Statistical approaches to image modeling have largely relied upon random models that characterize the 2-D process in terms of its first- and second-order statistics, and therefore cannot completely capture phase properties of random fields that are non-Gaussian. This constrains the parameters of noncausal image models to be symmetric and, therefore, the underlying random field to be spatially reversible. Recent research indicates that this assumption may not be always valid for texture images. In this paper, higher- than second-order statistics are used to derive and implement two classes of inverse filtering criteria for parameter estimation of asymmetric noncausal autoregressive moving-average (ARMA) image models with known orders. Contrary to existing approaches, FIR inverse filters are employed and image models with zeros on the unit bicircle can be handled. One of the criteria defines the smallest set of cumulant lags necessary for identifiability of these models to date. Consistency of these estimators is established, and their performance is evaluated with Monte Carlo simulations as well as texture classification and synthesis experiments.