Therefore, this sparsity on the phase errors is incorporated into the problem by using the regularization term ∥β−1∥1.
In this paper, our main purpose is to adapt the algorithm (1.9) by using the regularization means such that the strong convergence is guaranteed.
From Table 2, we easily see that by using the regularization method and with iterative number increasing, (x_{n}) approaches to (x^) and the errors gradually approach to zero.
Therefore, this group sparsity nature on the phase errors is incorporated into the problem by using the regularization term (sum ^{I}_{i=1}left (sum ^{M}_{m=1}left |mathbf {Q}(i,m -1 right |^{2}right)^{1/2}).
The geometry component, obtained by using the regularization PDE based on a trace operator, was inpainted by a tensor-driven PDE algorithm that takes curvatures of line integral curves into account, and the texture component, obtained by subtracting the given image from the geometry component, was reconstructed by the modified exemplar-based inpainting algorithm.
The stabilisation/regularization of this inverse problem is achieved by using the Tikhonov regularization method (Tikhonov and Arsenin, 1986), whilst the optimal value of the regularization parameter is selected by employing Hansen's L-curve method (Hansen, 1998).
Accordingly, two factors originated from Bauwens model are redeveloped by using the Bayesian Regularization Artificial Neuron Network (BRANN) algorithm.
Since the nonlinear term f satisfies the condition (P2), by using the similar regularization method in [20], we can prove that u ∈ C2+μ,1]μ/2([0, 1] × J) is a classical solution of the problem (24).
(3.5) In general, such a problem is ill-posed, therefore we aim at solving it by using the Tikhonov regularization method, i.e., to minimize the following quantity in (L^{2} (0,pi )): Vert Kf-gVert ^{2}+mu^{2}Vert f Vert ^{2}.
A key tool was topological degrees for appropriate classes of operators in, e.g., [2 4, 8, 9, 14 16] and the method of approach was in many cases to use regularization by means of the duality operator, while in [6, 11] the eigenvalue problem was solved by a transformed equation in terms of the approximant without using the regularization method.
Reducing the dimensionality by some techniques including sure independence screening [ 22] is suggested before using the regularization methods to gain more stability.
