Non-uniform Fourier transform based image classification in single-particle Cryo-EM

In the single-particle Cryo-EM projection image classification, it is a common practice to apply the Fourier transform to the images and extract rotation-invariant features in the frequency domain. However, this process involves interpolation, which can reduce the accuracy of the results. In contrast, the non-uniform Fourier transform provides more direct and accurate computation of rotation-invariant features without the need for interpolation in the computation process. Leveraging the capabilities of the non-uniform discrete Fourier transform (NUDFT), we have developed an algorithm for the rotation-invariant classification. To highlight its potential and applicability in the field of single-particle Cryo-EM, we conducted a direct comparison with the traditional Fourier transform and other methods, demonstrating the superior performance of the NUDFT.