Stack filters are a class of nonlinear filters with excellent properties for signal restoration. Unfortunately, present algorithms for designing stack filters can only be used for small window sizes because of either their computational overhead or their serial nature. This paper presents a new adaptive algorithm for determining a stack filter that minimizes the mean absolute error criterion. The new algorithm retains the iterative nature of many current adaptive stack filtering algorithms, but significantly reduces the number of iterations required to converge to an optimal filter. This algorithm is faster than all currently available stack filter design algorithms, is simple to implement, and is shown in this paper to always converge to an optimal stack filter. Extensive comparisons between this new algorithm and all existing algorithms are provided. The comparisons are based both on the performance of the resulting filters and upon the time and space complexity of the algorithms. They demonstrate that the new algorithm has three advantages: it is faster than all other available algorithms; it can be used on standard workstations (SPARC 5 with 48 MB) to design filters with windows containing 20 or more points; and, its highly parallel structure allows very fast implementations on parallel machines. This new algorithm allows cascades of stack filters to be designed; stack filters with windows containing 72 points have been designed in a matter of minutes under this new approach.

The present approach to the MAE-based design of stack filters for image restoration does not always produce the desired visual result. Thus, in this paper, a new stack filter design algorithm is developed. It is based upon a weighted mean absolute error (WMAE) criterion instead of the traditional MAE criterion, which assigns the same weights to all errors. The weights in this WMAE criterion are designed with the aid of the visible differences predictor (VDP), which can estimate the sensitivity of the human visual system to changes in images. Experiments with this WMAE approach show that the stack filters it produces perform significantly better in image processing applications than those designed with the MAE approach.

The present approach to the MAE-based design of stack filters for image restoration does not always produce the desired visual result. Thus, in this paper, a new stack filter design algorithm is developed. It is based upon a weighted mean absolute error (WMAE) criterion instead of the traditional MAE criterion that assigns the same weights to all errors. The weights in the WMAE criterion are designed with the visible differences predictor (VDP), which can estimate the sensitivity of the human visual system to changes in images. Experiments with this WMAE approach show that the stack filters it produces perform significantly better in image processing applications than those designed with the MAE approach.