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In other words, regularization imposed smoothness on the solution.
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We use GraphNet regularization – imposing both signal smoothness and sparsity – to drastically reduce the number of diffusion-weighted images (DWIs) that is needed to represent the dMRI signal in the qτ-space.
Usually, during the modeling process, the SA is controlled through a rather simple regularization imposing smooth behavior in space and time.
This regularization imposes the constraint that neighboring source points have similar activation times (smooth activation pattern).
This explains the better predictive performance of BRANN over SCGANN: Bayesian regularization imposes a penalty for model complexity and prevents over-fitting, while SCGANN captures both signal and noise in the training set, leading to poor prediction.
First, we propose a generalized smoothing operator for the regularization to impose smooth modification on reservoir parameters.
It should also be noted that the SV in a spline-based model such CHAOS-5l at a particular epoch is not the true instantaneous SV, but a weighted time average, with the amount of time averaging varying with spherical harmonic degree according to the imposed regularization.
Then, a geostatistical constraint, in the form of an a priori model covariance matrix based on the variogram, was imposed as regularization to solve the electrical inverse problem.
Usually, an upper bound on the regularization parameter could be imposed, but this would introduce an extra tuning parameter in the algorithm.
Finally, we show how to design multicore versions of an analytical regularization method that imposes smoothness constraints on the deformation derived by both unimodal and multimodal registration.
In the first extension, we use group-sparsity enforcing regularization term to impose the sparse structure.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com