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.
To cope with the inherent large data variance, we introduce a second approach which imposes Tikhonov regularization on the kernel-smoothed estimator.
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.
Because of the ill-posedness of the inverse problem, we need to impose a regularization term in the optimization function.
Using a similar approach as before, the only-regularized version of the NLMS algorithm is considered (also imposing that the regularization parameter is time dependent), with the update begin{array}rcl@ widehat{mathbf{h}}(n) = widehat{mathbf{h}} n-1) + frac{mathbf{x} n-1e(n)} { left| mathbf{x}(n) right|^{2}_{2} + delta(n) }. end{array} (35).
Usually, during the modeling process, the SA is controlled through a rather simple regularization imposing smooth behavior in space and time.
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.
Our approach shares the spirit of that of Long et al. [ 27], where they regressed phenotypes on a kernel incidence matrix K by imposing an L1 regularization.
Based on the assumption that a real imaging genetic signal typically involves a small number of SNPs and QTs, sparse canonical correlation analysis (SCCA) has also been applied in several imaging genetic studies by imposing the Lasso regularization term to yield sparse results (Chi et al., 2013; Lin et al., 2014; Wan et al., 2011).
The proposed method is based on the minimization of a cost function which involves sparsity-imposing regularization terms on the reflectivity field to be imaged, considering that it admits a sparse representation as well as on the spatial structure of the motion-related phase errors, reflecting the assumption that only a small percentage of the entire scene contains moving objects.
