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Center for Nonlinear Studies |
In electron cryo-microscopy (cryo-EM) the goal is to reconstruct the 3D structure of a protein from many randomly oriented noisy 2D projection images. Typical noise levels for the images are around -15dB. Therefore, the resolution is not limited by the physics of the instrument, but rather the signal-to-noise ratio (SNR) of the measurements. There are various resolution measures that characterize features present in the noisy data. The most popular measure for 3D cryo-EM maps is the Fourier shell correlation (FSC) procedure, which quantifies the SNR of sinusoidal features across the entire map. Consequently, FSC produces a single resolution for the entire map and cannot assess locally varying resolution, which is commonly caused by protein flexibility. Quantifying the local resolution of a 3D map is critical for further biological study of the protein. We propose a definition of local resolution for noisy density maps which uses local sinusoidal features in a standard statistical testing framework. The local sinusoidal model is built on the "steerable filters" idea, which circumvents many practical issues such as orientation and discrete Fourier transform griding issues. The resulting method has no free algorithm parameters and is computationally efficient. Evaluating the local resolution of various 3D cryo-EM maps quantifies protein flexibility across a 4 to 40 Angstrom range of resolution. Future work will involve extending the theory to other imaging modalities, such as super-resolution microscopy, astronomy, and potentially even natural images.