Reducing Noise in Images by Forcing Monotonic Change Between Extrema
A novel method of reducing noise in images is presented. The significant extrema (maxima and minima) in the image are selected using a simple low pass Fourier filter. The method forces the pixel values in the image to vary monotonically between the selected extrema. For example, the pixel values in the filtered image should decrease monotonically in all directions from an isolated maximum. Because the algorithm that performs the monotonic fits is one dimensional, we approximate monotonic change in all directions by doing monotonic fits along line segments throughout the image. The filtering operation on each line segment replaces the pixel values on that segment with a monotonie sequence that fits the original pixel values best in a least squares sense. Monotonie change is enforced along line segments in as many directions as desired. The method is simple, reasonably fast and quite stable. Good results can be obtained for images with SNR’s as low as 0.5.
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