Noise equalization in resampling of images

Changing resolution of images is a common operation. Typical applications use linear interpolation or piecewise cubic interpolation. Enlarging an image by a factor of (L/M), is represented by first interpolating the image on a grid L times finer than the original sampling grid, and then resampling it every M grid points. An equivalent but more efficient implementation is to use L interpolation kernels, which are decimated versions of the original interpolation kernel. The appropriate kernel is applied according to the desired position of the output pixel. When enlarging an image by a factor of (L/M), every L samples of the output signal are produced "from" M input samples (and their neighborhood) using different kernels. This pattern of resampling repeats itself every L output samples. Since the frequency responses of these kernels are totally different, the resampling cause "modulation", with a period of L samples, to high frequencies, e.g., the sampling circuit noise. This paper describes a simple procedure for equalization of this noise modulation. The procedure is based on handling each of the L interpolation kernels separately. We discuss separable interpolation and so the analysis is conducted for the one-dimensional case.