However the regularization technique utilized here regularizes not only the underlying wavelength dependent Jacobian matrices J λ but also the spectral prior information M s incorporated within the spectral Jacobian matrix J s, which results in numerical error in the form of crosstalk on the reconstructed images, as demonstrated later in Section 3.1.
Compared with the classical TV regularizer, the proposed regularization term not only has a sparser property, but also protects the segmentation results from degeneration (being over-smoothed).
The regularization step not only improves the convergence rate of the presented algorithm, but also increases its stability bound.
The regularization does not only help to reduce the variance of the model, it also acts as an integrated parameter selection method for overparameterized models [see Gareth et al. (2013) for details].
In sparsity frame, the proposed sparse regularization method can not only determine the actual impact location from many candidate sources but also simultaneously reconstruct the time history of impact-force.
Moreover, the stress neighborhood manipulation on nonwords was so strong as to produce a large number, not only of "regularization" errors, but also of "irregularization" errors.
For minimizing the discrepancy functional we use the adjoint problem method; however, we use it not only in iterative regularization, but in Tikhonov and parametric ones as well.
This is due mainly to the suboptimal regularization of the spectral Jacobian matrix, which smoothes not only the image-data space, but also the spectral mapping space.
The regularization parameter (related to the σ in the prior model) not only provides the weight of the prior model but also determines the validity of the linear approximation.
We not only give the a priori choice of the regularization parameter, but also give the a posteriori choice of the regularization parameter which depends only on the measurable data.
