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Determining the proper regularization parameter requires multiple solutions of the regularized optimization problem (7), therefore the computational efficiency is also crucial.
By providing proper regularization our methods overcome some of these difficulties.
A proper regularization approach is then used to estimate the light source position, scene structure, and blur parameter.
In a word, it is helpful to improve the effect of image reconstruction by adding proper regularization term.
Clearly, their behavior is strongly biased in case of the small regularization parameter, while they perform similarly in case of a proper regularization.
It has been shown, under a proper regularization of the integrals preserving the group structure underlying the theory, that graphs topologically equivalent to sphere dominate the partition function when the only cutoff is sent to infinity in the renormalized couplings.
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The success of the methods is supported by both an efficient solver for the forward problem based on a highly accurate pseudospectral method and a proper selection of regularization parameters.
The bias of regularized solution can be estimated by (Bouman, 1998, p. 27; Xu, 1998; Eshagh, 2009): (5b) One important issue in the Tikhonov regularization is the proper selection of the regularization parameter α2.
The innovative algorithmic idea is to incorporate into the DEDR-optimized fixed-point iterative reconstruction/enhancement procedure the convex convergence enforcement regularization via constructing the proper multilevel projections onto convex sets (POCS) in the solution domain.
The innovative idea of this paper is to aggregate the DEDR-optimal fixed-point iterative reconstruction/enhancement procedures developed in the previous studies [7, 8, 10] with the multi-level robustness and convergence enforcing regularization via constructing the proper projections onto convex sets (POCS) in the solution domain.
To mitigate error propagation and ill-posed problem during the process of identification, a weighted regularization approach based on the proper orthogonal decomposition (POD) was proposed, where the regularization parameter was selected by the GCV method.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com