2D fast rotational matching for image processing of biophysical data.

In 3D single particle reconstruction, which involves the translational and rotational matching of a large number of electron microscopy (EM) images, the algorithmic performance is largely dependent on the efficiency and accuracy of the underlying 2D image alignment kernel. We present a novel fast rotational matching kernel for 2D images (FRM2D) that significantly reduces the cost of this alignment. The alignment problem is formulated using one translational and two rotational degrees of freedom. This allows us to take advantage of fast Fourier transforms (FFTs) in rotational space to accelerate the search of the two angular parameters, while the remaining translational parameter is explored, within a limited range, by exhaustive search. Since there are no boundary effects in FFTs of cyclic angular variables, we avoid the expensive zero padding associated with Fourier transforms in linear space. To verify the robustness of our method, efficiency and accuracy tests were carried out over a range of noise levels in realistic simulations of EM images. Performance tests against two standard alignment methods, resampling to polar coordinates and self-correlation, demonstrate that FRM2D compares very favorably to the traditional methods. FRM2D exhibits a comparable or higher robustness against noise and a significant gain in efficiency that depends on the fineness of the angular sampling and linear search range.