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We incorporated the formulated regularization term into the PR problem, which yields a new non-convex optimization problem.
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We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations.
Valmadre and Lucey [21] formulated the regularization of the trajectory basis with a temporal filter.
We formulate the regularization framework for information transferring of auxiliary data as follows: begin{array}{*{20}l} &minlimits_{textbf{U}} F textbf{U} =left|textbf{U}^{T}textbf{X}^{(a)}-textbf{T}^{(a)}right|_{F}^{2}+Omega textbf{U}), end{array} (16).
As most of the theory for Tikhonov regularization is formulated for real valued vector spaces, the forward operator A has to be formulated in a real setting.
Marks et al. [ 27] formulated an I-divergence regularization approach for despeckling.
Our main idea is to formulate sparse representation regularization term of utilizing TIHP tight frame for PR.
As formulated in Eq. 2, regularization parameters of MTL are α 1 and α 2, which control the sparsity of the dictionary matrix and the norm penalty respectively.
According to the above two sections, our general iterative regularization procedure can be formulated as follows.
The inverse problem is formulated as an optimization problem with a regularization term.
Therefore the models for the control of the field development are formulated as inverse problems and the iterative regularization methods are offered for their solutions.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com