Background: I'm working on a 2D Moving-Average (MA) estimator for image processing stuff and I'm trying to follow along from a paper that defines the algorithm for estimation.
The main equation for the parameter estimation is: $$\eta_i = (1/N_i) \sum_{u \in \Omega_i}|Y(u)|^2 $$
where $\Omega_i = \{u \in \Omega_u | ||Au|| = \rho_i\} $
However, $\Omega_u$ is defined earlier as $\Omega_u = \{(u_1, u_2) \in \Omega | 0 \le u_1 \lt N, 0 \le u_2 \le N/2 , (u_1, u_2) \neq (0,0)\}$. Since we're dealing with images, $N$ is the image size, which in my case is 128 for a 128x128 image. $u_1, u_2$ are both indices in the frequency domain after the DFT is used on the original image.
I'm hung up on what the set $\Omega_i$ actually entails and consequently, what the I'm summing over. Is this saying there are two sets like $\Omega_{i1}$ and $\Omega_{i2}$?
My current interpretation is that $u_1 = \{0...127\}, u_2 = \{0...64\}$ where $u_1$ is the "row" of $Y$ and $u_2$ is the "column" of $Y$. Then in the algorithm, I'm summing across the row of $Y$ for all $u_2$'s. Yet this leads to drastically different results for $\eta_i$ than what the paper has.
