  We present a new iterative rotation inversion technique based on the
Simultaneous Algebraic Reconstruction Technique developed for image
reconstruction. We describe in detail our algorithmic implementation and
compare it to the classical inversion techniques like the Regularized Least
Squares (RLS) and the Optimally Localized Averages (OLA) methods. In our
implementation, we are able to estimate the formal uncertainty on the inferred
solution using standard error propagation, and derive the averaging kernels
without recourse to any Monte-Carlo simulation. We present the potential of
this new technique using simulated rotational frequency splittings. We use
noiseless sets that cover the range of observed modes and associate to these
artificial splittings observational uncertainties. We also add random noise to
present the noise magnification immunity of the method. Since the technique is
iterative we also show its potential when using an apriori solution. With the
right regularization this new method can outperform our RLS implementation in
precision, scope and resolution. Since it results in very different averaging
kernels where the solution is poorly constrained, this technique infers
different values. Adding such a technique to our compendium of inversion
methods will allow us to improve the robustness of our inferences when
inverting real observations and better understand where they might be biased
and/or unreliable, as we push our techniques to maximize the diagnostic
potential of our observations.
