  Further studies on the corner singularity of GS reconstruction are are
compiled in this paper. It's focused on solution of the Data Completion (DC)
problem with the Extended Hilbert Transform (EHT) over plane rectangular
region. Optimal selections of the regular parameters in{\it Tikhonov} solution
of corresponding DC problem are developed in this study. The 6-parameter
regular solutions and the {\it Jacobian} matrix and one {\it Hessian} tensor to
the regular parameters are derived in this work. A concise formula for EHT in
the near field of corners, which shows property for EHT near the corner, are
also provided. It serves as the additional constraints for our parameter
optimization problem (OP). Third, a nonlinear convex function defined by the
regular solution and the corner constraints is introduced and is taken as the
object function for the OP of the 6 regular parameters on half-space
$(\mathbf{p}>0)$. Given an initial guess of $\mathbf{p}_0$, the optimal
parameters are solved from the OP through a well known constrained nonlinear
optimization method. Last, the benchmark tests to the proposed solution
approach are carried out, and detailed results from totally 9 different
bench-cases are tabulated. In contrast to solutions with given regular
parameters, our bench results demonstrate that an objective way for selection
of the optimal $\mathbf{p}$ is successfully laid out here. Robustness and
efficiency of the suggested new approach are also highlighted in this study.
