An Approximate Expectation-Maximization for Two-Dimensional Multi-Target Detection

Abstract

A single-particle cryo-electron microscopy (cryo-EM) measurement, called a micrograph, consists of multiple two-dimensional tomographic projections of a three-dimensional molecular structure at unknown locations, taken under unknown viewing directions. All existing cryo-EM algorithmic pipelines first locate and extract the projection images, and then reconstruct the structure from the extracted images. However, if the molecular structure is small, the signal-to-noise ratio (SNR) of the data is very low, and thus accurate detection of projection images within the micrograph is challenging. Consequently, all standard techniques fail in low-SNR regimes. To recover molecular structures from measurements of low SNR, and in particular small molecular structures, we devise a stochastic approximate expectation-maximization algorithm to estimate the three-dimensional structure directly from the micrograph, bypassing locating the projection images. We corroborate our computational scheme with numerical experiments, and present successful structure recoveries from simulated noisy measurements.

Multi-target detection with rotations

“…This model is a simplified version of cryo-EM data that, informally speaking, consists of a large noisy measurement that contains many tomographic projections of a 3D density at arbitrary locations and random orientations. While the 2D model we study is not directly applicable to cryo-EM data, it does represent a step towards understanding the application of invariant feature based approaches for cyro-EM by building upon past work on multi-target detection [8,20,21,22,40]. Moreover, the model considered in this paper corresponds to a degenerate case in cryo-EM in which the molecule has a preferred orientation.…”

“…We mention that our results were recently extended, after this paper appeared online, to account for an arbitrary distribution of the target images [20]. In addition, an approximate expectation-maximization algorithm for the MTD model with rotations was developed in [22,21], and a generalized method of moments framework was designed in [40].…”