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On the symmetries of the synchronization problem in Cryo-EM: Multi-Frequency Vector Diffusion Maps on the Projective Plane
Gabriele Cesa · Arash Behboodi · Taco Cohen · Max Welling

Tue Nov 29 09:00 AM -- 11:00 AM (PST) @ Hall J #705

Cryo-Electron Microscopy (Cryo-EM) is an important imaging method which allows high-resolution reconstruction of the 3D structures of biomolecules. It produces highly noisy 2D images by projecting a molecule's 3D density from random viewing directions. Because the projection directions are unknown, estimating the images' poses is necessary to perform the reconstruction. We focus on this task and study it under the group synchronization framework: if the relative poses of pairs of images can be approximated from the data, an estimation of the images' poses is given by the assignment which is most consistent with the relative ones.In particular, by studying the symmetries of cryo-EM, we show that relative poses in the group O(2) provide sufficient constraints to identify the images' poses, up to the molecule's chirality. With this in mind, we improve the existing multi-frequency vector diffusion maps (MFVDM) method: by using O(2) relative poses, our method not only predicts the similarity between the images' viewing directions but also recovers their poses. Hence, we can leverage all input images in a 3D reconstruction algorithm by initializing the poses with our estimation rather than just clustering and averaging the input images. We validate the recovery capabilities and robustness of our method on randomly generated synchronization graphs and a synthetic cryo-EM dataset.

Author Information

Gabriele Cesa (Qualcomm AI Research University of Amsterdam)
Arash Behboodi (Qualcomm AI Research)
Taco Cohen (Qualcomm AI Research)

Taco Cohen is a machine learning research scientist at Qualcomm AI Research in Amsterdam and a PhD student at the University of Amsterdam, supervised by prof. Max Welling. He was a co-founder of Scyfer, a company focussed on active deep learning, acquired by Qualcomm in 2017. He holds a BSc in theoretical computer science from Utrecht University and a MSc in artificial intelligence from the University of Amsterdam (both cum laude). His research is focussed on understanding and improving deep representation learning, in particular learning of equivariant and disentangled representations, data-efficient deep learning, learning on non-Euclidean domains, and applications of group representation theory and non-commutative harmonic analysis, as well as deep learning based source compression. He has done internships at Google Deepmind (working with Geoff Hinton) and OpenAI. He received the 2014 University of Amsterdam thesis prize, a Google PhD Fellowship, ICLR 2018 best paper award for “Spherical CNNs”, and was named one of 35 innovators under 35 in Europe by MIT in 2018.

Max Welling (Microsoft Research AI4Science / University of Amsterdam)

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