matrix [@Fisher1971] is maximized in order to reduce the Cram' er-Rao bound [@Cramer1946; @Rao1945]. The Fisher information matrix is maximized by maximizing some real-valued summary statistics (optimal) criteria), [@Atkinson2007]. The majority of matrix optimization methods are based on the maximization of the determinant of a matrix, referred to as D-optimal problem [@Berger1994; @StJohn1975]. The rest of the methods are mainly based on the maximization of the trace or maximization of the minimum eigenvalue of a matrix.

In the D-optimal framework, maximization of the cost function is given by $$\begin{aligned}
\begin{aligned}\label{D-opt}
& \underset{\upsilon_o}{\text{minimize}}
& & -\mbox{det}\Big(\mathcal{M}(\upsilon_o)\Big) \\
& \text{subject to}
& & \underline{\upsilon}_o \leq \upsilon_o \leq \overline{\upsilon}_o\\
\end{aligned}\end{aligned}$$ where $\det(\mathcal{M})$ denotes the determinant of $\mathcal{M}$. To be consistent with the optimization literature, the maximization of $z$ is written as the minimization of $-z$ throughout this paper. The solution to this optimization problem will provide the optimal parameters for 2D-MSPC.

For the PC-based image processing, we propose another optimization approach based on the norm of $\mathcal{M}$ as follows: $$\begin{aligned}
\begin{aligned}\label{norm-opt}
& \underset{\upsilon_o}{\text{minimize}}
& & -\left\| \mathcal{M}(\upsilon_o) \right\| \\
& \text{subject to}
& & \underline{\upsilon}_o \leq \upsilon_o \leq \overline{\upsilon}_o\\
\end{aligned}\end{aligned}$$ where $\| \mathcal{M}\|$ denotes the norm of $\mathcal{M}$. The matrix norm definition is 