample covariance matrix of the Fourier transformed projection images. It follows that the coefficients of the spherical harmonics expansion of the Fourier transformed volume are determined up to orthogonal matrix of size (2l+1)x(2l+1) for each order l. | |||
== Keywords == | == Keywords == | ||
Autocorrelation, 2D covariance, spherical harmonics | |||
== Links == | == Links == | ||
Latest revision as of 19:33, 18 March 2015
Citation
Z. Kam, “The reconstruction of structure from electron micrographs of randomly oriented particles,” Journal of Theoretical Biology, vol. 82, no. 1, pp. 15 – 39, 1980.
Abstract
If the viewing directions of the projection images are uniformly distributed, then the Fourier projection slice theorem implies that the 3D autocorrelation of the 3D reciprocal space representation of the volume with itself can be estimated from the 2D sample covariance matrix of the Fourier transformed projection images. It follows that the coefficients of the spherical harmonics expansion of the Fourier transformed volume are determined up to orthogonal matrix of size (2l+1)x(2l+1) for each order l.
Keywords
Autocorrelation, 2D covariance, spherical harmonics