I have this Equation, that I modeled from my measurements and simulations. $I^{exp}_{l,m} = (\mathbf{F}^{H}.\mathbf{A}.I^{true})_{l,m}$; $H$ is the Hermitian transpose and $\mathbf{F}^{H}$ is a block diagonal inverse Fourier transform operator. $I^{exp}_{l,m}$ and $I^{true}_{l,m}$ are the expected and real images of size $N_{pix}\times N_{pix}$ pixels. $\mathbf{A}_{}$ is a complex matrix expressed as follows:
$\mathbf{A}_{}= \begin{bmatrix} \mathbf{C}_{01,(t,\nu)}\cdot \mathbf{W}_{01,(t,\nu)}\cdot \mathbf{S}_{01,(t,\nu)} \cdot\mathbf{G}\\ \vdots\\ \mathbf{C}_{ik,(t,\nu)}\cdot \mathbf{W}_{ik,(t,\nu)}\cdot \mathbf{S}_{ik,(t,\nu)} \cdot\mathbf{G}\\ \vdots \\ \mathbf{C}_{jl,(t,\nu)}\cdot \mathbf{W}_{jl,(t,\nu)}\cdot \mathbf{S}_{jl,(t,\nu)}^{n} \cdot\mathbf{G}\\ \end{bmatrix}$
$\mathbf{F}^{H}$ and $\mathbf{A}_{}$ are of shape $(N_{v})\times(N_{pix}N_{pix})$ and $(N_v)\times (N_{pix}N_{pix})$ respectively. Please ignore the elements in $\mathbf{A}_{}$ but consider the shape. This equation model data compression and imaging (in interferometry synthesis imaging). From my model, $I^{true}_{l,m}$ and $\mathbf{A}_{}$ are known. What is the best approach to use to compute $I^{exp}_{l,m}$? Is there any Python tools for this Fourier interpolation?