Polyphase Antialiasing in Enlargements.
Daniel Seidner · 2003
Changing resolution of images is a common operation. It is also common to use simple, i.e., small interpolation kernels satisfying some ”smoothness ” qualities that are determined in the spatial domain. Typical applications use linear interpolation or piecewise cubic interpolation. These are popular since the interpolation kernels are small and the results are acceptable. However, since the interpolation kernel, i.e., the impulse response, has a finite, and small length, the frequency domain characteristics are not good. Therefore, when we enlarge the image by a rational factor of ¢¡¤£¦¥¨ § , aliasing effects usually appear and cause a noticeable degradation in quality of the image. One such effect is jagged edges. Another effect is low frequency modulation of high frequency components such as sampling noise. Enlarging an image by a factor of ¢¡©£�¥¨ § , is represented by first interpolating the image on a grid ¡ times finer than the original sampling grid, and then resampling it every ¥ grid points. While the usual treatment of the alias-ing created by the resampling operation is aimed towards improving the interpolation filter in the frequency domain, this paper suggests reducing the aliasing effects using a polyphase representation of the interpolation process, and treating the polyphase filters separately. We discuss separable interpolation and so the analysis is conducted for the one-dimensional case. Finally, we compare a 6 coefficient polyphase filters found using the suggested procedure with a 6 coefficient polyphase filters capable of reconstructing a 3rd order polynomial.