Frequency domain median-like filter for periodic and quasi-periodic noise removal

TLDR: A new frequency domain filter for periodic and quasi-periodic noise reduction is introduced, which completely eliminates periodic noise, and shows quite good results on quasi- periodic noise while completely preserves the image boundaries.

Abstract: Removal of periodic and quasi-periodic patterns from photographs is an important problem. There are a lot of sources of this periodic noise, e.g. the resolution of the scanner used to scan the image affects the high frequency noise pattern in the acquired image and can produce moire patterns. It is also characteristic of gray scale images obtained from single-chip video cameras. Usually periodic and quasi-periodic noise results peaks in image spectrum amplitude. Considering this, processing in the frequency domain is a much better solution than spatial domain operations (blurring for example, which can hide the periodic patterns at the cost of the edge sharpness reduction). A new frequency domain filter for periodic and quasi-periodic noise reduction is introduced in this paper. This filter analyzes the image spectrum amplitude using a local window, checks every spectral coefficient whether it needs the filtering and if so, replaces it with the median taken from the local window. To detect the peaks in the spectrum amplitude, a ratio of the current amplitude value to median value is used. It is shown that this ratio is stable for the non-corrupted spectral coefficients independently of the frequencies they correspond to. So it is invariant to the position of the peaks in the spectrum amplitude. This kind of filtering completely eliminates periodic noise, and shows quite good results on quasi-periodic noise while completely preserves the image boundaries.