https://3demmethods.i2pc.es/index.php?action=history&feed=atom&title=2023Bendory_Autocorrelation2023Bendory Autocorrelation - Revision history2026-05-24T20:20:10ZRevision history for this page on the wikiMediaWiki 1.44.2https://3demmethods.i2pc.es/index.php?title=2023Bendory_Autocorrelation&diff=4335&oldid=prevWikiSysop: Created page with "== Citation == Bendory, Tamir / Khoo, Yuehaw / Kileel, Joe / Mickelin, Oscar / Singer, Amit. Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample c..."2023-06-15T05:59:11Z<p>Created page with "== Citation == Bendory, Tamir / Khoo, Yuehaw / Kileel, Joe / Mickelin, Oscar / Singer, Amit. Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample c..."</p>
<p><b>New page</b></p><div>== Citation ==<br />
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Bendory, Tamir / Khoo, Yuehaw / Kileel, Joe / Mickelin, Oscar / Singer, Amit. Autocorrelation analysis for cryo-EM with sparsity constraints: Improved sample complexity and projection-based algorithms. 2023. Proc. Natl. Acad. Sci. USA , Vol. 120, No. 18, p. e2216507120 <br />
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== Abstract ==<br />
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The number of noisy images required for molecular reconstruction<br />
in single-particle cryo-electron microscopy (cryo-EM) is governed by the<br />
autocorrelations of the observed, randomly-oriented, noisy projection images.<br />
In this work, we consider the eect of imposing sparsity priors on the molecule.<br />
We use techniques from signal processing, optimization, and applied<br />
algebraic geometry to obtain new theoretical and computational contributions<br />
for this challenging non-linear inverse problem with sparsity constraints. We<br />
prove that molecular structures modeled as sums of idealized point masses are<br />
uniquely determined by the second-order autocorrelation of their projection<br />
images, implying that the sample complexity is proportional to the square of<br />
the variance of the noise. This theory improves upon the non-sparse case,<br />
where the third-order autocorrelation is required for uniformly-oriented particle<br />
images and the sample complexity scales with the cube of the noise variance.<br />
Furthermore, we build a computational framework to reconstruct molecular<br />
structures which are sparse in the wavelet basis. This method combines the<br />
sparse representation for the molecule with projection-based techniques used<br />
for phase retrieval in X-ray crystallography.<br />
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== Keywords ==<br />
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== Links ==<br />
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https://www.pnas.org/doi/abs/10.1073/pnas.2216507120<br />
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== Related software ==<br />
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== Related methods ==<br />
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== Comments ==</div>WikiSysop