The filtering of two-dimensional (2-D) signals is treated using a self-tuning technique based on a truncated innovations model of the data. The resultant algorithms offer two key advantages over their fixed-coefficient counterparts. First, the self-tuning filters quickly and automatically set their own coefficients, thus avoiding the normal off-line design cycle. Secondly, self-tuning filters can function in an adaptive manner, such that the filter retunes to track time variations in the two-dimensional data. The self-tuning algorithms are formulated in terms of input/output models and thus complement the more usual state-space approach to the 2-D filtering problem.