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Frequency Domain Self-filtering for Pattern Detection

Filtering is often used in image processing to smooth noise, and to enhance or detect features within an image. Images which have regular patterns in the spatial domain have peaks in the frequency domain corresponding to the spatial frequencies of the regular patterns. When processing such images, it is often desirable to keep such peaks, enhancing the pattern and removing noise or irregularities. This is effectively a bandpass filtering operation. The problem with such filtering is that it requires a priori knowledge of the contents of the image so that the filter can be 'tuned' to select the appropriate frequencies. The approach proposed here to overcome this problem is frequency domain self-filtering. By multiplying the frequency domain image with its own magnitude, peaks in the frequency domain are enhanced based on the strength of those peaks. Regions of low activity in the frequency domain are attenuated relative to the peaks. This gives a bandpass filter which is automatically tuned to the frequency content of the image. Applications of such a filter include: detecting and enhancing regular patterns; interpolating or extrapolating the regular pattern to regions in the image where it is not present; and smoothing or reducing noise in the image.