1,502 research outputs found
On the Regularized Fermionic Projector of the Vacuum
We construct families of fermionic projectors with spherically symmetric
regularization, which satisfy the condition of a distributional -product. The method is to analyze regularization tails with a power-law or
logarithmic scaling in composite expressions in the fermionic projector. The
resulting regularizations break the Lorentz symmetry and give rise to a
multi-layer structure of the fermionic projector near the light cone. The
remaining freedom for the regularization parameters and the consequences for
the normalization of the fermionic states are discussed.Comment: 66 pages, LaTeX, 8 figures, minor improvements (published version
Truncated decompositions and filtering methods with Reflective/Anti-Reflective boundary conditions: a comparison
The paper analyzes and compares some spectral filtering methods as truncated
singular/eigen-value decompositions and Tikhonov/Re-blurring regularizations in
the case of the recently proposed Reflective [M.K. Ng, R.H. Chan, and W.C.
Tang, A fast algorithm for deblurring models with Neumann boundary conditions,
SIAM J. Sci. Comput., 21 (1999), no. 3, pp.851-866] and Anti-Reflective [S.
Serra Capizzano, A note on anti-reflective boundary conditions and fast
deblurring models, SIAM J. Sci. Comput., 25-3 (2003), pp. 1307-1325] boundary
conditions. We give numerical evidence to the fact that spectral decompositions
(SDs) provide a good image restoration quality and this is true in particular
for the Anti-Reflective SD, despite the loss of orthogonality in the associated
transform. The related computational cost is comparable with previously known
spectral decompositions, and results substantially lower than the singular
value decomposition. The model extension to the cross-channel blurring
phenomenon of color images is also considered and the related spectral
filtering methods are suitably adapted.Comment: 22 pages, 10 figure
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