I am trying to minimize the following problem: $$\hat{x} = \underset{\bar{x}}{\operatorname{argmin}} \left( \left\|y- A_{MV}^{EPG} \bar{x}\right\|^2 + \|\mu_{T} \bar{x}\|^2 + \|D_{s} \bar{x}\|^2 \right)$$
Where $\bar{x}$, a column vector, is my parameter of interests.
First term is my data fidelity term; the second term is regularization along temporal domain and third term is spatial regularization term.
Additionally, the system matrix, $A_{MV}^{EPG}$, depends on other column vector: flip angle errors $\bar{\delta}$, which is also unknown.
I solve using iterative procedure:
Step-1: I start with reasonable approximation of FAE-maps:$\bar{\delta}$ and then minimize to solve for $\bar{x}$.
Step-2: Using $\bar{x}$ as true solution, I refine $\bar{\delta}$.
Step-3: I iterate between step-1 and step-2 until convergence.
Of course, I have checked and it converges.
My questions are: 1) Can I call my algorithm as EM alogirthm? 2) Can I claim that convergence is guaranteed as it’s an EM algorithm?
