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		<title>WikiSysop: Created page with &quot;== Citation ==  Cesa, G., Pratik, K. and Behboodi, A. 2023. Equivariant self-supervised deep pose estimation for Cryo EM. Topological, Algebraic and Geometric Learning Workshops 2023 (2023), 21–36.  == Abstract ==  Reconstructing the 3D volume of a molecule from its differently oriented 2D projections is the central problem of Cryogenic Electron Microscopy (cryo-EM), one of the main techniques for macro-molecule imaging. Because the orientations are unknown, the estima...&quot;</title>
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		<updated>2025-09-25T05:56:29Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;== Citation ==  Cesa, G., Pratik, K. and Behboodi, A. 2023. Equivariant self-supervised deep pose estimation for Cryo EM. Topological, Algebraic and Geometric Learning Workshops 2023 (2023), 21–36.  == Abstract ==  Reconstructing the 3D volume of a molecule from its differently oriented 2D projections is the central problem of Cryogenic Electron Microscopy (cryo-EM), one of the main techniques for macro-molecule imaging. Because the orientations are unknown, the estima...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;== Citation ==&lt;br /&gt;
&lt;br /&gt;
Cesa, G., Pratik, K. and Behboodi, A. 2023. Equivariant self-supervised deep pose estimation for Cryo EM. Topological, Algebraic and Geometric Learning Workshops 2023 (2023), 21–36.&lt;br /&gt;
&lt;br /&gt;
== Abstract ==&lt;br /&gt;
&lt;br /&gt;
Reconstructing the 3D volume of a molecule&lt;br /&gt;
from its differently oriented 2D projections is&lt;br /&gt;
the central problem of Cryogenic Electron Microscopy&lt;br /&gt;
(cryo-EM), one of the main techniques&lt;br /&gt;
for macro-molecule imaging. Because the orientations&lt;br /&gt;
are unknown, the estimation of the images’&lt;br /&gt;
poses is essential to solve this inverse problem.&lt;br /&gt;
Typical methods either rely on synchronization,&lt;br /&gt;
which leverages the estimated relative poses of&lt;br /&gt;
the images to constrain their absolute ones, or&lt;br /&gt;
jointly estimate the poses and the 3D density of&lt;br /&gt;
the molecule in an iterative fashion. Unfortunately,&lt;br /&gt;
synchronization methods don’t account&lt;br /&gt;
for the complete images’ generative process and,&lt;br /&gt;
therefore, achieve lower noise robustness. In the&lt;br /&gt;
second case, the iterative joint optimization suffers&lt;br /&gt;
from convergence issues and a higher computational&lt;br /&gt;
cost, due to the 3D reconstruction steps.&lt;br /&gt;
In this work, we directly estimate individual poses&lt;br /&gt;
with an equivariant deep graph network trained&lt;br /&gt;
using a self-supervised loss, which enforces agreement&lt;br /&gt;
in Fourier domain of image pairs along the&lt;br /&gt;
common lines defined by their poses. In particular,&lt;br /&gt;
the equivariant design turns out essential for&lt;br /&gt;
the proper convergence. As a result, our method&lt;br /&gt;
can leverage the synchronization constraints - encoded&lt;br /&gt;
by the synchronization graph structure - to&lt;br /&gt;
improve convergence as well as the images generative&lt;br /&gt;
process - via the common lines loss -, with&lt;br /&gt;
no need to perform intermediate reconstructions.&lt;br /&gt;
&lt;br /&gt;
== Keywords ==&lt;br /&gt;
&lt;br /&gt;
== Links ==&lt;br /&gt;
&lt;br /&gt;
https://proceedings.mlr.press/v221/cesa23a.html&lt;br /&gt;
&lt;br /&gt;
== Related software ==&lt;br /&gt;
&lt;br /&gt;
== Related methods ==&lt;br /&gt;
&lt;br /&gt;
== Comments ==&lt;/div&gt;</summary>
		<author><name>WikiSysop</name></author>
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