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	<updated>2026-09-01T04:15:20Z</updated>
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		<title>WikiSysop: Created page with &quot;== Citation ==  Kreymer, S., Singer, A. and Bendory, T. 2026. Expectation-maximization for structure determination directly from cryo-em micrographs. Inverse problems and imaging. 27, (2026), 110.  == Abstract ==  A single-particle cryo-electron microscopy (cryo- EM) measurement, called a micrograph, consists of multiple two-dimensional tomographic projections of a three-dimensional (3-D) molecular structure at unknown locations, taken under unknown viewing directions. A...&quot;</title>
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		<updated>2026-08-31T04:37:26Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;== Citation ==  Kreymer, S., Singer, A. and Bendory, T. 2026. Expectation-maximization for structure determination directly from cryo-em micrographs. Inverse problems and imaging. 27, (2026), 110.  == Abstract ==  A single-particle cryo-electron microscopy (cryo- EM) measurement, called a micrograph, consists of multiple two-dimensional tomographic projections of a three-dimensional (3-D) molecular structure at unknown locations, taken under unknown viewing directions. A...&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;
Kreymer, S., Singer, A. and Bendory, T. 2026. Expectation-maximization for structure determination directly from cryo-em micrographs. Inverse problems and imaging. 27, (2026), 110.&lt;br /&gt;
&lt;br /&gt;
== Abstract ==&lt;br /&gt;
&lt;br /&gt;
A single-particle cryo-electron microscopy (cryo-&lt;br /&gt;
EM) measurement, called a micrograph, consists of multiple&lt;br /&gt;
two-dimensional tomographic projections of a three-dimensional&lt;br /&gt;
(3-D) molecular structure at unknown locations, taken under&lt;br /&gt;
unknown viewing directions. All existing cryo-EM algorithmic&lt;br /&gt;
pipelines first locate and extract the projection images, and then&lt;br /&gt;
reconstruct the structure from the extracted images. However, if&lt;br /&gt;
the molecular structure is small, the signal-to-noise ratio (SNR)&lt;br /&gt;
of the data is very low, making it challenging to accurately&lt;br /&gt;
detect projection images within the micrograph. Consequently,&lt;br /&gt;
all standard techniques fail in low-SNR regimes. To recover&lt;br /&gt;
molecular structures from measurements of low SNR, and in&lt;br /&gt;
particular small molecular structures, we devise an approximate&lt;br /&gt;
expectation-maximization algorithm to estimate the 3-D structure&lt;br /&gt;
directly from the micrograph, bypassing the need to locate the&lt;br /&gt;
projection images. We corroborate our computational scheme&lt;br /&gt;
with numerical experiments and present successful structure&lt;br /&gt;
recoveries from simulated noisy measurements.&lt;br /&gt;
&lt;br /&gt;
== Keywords ==&lt;br /&gt;
&lt;br /&gt;
== Links ==&lt;br /&gt;
&lt;br /&gt;
https://www.aimsciences.org//article/doi/10.3934/ipi.2026033&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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