On the nature of variational salt-and-pepper noise removal and its fast approximation

So far there are two separate approaches to removing salt-and-pepper noise: the median type filtering and the variational formulation. The first approach usually has fast speed, while the latter produces greatly improved result at much slower speed. In this paper we show that the variational approach can be approximated as a region growing process and propose a novel iterative algorithm that combines the strength of these two approaches. When viewed within a single iteration, the algorithm acts like a median type filter. When viewed across iterations, the filter achieves the region growing effect accomplished by the variational approach. Extensive simulations show that the proposed algorithm achieves the state of the art performance with the fastest speed published so far. The insight gained in this paper could have broader applications.