In accordance with Tikhonov regularization (Doicu et al. 2010), a good regularization strength is achieved by making it stronger within the range in which the residuals of observational parameters, i.e., the first term of the cost function (9), are almost constant.
Second, by further combining the PCRF with the manifold regularization, the precise manifold and pairwise constraint jointly regularized formula (MPCJRF) is achieved.
This is achieved through Thikonov regularization.
This is achieved by adding a regularization term to the FCM objective function using the transformation result of the PET image by the à trous wavelet transform with the aim of incorporating information about lesion heterogeneity.
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).
Regularization for both the first and the second problems is achieved by a Krylov subspace method.
It is achieved by adding sparsity penalties or regularizations to the optimization problem.
Neglecting the regularization constant (i.e., δ≈0), the fastest convergence mode is achieved for α≈1, which is a well-known result [1, 11, 12].
An efficient solution to the problem is achieved by using a new form of regularization applied to dual Dini series equations.
The inversion is achieved using a combination of orthogonal collocation and regularization techniques.
In DCA, the compensation for depth is achieved by introducing a weight matrix within L2 regularization to counter-balance the reduced sensitivity of measurement at deeper depth.
