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The regularization of the Green's function removes its singularity by introducing a regularization radius which is related to the discretization length and hence imposes a minimum resolved scale.
The tendency to select model parameters resulting in complex models could be moderated by introducing a regularization term, penalizing solutions with greater model complexity [23] or by considering the Akaike Information Criterion (AIC) [24].
The more recent paper Ren et al. (2016b) established the comparison for fully nonlinear degenerate PPDEs, by introducing a regularization operator which can be viewed as the counterpart of the sup-convolution in the PDE literature.
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In DCA, the compensation for depth is achieved by introducing a weight matrix within L2 regularization to counter-balance the reduced sensitivity of measurement at deeper depth.
This paper addresses this problem by introducing a generic deformable registration algorithm with a new regularization scheme, which is performed through bilateral filtering of the deformation field.
Regularization of the solution was accomplished by introducing a mild rate dependence of the material.
Our approach, coined fr-MKLR, generalizes MKLR by introducing a feature weighting scheme in the Gaussian kernel and using the so-called ℓ0- norm" as sparsity-promoting regularization.
The choice of the regularization parameters is determined according to the Bayesian Information Criterion [ 33] that mitigates the problem of over-fitting by introducing a penalty term for the complexity of the model.
In this study, we develop a new model regularization method by introducing an edge-preserving smoothing operator to detect the model edges in traveltime tomography.
We can introduce a regularization by applying the singular value decomposition to Z as Z ≈ U qD qV q T, where D q is a diagonal matrix of q singular values, and U q and V q are matrices of singular vectors associated with the q singular values.
We introduce a regularization method that gives a smooth formulation for the fundamental solution to Stokes flow driven by an infinite, triply-periodic array of point forces.
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