In this paper, we apply the l p (0 < p ≤ 1) sparsity regularization by partial use of the focal underdetermined system solver (FOCUSS) algorithm, which was introduced by He et al. [ 23] to solve linear underdetermined inverse problems, and investigate the effects of the regularization on the non-linear time-domain DOT image reconstruction.
Thereafter, it is parameterized and implemented by a modified regularization network, called partial linear regularization network (PLRN), which introduces a parametric linear part into the traditional regularization network.
No spatial regularization is applied.
Defining them using continuous partial differential equations yields highly parallelizable regularization processes allowing to obtain well-defined estimations of these quantities.
Also, ill-posed parabolic backward problems in time partial differential equations can be regularized with the aid of integral boundary conditions; see, for example, mathematical models for bacterial self-regularization [10].
We investigate solution properties of a class of evolutionary partial differential equations (PDEs) with viscous and inviscid regularization.
Indirect relationships can be excluded from the graph using partial correlation, or inverse covariance matrix estimation, but regularization estimators must be employed for large number of brain areas [ 17, 33].
Also, integral boundary conditions are applied to regularize ill-posed parabolic backward problems in time partial differential equations, see, for example, mathematical models for bacterial self-regularization [8].
These problems of smaller metabolomics studies could be dealt with by regularization approaches or the usage of low-order partial correlation [ 26].
In this paper, the sinc-collocation method was applied to solve linear Volterra partial integro-differential equations by using the Linsolve package and Tikhonov regularization methods for a final ill-conditioned system.
