Adaptive stack filtering under the mean absolute error criterion

An adaptive filter algorithm is developed for the class of stack filters, which is a class of nonlinear filters obeying a weak superposition property. The adaptation algorithm can be interpreted as a learning algorithm for a group of decision-making units, the decisions of which are subject to a set of constraints called the stacking constraints. Under a rather weak statistical assumption on the training inputs, the decision strategy adopted by the group, which evolves according to the proposed learning algorithm, is shown to converge to an optimal strategy in the sense that it corresponds to an optimal stack filter under the mean absolute error-criterion, this adaptive algorithm requires only increment, decrement, and comparison operations and only local interconnections between the learning units. Implementation of the algorithm in hardware is therefore very feasible. An example is provided to show how the adaptive stack filtering algorithm can be used in an application in image processing