Quantum Collapsing Median Filter

Abstract

The quantum collapsing median filter for the removal of salt and pepper noise is proposed in this paper based on quantum information theory. Following the quantum measurement, the possible noisy pixels are firstly collapsed to state 0 while remaining unsorted, and the non-possible noisy pixels are collapsed to state 1. Secondly, as the noise intensity increases, the size of the window of the structural elements of superposition states is adaptively enlarged from 1×1 to 11×11 with an odd number of steps. Finally, the image pixels whose superposition states are 1 in the window of the structural elements are filtered through a median filter. The experimental results show that the peak signal to noise ratio (PSNR) of the filtered image is about 4 times of that of the original image corrupted by 90% salt & pepper noise. The new method is shown to be considerably better than the standard median filter and the adaptive median filter, which is consistent with subjective evaluation.KeywordsQuantum collapsingMedian filterSalt and pepper noise