$o=1,\ldots,6$   0.1374    44.1869   $\mbox{det}(\mathcal{M})^*=\mbox{inf}$
     $o=1$            0.0100    50.0000   $\|\mbox{PC}_1^2\|_F^*=8.3413\times 10^{3}$
     $o=2$            0.0100    50.0000   $\|\mbox{PC}_2^2\|_F^*=6.3400\times 10^{3}$
     $o=3$            0.0100    50.0000   $\|\mbox{PC}_3^2\|_F^*=3.2968\times 10^{3}$
     $o=4$            0.0100    49.9998   $\|\mbox{PC}_4^2\|_F^*=2.9181\times 10^{3}$
     $o=5$            0.0100    50.0000   $\|\mbox{PC}_5^2\|_F^*=4.7028\times 10^{3}$
     $o=6$            0.0100    50.0000   $\|\mbox{PC}_6^2\|_F^*=7.6949\times 10^{3}$
     $o=1,\ldots,6$   0.0100    50.0000   $\|\mathcal{M}\|_F^*=3.0379\times 10^{4}$

\[table:resultex1\]

Illustrative Examples {#sec:ex}
=====================

Example 1 {#sec:ex1}
---------

Consider the Lena’s image (Figure \[fig:lena-orig\]). The objective in this example is to find the optimal values for the parameters of the weighting function while keeping the other parameters constant, where $$\begin{aligned}
 & \lambda_{\min o} =3,~ \sigma_{no} =0.55,~ \eta_o=2.1,~ k_o =2,\\& \varepsilon=0.0001 ,~ N_o =4,~ O=6. \end{aligned}$$

The parameter vector in this example contains only $c_o$ and $g_o$, thus $$\begin{aligned}
\upsilon_o= [ \begin{array}{cc}
    c_o & g_o \end{array}]
    \end{aligned}$$ We set fixed upper and lower limits $\upsilon_o$ as follows: $$\begin{aligned}
    & \underline{\upsilon}_o=[ \begin{array}{cc}
    0.1 & 1 \end{array}] \\
    & \overline{\upsilon}_o=[ \begin{array}{cc}
    0.9 & 50 \end{array}].\end{aligned}$$ With $c_o < 0.1$, almost all spreads of frequencies (even narrow ones) will be kept, but that is not desirable. The change in the slope of the weighting function is also not significant for $g_o > 50$.

In order to compare , , and , this example focuses on $\mu_1=\mu_2=1$, and therefore, $$\begin{aligned}
\mathcal{M}=M+m.\end{aligned}$$

Table \[table:resultex1\] shows the 