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Phase discontinuity predictions using a machine-learning trained kernel
Applied Optics, 2014Phase unwrapping is one of the key steps of interferogram analysis, and its accuracy relies primarily on the correct identification of phase discontinuities. This can be especially challenging for inherently noisy phase fields, such as those produced through shearography and other speckle-based interferometry techniques.
Sawaf, F. (author) +1 more
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Integral operators with kernels that are discontinuous on broken lines
Sbornik: Mathematics, 2006In this paper we study the equiconvergence of expansions in trigonometric Fourier series and in eigenfunctions and associated functions of an integral operator whose kernel has discontinuities of the first kind on broken lines formed from the sides and diagonals of the squares obtained by dividing the unit square into equal squares.
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To the theory of volterra integral equations of the first kind with discontinuous kernels
Computational Mathematics and Mathematical Physics, 2016This paper deals with one class of Volterra integral equations of the first kind with piecewise continuous kernels \(K(t,s)\) in the domain ...
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Finite-Dimensional Perturbations of Integral Operators with Kernels Discontinuous on the Diagonals
Results in Mathematics, 2000The simplest integral operator \(A_0\) whose kernel is discontinuous on the diagonal is considered. In addition, \(B\) is a finite-dimensional operator. The author derives simple sufficient conditions that provide equiconvergence of spectral expansions of \(A_0\) and \(A=A_0+B\) in space \(L^1[0,1]\). In addition, the invertibility conditions for \(A\)
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Discrete approximation of hammerstein integral equations with discontinuous kernels
Numerical Functional Analysis and Optimization, 1998An approximation of the Hammerstem integral equation with so discontinuous kernels that we are forced to look for a solution in the space L ∞, is considered. The notion of the discrete convergence of vectors with increasing dimension to an essentially bounded function is introduced, defining a consistent system of linear piecewise integral connection ...
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Estimation and inference in regression discontinuity designs with asymmetric kernels
Journal of Applied Statistics, 2014We study the behaviour of the Wald estimator of causal effects in regression discontinuity design when local linear regression (LLR) methods are combined with an asymmetric gamma kernel. We show that the resulting statistic is no more complex to implement than existing methods, remains consistent at the usual non-parametric rate, and maintains an ...
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Optimal kernel estimates for elliptic operators with second order discontinuous coefficients
Journal of Mathematical Analysis and Applications, 2020G Calvaruso, G Metafune, L Negro
exaly