https://3demmethods.i2pc.es/index.php?action=history&feed=atom&title=2026Van_Polar 2026-08-08T06:16:12Z Revision history for this page on the wiki MediaWiki 1.44.2 https://3demmethods.i2pc.es/index.php?title=2026Van_Polar&diff=5238&oldid=prev 2026-08-07T11:08:02Z

<p>Created page with &quot;== Citation == Van, C.T., Reboul, C.F., Caesar, J.J., Meana-Pañeda, R. and Elmlund, H. 2026. A polar Fourier geometric approach to volume-free single-particle 3D reconstruction. IUCrJ. 13, 4 (2026). == Abstract == We introduce a compact mathematical formulation for the inverse singleparticle 3D reconstruction problem, a high-dimensional inverse problem in which millions of parameters are estimated from extremely noisy experimental measurements. Given a collection of...&quot;</p> <p><b>New page</b></p><div>== Citation ==<br /> <br /> Van, C.T., Reboul, C.F., Caesar, J.J., Meana-Pañeda, R. and Elmlund, H. 2026. A polar Fourier geometric approach to volume-free single-particle 3D reconstruction. IUCrJ. 13, 4 (2026).<br /> <br /> == Abstract ==<br /> <br /> We introduce a compact mathematical formulation for the inverse singleparticle<br /> 3D reconstruction problem, a high-dimensional inverse problem in<br /> which millions of parameters are estimated from extremely noisy experimental<br /> measurements. Given a collection of noisy 2D projection images (particles) of an<br /> unknown 3D charge-density distribution, the objective is to infer the unknown<br /> particle orientations and thereby enable ab initio 3D reconstruction via tomographic<br /> methods. We develop a method for generating regularized reprojections<br /> directly from the noisy particles that does not rely on explicit 3D density<br /> reconstruction. Instead, we recast the ab initio orientation-recovery problem in<br /> polar Fourier coordinates through discretization of the rotation group SO(3).<br /> The directions of projection are mapped onto slices intersecting the origin of the<br /> 3D Fourier transform. The rotations in the plane normal to a projection<br /> direction are mapped onto radial lines in the 2D Fourier transforms of the<br /> particles. An optimization procedure jointly estimates particle projection<br /> directions, in-plane rotation angles and rotational origin offsets. Regularized<br /> reprojections are computed by averaging along lines in the polar Fourier<br /> representation, exploiting data redundancy to suppress noise and improve<br /> stability. We present the mathematical framework in detail and provide initial<br /> benchmarks demonstrating the performance and robustness of the approach.<br /> <br /> == Keywords ==<br /> <br /> == Links ==<br /> <br /> https://journals.iucr.org/m/issues/2026/04/00/rq5017/index.html<br /> <br /> == Related software ==<br /> <br /> == Related methods ==<br /> <br /> == Comments ==</div>

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