This regularization is performed before any discretization.
It works so well probably because all it needs to do is to let all of the important markers pass to the next step whereas, because the final variable regularization is performed by the multilocus association model, it does not matter if unimportant ones are also selected.
Then, selective partial regularization of the MM was performed.
More concretely, the gradient step size was set at 0.1, multiresolution parameters were 45 × 15 × 5 × 0 × 0, and regularization to Gauss [3,1] was performed.
To avoid overfitting or over-regularization an L-curve analysis was performed to select the optimal parameters for the inversion.
Parameter optimization was performed for the regularization term that defined the costs for false classifications (5 steps for each, range: 2n, n = -4, -2, 0, 2, 4).
The reconstruction was performed with Tikhonov regularization by minimizing, separately for each time point, the functional ‖ Δ y − J Δ x ‖ 2 + α ‖ L Δ x ‖ 2 (1)where Δ y is the measurement data, Δ x the differential absorption coefficient to be reconstructed, J the sensitivity matrix, α the regularization parameter (αlow = 5 and αhigh = 10 used in this study) and L the discrete Laplace operator.
Volumetric image reconstruction was performed using both regularizations.
Parameter optimization was performed on the training data for the regularization term and the kernel width.
Recovering the DTOF from Eq. (1) was performed using a two-stage deconvolution technique based on signal denoising and two-stage Tikhonov regularization [ 30, 31].
