1980Kam AutoCorrelation

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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.


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.


Autocorrelation, 2D covariance, spherical harmonics


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