How anti-aliasing filter affects image contrast: An analysis from majorization theory perspective

When we design an anti-aliasing low pass filter, it is usually an IIR filter. We need to truncate the filter to an FIR filter. One may think that the more taps there are, the better the image quality is. However, we find that there exists an optimal value of tap number that will give the best visual quality. Filters with larger or smaller number of taps will degrade the image quality, due to the fact that the image contrast is reduced. In this paper we analyze this phenomenon using majorization theory and find that the image contrast can be formulated as a Schur convex function on filter coefficients. We also propose an effective method to choose the best filter so that the image contrast is maximized, so as to give best visual quality.