https://3demmethods.i2pc.es/index.php?action=history&feed=atom&title=2019Havelkova_Regularization 2026-06-13T12:13:33Z Revision history for this page on the wiki MediaWiki 1.44.2 https://3demmethods.i2pc.es/index.php?title=2019Havelkova_Regularization&diff=3461&oldid=prev 2019-03-26T22:24:32Z

<p>Created page with &quot;== Citation == Havelkova, E. Regularization methods for discrete inverse problems arising in single particle analysis. Fac. Mathematics and Physics, Charles University, Fac....&quot;</p> <p><b>New page</b></p><div>== Citation ==<br /> <br /> Havelkova, E. Regularization methods for discrete inverse problems arising in single particle analysis. Fac. Mathematics and Physics, Charles University, Fac. Mathematics and Physics, Charles University, 2019<br /> <br /> == Abstract ==<br /> <br /> The aim of this thesis is to investigate applicability of regularization by Krylov subspace methods to discrete inverse problems arising in single<br /> particle analysis (SPA). We start with a smooth model formulation and describe<br /> its discretization, yielding an ill-posed inverse problem Ax ≈ b, where A is a linear operator and b represents the measured noisy data. We provide theoretical<br /> background and overview of selected methods for the solution of general linear<br /> inverse problems. Then we focus on specific properties of inverse problems from<br /> SPA, and provide experimental analysis based on synthetically generated SPA<br /> datasets (experiments are performed in the Matlab enviroment). Turning to<br /> the solution of our inverse problem, we investigate in particular an approach<br /> based on iterative Hybrid LSQR with inner Tikhonov regularization. A reliable<br /> stopping criterion for the iterative part as well as parameter-choice method for<br /> the inner regularization are discussed. Providing a complete implementation of<br /> the proposed solver (in Matlab and in C++), its performance is evaluated on<br /> various SPA model datasets, considering high levels of noise and realistic distribution of orientations of scanning angles. Comparison to other regularization<br /> methods, including the ART method traditionally used in SPA, clearly shows<br /> various advantages of the proposed approach.<br /> <br /> == Keywords ==<br /> <br /> == Links ==<br /> <br /> https://dspace.cuni.cz/handle/20.500.11956/105272<br /> <br /> == Related software ==<br /> <br /> == Related methods ==<br /> <br /> == Comments ==</div>

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