Non-uniform Fourier transform based rotational alignment in single-particle Cryo-EM

In the realm of single-particle Cryo-EM's 2D align-ment problem, conventional practice necessitates interpolation as an intermediate step before applying the Fourier transform to address the in-plane rotation angle. Unfortunately, this interpo-lation process tends to introduce errors, making the process less precise. In contrast, the Non-uniform Fourier transform offers a more direct and accurate mathematical foundation for analyzing and computing the in-plane rotation angle, eliminating the need for interpolation in related problem-solving tasks. Leveraging the capabilities of the Non-uniform Fourier transform, we have developed an algorithm for in-plane rotation angle estimation. To underscore its potential and applicability in the field of single-particle Cryo-EM, we have conducted a direct comparison with the traditional Fourier transform, demonstrating the superior performance of the Non-uniform Fourier transform.