Minor nitpicks- "Convolved" with the pixels. And the FIR filter doesn't depend on the frequency information in the adjacent pixels, but rather the intensity of

Minor nitpicks- "Convolved" with the pixels. And the FIR filter doesn't depend on the frequency information in the adjacent pixels, but rather the intensity of the pixels. A short FIR filter must have large frequency support, so the filtering depends on the frequency information given by all pixels.