Iterative methods are the key tools in inverse problems due to their implicit regularization behaviour, or semi-convergence, when combined with an early-stopping criterion to prevent overfitting of the noise on the data. In this framework, non-isotropic geometrical approaches are very useful, since they allow to adjust different regularization levels to different regions of the domain or subsets of unknowns. Among those, we discuss regularization in Orlicz spaces, which can be considered a generalization of Lebesgue spaces, where the exponent function is replaced by a more general function. In these normed spaces, where the least square fitting does not lead to a linear equation, iterative methods require the application of the so-called duality maps, which, basically, are the sub-gradient of powers of the norm. Unfortunately, duality maps may not exhibit closed forms useful for a direct numerical computation. Hence, we study special approximations of the duality maps of dual spaces, which allow actual implementations of iterative methods in Orlic spaces for inverse problems. As part of the DHEAL-COM project, this approach is useful to implement robust computational techniques in the case of biomedical imaging for proximity medicine applications. \begin{thebibliography}{99} \bibitem{Prec_iter_Banach} Brianzi, P., Di Benedetto, F., and Estatico, C. Preconditioned iterative regularization in Banach spaces. Comput Optim Appl, (2013) 54:263–282. https://doi.org/10.1007/s10589-012-9527-2. \bibitem{dual_desc} Bonino, B., Estatico, C. and Lazzaretti, M. Dual descent regularization algorithms in variable exponent Lebesgue spaces for imaging. Numer Algor (2023) 92:149–182. https://doi.org/10.1007/s11075-022-01458-w. \end{thebibliography}