2. Figures \[fig:pc-Fnorm-mpm-full\] and \[fig:pc-Fnorm-pc-full\] shows the images of $\mathcal{M}^*$ with optimal parameters obtained through and , respectively. Figure \[fig:diff\] shows the difference by subtracting the images. []{data-label="fig:lena-7par"}](pc_lena_Fnorm_Mpm_m_PC_full "fig:"){width="\linewidth"}

[0.5]{} ![image](IM-0004-0054_patient6_T2-origPaper){width="1\linewidth"}

[0.5]{} ![image](cost_IM-0004-0054_patient6_T2_Fnorm_M_full_Paper){width="1\linewidth"}

Example 2:
----------

The objective of this example is to find the optimal values for the number of scales, number of orientations, and the parameters of the weighting function parameters and bank of filters, with the noise and ill-conditioning parameters fixed to $$\begin{aligned}
 k_o =2, \varepsilon=0.0001\end{aligned}$$

The parameter vector in this example is $$\begin{aligned}
\upsilon_o= [ \begin{array}{ccccccc}
     c_o &g_o & \lambda_{\min o} & \sigma_{no} & \eta_o & N_o & O \\
     \end{array}]
    \end{aligned}$$ We set fixed upper and lower limits to $\upsilon_o$ as follows $$\begin{aligned}
&\underline{\upsilon}_o= [ \begin{array}{ccccccc}
    0.1 & 1.0 & 2.0 & 0.4 & 1.0 & 1 & 1 \\
        \end{array}]\\
&\overline{\upsilon}_o= [ \begin{array}{ccccccc}
       0.9 & 50.0 & 5.0 & 1.0 & 4.0 & 4 & 6 \\
     \end{array}]
    \end{aligned}$$

Because the Lena’s IFD has shown robustness to the norm type as demonstrated above, we only test the Frobenius norm-based optimization problems and . The resulting optimal values are given in Table \[table:resultex2\]. Notably, the optimal number of orientations where $O^*=1$ is achieved. Another noticeable 