Unsupervised design of stack filters by tree structure optimization

In this paper, an unsupervised design of stack filters for recovering images from the impulse noise is proposed. Stack filters consist of logical AND/OR or integer MIN/MAX operations between the elements of the filter window, which can be expressed as tree structures. The shape of filter window and the combination of MIN and MAX operators widely affect the processing result of the filter. In this paper, a tree structuring stack filters are optimized by hill climbing method that is effective method in solving the discrete structure with a small calculation cost. An objective function that considers two evaluation values of non-corrupt pixels and corrupt pixels without using training images is adopted. To increase the possibility to discover better solution, no rules to limit design variables such as symmetric property between elements of the filter are used. Through experiments, it was shown that the proposed method can design a superior stack filter with a relatively small tree structure compared to a conventional filter.